Deep Fuzzy Multi-view Learning for Reliable Classification
Authors: Siyuan Duan
Yuan Sun
Dezhong Peng
Guiduo Duan
Xi Peng
Peng Hu
Venue: ICML 2025 poster (2025)
Keywords: Multi-view Learning
Trustworthy Machine Learning
Fuzzy Deep Learning
Primary area: general_machine_learning->representation_learning
TL;DR: Deep Fuzzy Multi-view Learning is proposed based on fuzzy set theory in order to achieve accurate classification of conflicting multi-view instances and accurate uncertainty estimation.

Abstract: Multi-view learning methods primarily focus on enhancing decision accuracy but often neglect the uncertainty arising from the intrinsic drawbacks of data, such as noise, conflicts, etc. To address this issue, several trusted multi-view learning approaches based on the Evidential Theory have been proposed to capture uncertainty in multi-view data. However, their performance is highly sensitive to conflicting views, and their uncertainty estimates, which depend on the total evidence and the number of categories, often underestimate uncertainty for conflicting multi-view instances due to the neglect of inherent conflicts between belief masses. To accurately classify conflicting multi-view instances and precisely estimate their intrinsic uncertainty, we present a novel Deep \underline{Fu}zzy \underline{M}ulti-View \underline{L}earning (\textbf{FUML}) method. Specifically, FUML leverages Fuzzy Set Theory to model the outputs of a classification neural network as fuzzy memberships, incorporating both possibility and necessity measures to quantify category credibility. A tailored loss function is then proposed to optimize the category credibility. To further enhance uncertainty estimation, we propose an entropy-based uncertainty estimation method leveraging category credibility. Additionally, we develop a Dual Reliable Multi-view Fusion (DRF) strategy that accounts for both view-specific uncertainty and inter-view conflict to mitigate the influence of conflicting views in multi-view fusion. Extensive experiments demonstrate that our FUML achieves state-of-the-art performance in terms of both accuracy and reliability.

Deep Fuzzy Multi-view Learning for Reliable Classification
Siyuan Duan Yuan Sun
Dezhong Peng 23 Guiduo Duan
Xi Peng'
Peng Hu
Abstract
RGB view
Text view
Depth view
Multi-view learning methods primarily focus on enhancing decision accuracy but often neglect the uncertainty arising from the intrinsic drawbacks of data, such as noise, conflicts, etc. To address this issue, several trusted multi-view learning ap- proaches based on the Evidential Theory have been proposed to capture uncertainty multi- view data. However, their performance is highly sensitive to conflicting views, and their uncer- tainty estimates, which depend on the total ev- idence and the number of categories, often un- derestimate uncertainty for conflicting multi-view instances due the neglect of inherent conflicts between belief masses. To accurately classify conflicting multi-view instances and precisely es- timate their intrinsic uncertainty, present novel Deep Fuzzy Multi- Learning (FUML) method. Specifically, FUML leverages Fuzzy Set Theory to model the outputs of a classification neural network as fuzzy memberships, incorpo- rating both possibility and necessity measures to quantify category credibility. tailored loss func- tion is then proposed to optimize the category credibility, To further enhance uncertainty esti- mation, we propose an entropy-based uncertainty estimation method leveraging category credibility. Additionally, we develop a Dual Reliable Multi- view Fusion (DRF) strategy that accounts for both view-specific uncertainty and inter-view conflict to mitigate the influence of conflicting views in multi-view fusion. Extensive experiments demon- strate that our FUML achieves state-of- oott-h--rttttttttoe per- formance in terms of both accuracy and reliability.
This Bathroom really cleon
Conficting
Visualization of the conflicting multi-view instance
RGB Text view d Depth
RGB view
Text view A Depth view
Conflict
Uncertainty
DST
DDF
Vilue
Contloting
Conficting
Bedroom
Bathroom
Bedroom
Bathroom
i Bellef mass
Uncertainty
Membeershi
Uncertainty
(b) EDL-baase TMVC
(c) Ours
Figure I. (a) Visualization of the confficting multi-view instance: the depth view related to "Bedroom" category, while the other views show confficting information, such as "Bathroom." (b) EDL-based TMVC methods are sensitive to such conflicting multi-view instances. On one hand, because they neglect the global conflict between views multi-view fusion, classification errors often made. On the other hand, their uncertainty estimation is only related to the total evidence and the number of categories. For conflicting multi-view instances, long as the total evidence is large, the uncertainty is seriously underestimated. (c) In our method, both global conflict and uncertainty are considered during fusion. allowing the conflicting multi-view instances to be clas- sified correctly. Additionally, this method can estimate decision uncertainty more accurately.
1. Introduction
Multi-view/modal data encapsulates comprehensive infor- mation from various modalities, sources, and other perspec- tives (Yan et al., 2021; Qin et al., 2024; He et al., 2024). Multi-view classification (MVC) aims to utilize the consis- tency and complementary nature of these data to achieve more accurate classification. With the explosive growth of multi-view data in fields such as video surveillance (Wang et al., 2024a), medical detection (Yang et al., 2024; Nasarian et al., 2024), and autonomous driving (Hong et al., 2024), MVC has garnered great attention from both academia and industry in recent years. Despite the promising performance of existing MVC methods (Yang et al., 2019; Han et al., 2022a; Lin et al., 2022; Mittal et al., 2022; Zhang et al.,
'Colleee of Computer Science, Sichuan University, Chengdu, China. Sichuan National Innovation New Vision UHD Video Technology Co., Ltd, Chengdu, China. 'Tianfu Jincheng Lab- oratory. Chengdu, China. School of Computer Science and Engineering, University of Electronic Science and Technology of China, Chengdu, China. Correspondence to: Peng Hu <penghu.mle gmail.com>.
Proceedings of the 4 International Conference Machine Learning, Vancouver, Canada. PMLR 267, 2025. Copyright 2025 by the author(s).

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Deep Fuzzy Multi-viww Learning for Reliable Classification
2023), these approaches predominantly prioritize classifica- tion accuracy while often neglecting decision uncertainty. This could lead to unreliable decisions, limiting their appli- cability in reliability-criitee critticl scenarios.
view-specific decision uncertainty and inter-view conflicts. Unlike existing uncertainty- -aaare fusion techniques in EDL- based TMVC that operate sequentially, our DRF employs a global one- tiettmme fusion strategy that reduces the influence of high-uncertainty and high-conflict views, ensuring more robust multi-view classification. The main contributions of this work are summarized as follows:
To address this limitation, a series of trusted multi-view classification (TMVC) methods (Geng et al., 2021; Han et al., 2020; Liu al., 2022: Xie al., 2023; Liu et al., 2023; Xu al.,, 2024b) based on Evidential Deep Learning (EDL) (Sensoy al., 2018; Bao et al., 2021) have been pro- posed to estimate the uncertainty. These methods provide classification predictions alongside the corresponding uncer- tainty (inverted to reliability). However, they typically as- sume strict alignment across different views, which is often unrealistic due to noise, misalignment, or conflicting infor- mation in real-world scenarios. More intuitively, case of multi-view user- seer-generated content is illustrated in Figure (a), where the RGB, text, and depth views exhibit conflict- ing categorical information. Such conflicts pose significant challenges to EDL-based TMVC methods as shown in Fig- ure 1 (b), remarkably degrading their performance. Specif- ically, these methods face two key issues: i) They heavily rely on Dempster-Shafer theory (DST) (Shafer, 1992) for multi-view fusion, which fails to account for global confticts among views overly emphasizes dominant evidence (Xiao, 2019b; Shang et al., 2021), often leading to misclassifica- tion. ii) Their uncertainty estimation relies solely on total evidence and the number of categories, neglecting inherent conflicts between belief masses, leading to inaccurate uncer- tainty quantification for conflicting multi-view instances.
We reveal and address the conflict sensitivity issue in existing EDL-based TMVC methods, proposing FUML, novel framework based on Fuzzy Set Theory for enhancing classification and uncertainty estimation.
We develop a Dual-reliable Multi-view Fusion (DRF) strategy that effectively reduces the impact of conflict- ing views, embracing more robust multi-view classifi- cation.
We propose an entropy- based uncertainty qualification technique, enabling more accurate uncertainty estima- tion for conflicting multi-view instances.
We conduct extensive experiments comparing our FUML against 13 state-of-the-ar MVC baselines on eight widely-used benchmarks, demonstrating superior accuracy, reliability, and robustness.
2. Related Work
Multi-view Learning. Studies have demonstrated that multi-view learning (MVL) significantly enhances perfor- mance across various tasks. Among them, the CCA-based mieti-view methods are representative (Chaudhuri et al., 2009; Rupnik & Shawe-Taylor, 2010). With the advance- ments in deep learning (Yan et al.,, 2020), some deep MVL. methods (Han al., 2022a; Lin et al., 2022; Zhang et al., 2023; Cao et al., 2024; Qu et al., 2024; Wang et al., 2024b; Chen et al., 2024; Bi & Dornaika, 2024; Xu et al., 2025) emerged. However, most of them focus on improving accuracy, ignoring reliability, limiting their applicability in reliability- critticl domains. To achieve reliable deci- sions, a range of trusted muli-view classification (TMVC) methods (Geng et al., 2021: Han et al., 2020; Liu et al., 2022; 2023; Xie et al., 2023; Liu et al., 2023; Xu et al., 2024a;b; Wang et al., 2024c; Yue et al.. 2025; Wang et al., 2025) based on Evidential Deep Learning (EDL) (Sensoy et al., 2018; Gao et al., 2024) and Dempster-Shee (DST) (Shafer, 1992) are proposed. Among them, Trusted Multi-view Classification (TMC) (Han et al., 2020) and Enhanced TMC (ETMC) (Han et al., 2022b) assume that multi-view data is complete; they dynamically integrate dif- ferent views at the evidence level. However, the arbitrary view missing is widely present in practice. To solve this, Uncertainty-induce induced Incomplete Multi View Data Classi- fication (UIMC) (Xie et al., 2023) is proposed. Neverthe-
To address the aforementioned problems, this paper presents novel framework, Deep Fuzzy Multi-View Learning (FUML), grounded in Fuzzy Set Theory (Zadeh, 1965), which provides more precise decisions along with the corre- sponding accurate uncertainty estimates. Fuzzy Set Theory manages inherent uncertainty and fuzziness in data by in- troducing gradual membership between O and 1, allowing sample to belong to multiple categories to varying de- grees, thereby enabling effective uncertainty quantization and modeling. Based on this principle, as shown in Figure 2, we model the outputs of the classification network as fuzzy memberships corresponding to each category, representing the extent to which a sample belongs to each category. How- ever, memberships alone provide only a possibility measure, i.e., the likelihood of belonging to a category, without indi- cating the between-class relationship (called necessity) that the sample does not belong to other categories. To integrate both aspects, we introduce category credibility, optimized via the proposed category credibility learning loss. Further- more, we propose an entropy- based uncertainty estimation method that leverages category credibility to enhance un- certainty quantification. To mitigate the impact of conflict- ing views in multi-view fusion, we develop Dual-reliable Multi-view Fusion (DRF) strategy, which considers both
theory
2

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Deep Fuzzy Multi-viww Learning for Reliable Classification
less, UIMC assumes views are strictly aligned, while multi- view data often contains low-quality conflicting instances. To address this, Evidential Conflictive Multiview Learn- ing (ECML) (Xu et al., 2024a) designs a conflict opinion aggregation strategy and achieves reliable results for con- flicting instances. However, ECML overly relies on the latter combined views, making its final decision vulnerable to conflicting views. Given this, we suggest jumping out of the Evidence Theory, and re-examining TMVC based the Fuzzy Set Theory (Zadeh, 1965; Liu & Liu, 2010) to achieve a more accurate and robust TMVC.
3.2. Deep Fuzzy Multi-view Learning
3.2.1. CATEGORY CREDIBILITY MODELING
The core idea of Fuzzy Set Theory is to allow samples to be- long set to certain degree, rather than either absolutely belonging or not belonging (Zadeh, 1965). Based on this, fuzzy systems can effectively handle the uncertainties and ambiguities inherent in real-world data (Das et al., 2020; Wu et al., 2025). According to Fuzzy Set Theory, membership quantifies the degree to which a sample belongs to a fuzzy set. Similarly, the output probabilities of classification network, ranging from 0 I, represent the possibility of a sample belonging each category, with higher values indi- cating a greater possibility of classification into that category. This parallel enables us to model the classifier's 's prediction for a category as a membership for that category. There- fore, for a given sample x", the memberships across all categories can be expressed as my, my..................... m where K represents the total number of categories.
Uncertainty-aware Deep Learning. Although deep learn- ing has achieved great success in many tasks, it is difficult to provide reliable uncertainty estimates, which is crucial for reliable models (Wen et al., 2023; Chen et al., 2023). To solve this, early works endowed Deep Neural Networks (DNNss with uncertainty by using distributions instead of deterministic weight parameters (Gal & Ghahramani, 2015; Molchanov et al., 2017; Lakshminarayanan et al.. 2017), but they often suffer from high computational costs. The recently proposed test-time augmentation (Lyzhov et al., 2020) estimates uncertainty at test time, but it still needs multiple inferences. In contrast, Evidential Deep Learning (EDL) (Sensoy al., 2018; Qin et al., 2022; Li et al., 2025) directly infers uncertainty from network outputs. Recently, researchers have extended EDL to the field of multi-view learning and pionecred a series of methods (Geng et al., 2021; Han et al., 2020; Liu et al., 2022; Xie et al., 2023; Liu et al., 2023; Xu et al., 2024a;b). Although these methods achieve promising uncertainty estimates, their uncertainty depends only on the number of categories and the total evi- dence, and the uncertainty of confficting multi-view instance is often underestimated. In this paper, we draw on the Fuzzy Set Theory (Zadeh, 1965; Liu & Liu, 2010), which provides a more nuanced perspective that combines possibility and necessity measures to capture uncertainty more accurately.
Nevertheless, the memberships only provide the possibility measure which represents the likelihood of belonging to a category, not the necessity measure-the certainty that the sample does not belong to other categories (Liu & Liu, 2010; Duan et al., 2025). To complement membership by quantifying these certainties, we introduce the concept of necessity:
c where max max(ma 1 + 133 is the highest membership for the other categories {1144. By integrating both possibility measure and necessity measure, we can obtain more com- prehensive information. Therefore, we define the category credibility as the arithmetic mean of the possibility measure and the necessity measure:
- - (m
1, K,
(1)
Definition 3.1. Let m [m my .... mixl be the vector of memberships of the i-th sample in v-th view, and Vmnie [0, 1], A 2, ..... K. Then, the category credibility of the i-th sample to the k-th category is defined by
3. The Proposed Method
1 (m -m² +1 max | [+ k)), k = 1,2, ..., K, c² 2
3.1. Problem Definition
For a clear presentation, we first introduce the following notations. Given N training imputs J with V views, ie., x== {x")>= and the corresponding labels {ym) The goal of trusted multi-view classification is to learn a model f >= + y that accurately predicts the label for unseen sample by effectively integrating information from all available views and provide the corresponding de- cision uncertainty. The main challenge lies in utilizing the consistent and complementary information from each view while managing conflicting views, ultimately improving overall classification performance and providing accurate uncertainty estimation.
(2)
which can be arranged as cf = |ch c0 ... Gx E R
3.2.2. CATEGORY CREDIBILITY LEARNING
To map the logits of a neural network memberships, first, Lp no-maallzztionn is applied to the logits to limit the value in the range of [-1,1]. Subsequently, an activation function (i.e., ReLU) is used to yield output values in the range of [0.1]. These values can be modeled as memberships for the corresponding category. To be specific, the calculation formula is as follows:
m = ReLU a²
(3)
|a P
3

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Deep Fuzzy Multi-viww Learning for Reliable Classification
Conflict
Trusted results
View 1: x²
e
D!
0.
ns
1,0
m
Class 1
Class 2
View 2: 2t2
(*)-)
m
Membership
Class
:
Necessity
Uncertainty
Category crediblity
Uncertainty
View V: x²
Figure 2. Illustration of FUML. Firstly, siew-specific DNNs (())()))=))) collect memberships (fm") Hi=1) from multi-view instances ((2"")=))) je-1). 1). which could be termed as a possibility for each category. Secondly, the uncertainty of each view (fu H and the conflicts ((o")=)) between views are calculated based on these memberships. Thirdly, the weights [w") of each view could be calculated and are used to aggregate memberships from all views, thereby realizing Dual-reliable Multi-view Fusion (DRF). Finally, the aggregated memberships are used to construct trusted classification results, where the decision uncertainty will increase if aggregated memberships are conflicting.
where a, denotes the logits of a neural network. The cor- responding category credibility of can also be derived by Equation (2).
that this loss function ensure mi, approaches 1 for matched categories where vix = 1 and approaches 0 for unmatched
category where Vik = 0, by leveraging label information. To be specifie, when yo 0 and ya = 1 (where / arg max vie), we expect the membership of the matched
To achieve discriminative learning, each sample should ex- hibit the highest possible category credibility for its matched category while maintaining the lowest possible category credibility for all other categories. Intuitively, this could be achieved by directly aligning the category credibility of with the corresponding one-hot labels y". i.e., mini- mizing mean squared error (lle," - 122 or cross-entropy loss (-y.- log(e") (1 - yy)) log(1 - c)")) However, both approaches risk over-optimizing the necessity (e)) for unmatched categories, resulting in the neural network converging to a local optimum. The reason is follows: When 1it = 0, mi would tend to O, and the necessity <t = 1 - max [m 1 A k-} would also approach 0, driy- ing m. towards 1. This is problematic because mi should approach when v² = O, rather than 1. To tackle this issue, we propose category credibility learning loss to optimize the category credibility, thereby guiding the model toward the correct optimization:
category to be greater than that of any unmatched categories after training. For matched categories, the necessity during training should be calculated as 1 max(m;; 1 ( * k). driving max(m) m | 1 + k} toward For unmatched cate- gories, the necessity during training should be calculated as - mm- forcing my to approach 1. Therefore, this approach effectively guides the necessity and category credibility op- timization, avoiding over-optimization and ensuring correct model convergence.
3.2.3. CONFLICTIVE VIEW FUSION
Environmental factors, such as sensor failure, adverse weather conditions, and data communication issues, often introduce noisy and unaligned views in multi-view data, i.e., create confficting views (Xiao, 2019a; Zhang et al., 2024). Addressing these issues is essential for enhancing the pre- cision and robustness of multi-view classification. Noisy views generally exhibit high uncertainty, complicating accu- rate decision-making and potentially leading to erroncous decisions. Therefore, the influence of noisy views should be minimized in multi-view fusion prioritize the contri- butions of cleaner views. In contrast, unaligned views tend to generate highly conflicting but low-uncertainty decisions. Reducing their misleading impact on the final decision and limiting their influence in the fusion process is also crucial. Therefore, below, we first define the uncertainty and then the conflict, and finally use them to build multi-view fusion strategy that can resist conflicting views.
N₂
1 No
Leel =
y: log(r!)) - (1- llog(1 - r,), (4)
1=1
where No is the batch size, r 6t (m..y.)
[ra rige-.. "ir rix] E RK represents category credibility dur-
ing training, and
mi + 1 - mm | k}
if va = 1,
2
ri
mik + 1 - m
if vI 0, 1= arg max yike
2
(5)
where k = 1, 2, ..., K. From Equation (4), it can be seen
4

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Deep Fuzzy Multi-viww Learning for Reliable Classification
Uncertainty Inference. Although the category credibility reflects the uncertainty of a single predicted category, it fails to capture the uncertainty of the entire prediction out- come. To overcome this limitation, we take into account the category credibility of all categories to calculate decision uncertainty. To be specific, inspired by Shannon's 's entropy, which measures uncertainty arising from information defi- ciency, we define uncertainty as follows:
where g(-) is monotonically increasing function. In this work, we use the exponential function exp(.) as 9()). Note that, during training, the uncertainty is calculated based on the category credibility during training, i.e., Equation (5), According to DRF, we could get the final memberships of each category and thus infer the overall uncertainty by Equation (6).
Definition 3.2. Let c [ci |ci,c22..... S......, cx] be the vector of category credibility of the i-th sample in v-th view, and Ve, E [0, 11, k = 1, 2,,, K. Then, uncertainty is defined by
3.2.4. LOSS FUNCTION
To ensure that all views can simultancously form reasonable decisions and thus improve the overall performance, we use a multi-task strategy with the following overall loss function:
Σ k= H((())
K
u
K In2
V
Σ 1= Cik [n(()))) (1 5/h In((1 ((+))
Liotal = (1", ,y) +
Σ (ra .y)
(9)
In2
(6)
The pscudo-code of our FUML can be found in the Ap- pendix B.3.
where K is the number of categories and H(C))) is the entropy of category credibility c This uncertainty lies within the range [o, 1J. where higher values denote greater uncertainty.
3.3. Discussion and Analyses
In this section, we analyze the advantages of FUML, espe- cially the conflicting view fusion. The following proposi- tions provide the theoretical analysis to support the conclu- sions. The proofs are shown in the Appendix A.
Conflict Inference. The above-defined uncertainty does not allow for the assessment of inconsistencies between views. To address this, below, we define conflict:
Definition 3.3. Let {m²) represent the set of multi- view membership vectors for the i-th sample. The conflict of the v-th view relative to other views is defined as:
Proposition 3.4. For the i-th multi-view instance, when a clean view I with uncertainty uf is fused with a conflict- ing view caused by noise with uncertainty ui, the fused uncertainty uZ > u..
Σ j
m m
-
| [mm]]
Proposition 3.5. For the i-th multi-view instance, when a clean view 1 with uncertainty u, is fused with a conflicting view 2 caused by misalignment with uncertainty u², the fused uncertainty uf un and uē > uf. Based on Proposition 3.4 and Proposition 3.5, during the multi-view fusion stage, our FUML achieves more accurate uncertainty estimation when fusing with a conflicting view.
Since the range of all elements in m is in the range [0, the conflict of is in the range [0,1], where higher values denote greater conflict.
Views with relatively high conflict are considered unaligned with other views, whereas views with relatively low conflict are precisely the ones that should participate in the fusion. Next, we utilize view-specific uncertainty and the above conflict between views to propose a Dual-reliable Multi- view Fusion, which means both noisy views and unaligned views can be reliably fused.
Intuitive explanation of the effectiveness of FUML. With- out loss of generality, we assume that view X' is clean, view 8 is noisy due unknown environmental factors or sensor failure, and view x is misaligned with other views for similar reasons. At this time, X' aligns with the distribution of clean training data, whereas view XB devi- ates significantly from it. Accordingly, we have ud < uB and A < BB, leading to w > w Therefore, in our FUML framework, the multi-view decision will tend rely more on the high-quality view A than on the noisy view x In addition, although the uncertainty of view X is not as high as that of view B its relative view 2' has a higher conflict with other views. Accordingly, we have A z uc and a < of thus A 2 W Therefore, for our method, the multi-view decision will tend to rely more on the low-conflict view 2 than the view XOC As for the
Dual-reliable Multi-view Fusion (DRF). In multi-viww decision-level fusion, we hope to fuse views with low un- certainty and low conftict with other views. Following Defi- nition 3.2 and Definition 3.3, we could fuse the final mem- berships m from different views as follows:
9 ((1 4 (1-)))) )f))
Σ 1= ((1 (1) 0}
m
Σ w m
5

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Deep Fuzzy Multi-viww Learning for Reliable Classification
weight between views 8 and view X it is related to the comprehensive consideration of its uncertainty and conflict. By dynamically determining the fusion weights of each view, FUML effectively mitigates the influence of noisy and misaligned views, i.e., conflicting views, embracing robust classification for conflicting multi-view instances.
baselines, i.e., can't provide decision uncertainty, include:
DFTMC (Han et al., 2022a), DCP(CV&CG) (Lin et al., 2022), QMF (Zhang et al., 2023), and PDF (Cao et al., 2024). (2) The trusted baselines include: DUA-Nets (Geng
et al., 2021), ), TMC (Han et al., 2020), ETMC (Han et al., 2022b), TMDL-OA (Liu et al., 2022), UIMC (Xie et al., 2023), ECML (Xu et al., 2024a), TMNR (Xu et al., 2024b), and CCML (Liu al., 2024).
4. Experiments
4.1. Experimental Setup
4.2. Comparison with State-of-the-Are Methods
We briefly present the experimental setup here, including the experimental datasets and comparison methods. Please refer to Appendix B for more detailed setup. The code of our FUML is available here'.
To evaluate the performance of our FUML, we apply multi- view classification on eight datasets over 10 different ran- dom seeds. The experimental results of the normal and conflicting test sets are shown in Table 2 and Table 3, re- spectively. Note that DFTMC does not converge on the NUSOBJ and Fashion datasets, so we can't 't report its re- sults and mark with '-'. The following key observations can be made from these results: (1) On the normal test sets, FUML outperforms all baselines on all datasets. For instance, on the Scene, Leaves, and PIE datasets, FUML achieves accuracy improvement of 1.62%, 1.59%, and 1.47% compared to the second-best baselines. (2) When the performance is compared on the conflicting test sets, all methods exhibit a noticeable drop in accuracy. How- ever, FUML consistently achieves superior performance, with particularly larger improvements on the Scene, Lan- dUse, and Leaves datasets (4.83%, 7.31%, and 14.60%. respectively). This could be attributed to the proposed dual- reliable multi-view fusion, which improves the robustness to conflicting multi-view instances by reducing the weights of noisy and unaligned views during fusion, as verified by the ablation studies in Section 4.5. More comprehensive conflicting multi-view classification results and analysis can be found in Appendix C.I.
Datasets. To validate the effectiveness of the proposed FUML, we conduct experiments on eight public datasets: Handwritten (HW)?, MSRC-V1 (MSRC) (Winn& & Jojic, 2005), NUS- WUD-OBD (NUSOBIJ', Fashion-MV (Fash- ion) (Wang et al., 2023), Scene15 (Scene)', Use (Yang & Newsam, 2010), Leaves100 (Leaves)², and PIE The training set and the test set are split in a ratio of 8:2. The detailed information shown in Table 1.
To create test set with conflicting instances, following the methodology outlined in (Xu et al., 2024a), we apply two transformations: (1) We add Gaussian noise with different standard deviations to some test instances.
(2) We alter the information in a random view for a subset of instances, making the view's 's label inconsistent with the true label.
Table A summary of datasets used for evaluation.
DATASET
SIze
CATEGORIES
DIMENSIONALITY
HW
2000
10
240; 76; 216; 47; 64; 6
MSRC
210
1302; 48; 512; 100; 256: 210
NUSOBJ
30000
31
65; 226; 145; 74: 129
FASHION
10000
784; 784;
4.3. Uncertainty Effectiveness Analysis
SCENE
4485
15
20; 59; 40
LANDUSE
2100
21
20; 59; 40
To validate the effectiveness of our FUML in estimating un- certainty for conflicting multi-view instances, we compare it with two typical EDL-based TMVC methods, i.c., ETMC and ECML., using the uncertainty density map. The results, shown in Figure 3, reveal the following observations: (1) Compared to the normal test set, the uncertainty of ETMC and ECML barely changed with the addition of conflicting views, and even decreased on the LandUse dataset. How- ever, as can be seen from Table 2 and Table 3, for ETMC and ECML, the addition of conflicting views greatly reduces the classification accuracy. Therefore, their uncertainty es- timates for conflicting multi-view instances are inaccurate. (2) In contrast, the uncertainty estimated by FUML is no- tably higher for conflicting test sets than for normal ones, demonstrating the accuracy of FUML in estimating uncer- tainty since it can facilitate discrimination between normal and conflicting instances. The corresponding quantitative
LEAVES
1600
100
64; 64; 64
PIE
680
68
484; 256; 279
Evaluation metrics. Owing to the inherent randomness, we report the mean accuracy and standard deviation across 10 different random seeds. Additionally, the improvements over the best- rest-performing baseline also reported.
Compared methods. For comprehensive comparison, we adopted the following baselines: (1) The untrusted
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Deep Fuzzy Multi-view Learning for Reliable Classification
Table 2. Accuracy (%) performance on normal test sets. The best and the second-best results are highlighted in boldface and underlined respectively. The means and standard deviations over ten runs are reported. The methods marked with * are trusted.
METHODS.
HW
MSRC
NUSOBJ
FASHION
SCENE
LANDUSE
LEAVES
PIE
DFTMC
98.75:00.39
96.9012.14
63.1013.60
34.95#1.69
69.9212.54
91.40+3.50
DCP-CV
98.75.10.59 92.8611.61
32.1919.48
97.9610.16
2.15
71.7112.09
95.6211.38
86.32.1.87
DCP-CG
99.00:10.47 95.2413.69
43.65#1.10
98.11+
77.79:1.73
75.74
98.1920.46
90.5911.99
QMF
98.724+048 97.86+1.22
45.41+0.43
98.93-0.32
68.58-1149
47.86+22.55
95.69#1.25
92.06++1.64
PDF
98.40#0.37 97.14=1.78
46.78+0.33
98.95=0.19
70.25=1.21
45.17:2.66
98. 98.03=0.71
92.57
DUA-NETS*
98.10++.32 84.67=3.03
27.75+0.00
91.08=0.17
65.01=1.555
90.31 45.24+1.85
90.56+0.47
TMC*
98.51=0.15 91.70=2.70
38.7720.81
95.40=0.40
67.71=0.30
31.6913.93
86.81=2.20
91,85:1..23
ETMC*
98.75=00.00 92.86+3.01
44.23:10.76
96.21=0.36
71.61
43.52#3.119
91.4412.39
93.75#1.06
TMDL-OA
98.55110.45 95.0011.67
27.8810.67
86.52.0.04
75.5710.02
25.0212.10
75.2813.57
92.33.1.336
UTMC*
98.25+0.00 98.81+1.19
43.42+00.1
98.13+0.13
77.70+0.00
57.95+0.61
95.31+0.71
91.6942.16
ECML*
98.7221..9 94.05=1.60
42.62::0.2
97.93=0.35
76.19=0.12
60.10:2.01
92.53=1.94
94.71
TMNR*
97.20.10.33
94.0513.24
34.5211..55
94.1010.50
68. 10.1.5
27.3811.88
90.1311.53
89.5311.89
CCML *
97.6011..2 96.9012.39
41.43:0.71
95.16=0.41
73.87=1.83
60.8611.93
97.7210.92
93.9711.67
FUML* *
99.20=10.36
99.7610.75
48.2310.42
98.96=0.25
79.41=1.34
76.7110.46
99.78:
0.27
96.18:1.24
IMPROVE
0.20
0.95
1.45
A 0.01
A 1.62
À 0.97
A 1.59
A 1.47
Table 3. Accuracy (%) performance on conflicting test sets. The best and the second-best results are highlighted in boldface and underlined respectively. The means and standard deviations over ten runs are reported. The methods marked with * are trusted.
METHODS
HW
MSRC
NUSOBJ
FASHION
SCeNe
LANDUSE
LEAVES
PIE
DFTMC
53.65+20.07
60.24
36.01 2.78 7.88+0.94
1.10#0.12
3.97
DCP-CV
98.20.10.56
84.7611.00
28.1017.80
92.7212.41
66.2212.12
59.98.1.93
76.9411.36
67.06.1..15
DCP-CG
98.70+0.64 90.00+1.78
38.61+1.29
90.38+2.17
66.44+0.32
61.83+2.48 19.06+1.22
69.56+3.77
QMF
97.5210.86
95.95=1.52
42.72:0.67
92.6940.78
59.53=1.63
40.17
1..47 82.50+2.81
PDF
94.3511.21
94.2213.02
43.5710.33
90.7310.53
58.7511.03
39.40.11.94
76.3411.26 74.9312.76
DUA-NETS*
87.1610.34
78.5714.45
25.6411.25
83.0310.188
26.1811.31
37.22110.56
65.6212.19 56.4511.75
TMC*
95.7610.15
86.20=4.90
36.0011.778
84.7610.78
42.27=1.61
19.67 70.2542.55 61.65#1.03
ETMC*
9.285111.26
87.14.14.54
40.4511.81
86.4811.05
56.9011.70
36.0512.50
74.1911.74 73.8214.77
TMDL-OA
92.45++0.05
84.52+2.20
27.02+0.75
74.55+0.07
48.42+1.02
21.71+1.83
62.2843.70
68. 1.30.4
U
97.72+1.118
96.43=11.19
41.72+0.31
89.7110.25
67.8810.48
50.43310.46
79,8410.92
70.6612.04
ECML *
94.52+0.79
90.00=2.78
39.89:0.59
84.0240.51
56.97=0.52
50.31 74.88+1.88
84.00+0.14
TMNR
92.7811101
90.7114.19
30.8810.58
85.76.1.811
60.0011.43
23.9541.92
74.0911.99
80.5913.226
CCMI
93.22+
94.29+2.118
37.38+0.65
83.84+1.01
+..0
52.48+2.74
78.87+2.31
83.24422.79
FUML* *
98.78.10.33
98.81 : 1.60
47.08 0.33
96.68 0.332
72.71 1.75
69.14
94,4411.118
88.01
IMPROVE
A 0.08
2.38
A 3.51
A 3.96
A 4.83
A 7.31
A 14.60
4.01
20
Norro
4.0
Nomel Curlicking
Norral
Nomea Corfickig
Nomal Carkuinn
Numal Carleiig
15
Corliding
3.0
3.5
2.5
Deeaty
Co fkdin
255
2.0
10
2.0
1.5
1,0
0.5
0.0
1.0
0.0
02
0.6 Unowteenty
0.0
1.0
0.8
0.2
Uncwstrrty
Uncerbality
Uncertarry
Unceraliity
Uncetsiity
(a) ETMC (Fashion)
(b) ECML (Fashion) (c) FUML (Fashion) (d) ETMC (LandUse) (c) ECML (LandUse) (f) FUML (LandUsec)
Figure Density of uncertainty the normal and conflicting test sets of the Fashion and LandUse datasets.
7

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Deep Fuzzy Multi-view Learning for Reliable Classification
Table 4. Ablation study on the conflicting test sets of the Fashion and LandUse datasets with all metrics in percentages (%).
HW
HW
Accura
0.0
MSRC
Accuracy
0.5
MSRC
NUSOR)
0.7
0.7
Fastion
Scere
Scene
METHOD
FASIION
LANDUSE
Londuse
0.6-
LandUse
C Feet
RULE
|ACC. 1
PREC. 1
1|F-SCORF 1 ACC. 1 PREC. 1 F-SCOOR f
DRF
96.33
96.31
96.30
68.00
68.72
67.53
02
34
0.8
1.
02
04
0.5
0.a
1.5
96.32
96.30
67.76
Uncertainty threshald
Uncertainty threshold
(a) Normal test set
(b) Confleting test
x
CONCAT
88.45
88.28
88.75
59.69
60.54
58.54
AVG
96.15
96.13
96.13
67.71
68.22
67.42
96.68
69.14
Figure 4. Accuracy with uncertainty thresholding.
View 1
Vew Vew
0.12
Visw 2
Viow 3
6.3
Vie
Nutt
0.10
0.66
6.3
0.04
(a) Original
(b) u & 0.8
(c) u & 0.6
Epach
Epoch
Figure 6. Visualization of aggregated memberships on the training set of LandUse dataset by sSNE (Van der Maaten & Hinton, 2008),
(a) Fashion
(b) LandUse
Samples belonging to the same calegory are rendered with the same color. (a) Display the results of fused memberships. (b)-(c) demonstrate the results fused memberships after samples with uncertainty greater than 0.8 and 0.6 removed, respectively.
Figure 5. Prediction error with different epochs.
results can be found in Appendix C.2.
Additionally, to observe the trend of classification accuracy of FUML as the uncertainty threshold varies, we plot Fig- ure It illustrates that FUML achieves significantly more accurate predictions as the prediction uncertainty decreases for both normal and conflicting test sets all eight datasets. This demonstrates that model's output, i.e., classification results and the corresponding uncertainty, supports making trusted decisions.
over 10 seeds. To be specific, we calculate metrics for each label and find their unweighted mean for precision and F-score. In addition, for simplicity, in this section, we rep- resent L (r", (r". y) fan and represent E (r y) as Ceet- The results, presented in Table 4, reveal: (1) Af- ter removing L or L all indicators decline to varying degrees, which shows that all components in the total loss function are indispensable. (2) When performing feature- level fusion, i.e., concatenating (Concat) all features and only using DNN for prediction, performance declines significantly. (3) Compared to the arithmetic mean (Avg), our DRF fusion demonstrates superior performance. In summary, all components of FUML are indispensable. Ad- ditional ablation experimental results on the normal test set can found Appendix C.4.
4.4. Multi-view Fusion Effectiveness Evaluation
To evaluate the effectiveness of our FUML for multi-view fusion, we compare the prediction error of multi-view leam- ing results (depicted as a red line, labeled "Multi-view") with the prediction error of each single-view learning re- sult on the Fashion and LandUse datasets. As shown in Figure 5, the prediction error of the multi-view is consis- tently lower than that of any single-view in the proposed method, demonstrating that it effectively reduces prediction error by integrating multiple views to achieve more accurate results. Results for the other six datasets are provided in Appendix C.3.
4.6. 1-SNE Visualization and Analysis.
We employ the f-SNE approach to embed the fused mem- berships of the training set from the LandUse dataset into a two-dimensional visualization plane, as shown in Figure 6. The results demonstrate: (1) Distinct categories occupy dif- ferent Spaces, and well distinguished, indicating that FUML learns discriminative information. (2) After filtering out samples with uncertainty greater than 0.8 and 0.6, the category boundaries gradually become more distinct. These improvements are attributed to the effective uncertainty esti- mation capability of FUMI..
4.5. Ablation Study
To demonstrate the effectiveness of each component of our FUML, we perform an ablation study on the conflicting test set of the Fashion and LandUse datasets with mean accuracy (Acc.), mean precision (Prec.), and mean F-score
8

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Deep Fuzzy Multi-view Learning for Reliable Classification
5. Conclusion
semi-supervised learning on multi-view data. Information Fusion, 102:102175, 2024.
This paper presents the Deep Fuzzy Multi-view Learning method (FUML), a novel multi-view classification frame- work designed to accurately classify conflicting multi-view instances and precisely estimate their intrinsic uncertainty. Based on the Fuzzy Set Theory, our FUML models the out- puts of classification neural networks as set of fuzzy mem- berships and quantifies category credibility by incorporating both possibility and necessity measures. To optimize cate- gory credibility, we propose a category credibility learning loss. In addition, we propose a Dual-reliable Fusion (DRF) strategy, which assigns weights based on view-specific certainty and inter-view conffict that effectively mitigates the influence of conflicting views. Extensive experiments on eight public datasets demonstrate FUML's superiority over 13 state-of ofte-offtheeart methods terms of accuracy, robustness, and reliability, particularly in challenging scenarios with conflicting views.
Cao, B., Xia, Y., Ding, Y., Zhang, C., and Hu, Q- Predictive dynamic fusion. International Conference on Machine Learning, 2024.
Chaudhuri, K., Kakade, S. M., Livescu, K., and Sridharan, K. Multi-view clustering via canonical correlation anal- ysis. In Proceedings of the 26th Annual International Conference on Machine Learning, pp. 129-136, 2009.
Chen, M., Gao, J., and Xu, C. Uncertainty awwae dual- evidential learning for weakly-supervised temporal action localization. IEEE Transactions on Pattern Analysis and Machine Intelligence, 2023.
Chen, Z., Lou, K., Liu, Z., Li, Y., Luo, Y., and Zhao, L. Joint long and short span self eeff-attention network for multi-view classification. Expert Systems with Applications, 235: 121152, 2024.
Acknowledgements
Das, R., Sen, S., and Maulik, U. A survey on fuzzy deep neural networks. ACM Computing Surveys (CSUR), 53 (3):1-25, 20110.,0020..
This work was supported in part by the National Key R&D Program of China 2024YFB4710604; in part by NSFC under Grant 62472295, 62176171, 62372315, and U24B20174; part by the Fundamental Research Funds for the Central Universities under Grant CJ202303, and CI202403; in part by Sichuan Science and Technology
Duan, S., Sun, Y., Peng. D., Liu, Z., Song, X., and Hu, P. Fuzzy multimodal learning for trusted cross-modal retrieval. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, 2025.
Planning Project under Grant 2024ZDZX0004, 2024NS- FTD0049, 2024ZHCG0005, and 24NSFTD0130; in part by TCL science and technology innovation fund; in part by System of Systems and Artificial Intelligence Laboratory pioneer fund grant; and in part by the Chengdu Science and Technology Project under Grant 2023- 2023-XT00-00004-GX.
Gal, Y. and Ghahramani, Z. Bayesian convolutional neural networks with bernoulli approximate variational infer- ence. arXiv preprint arXiv:1506.0211: 2015.
Gao, J., Chen, M., Xiang, L., and Xu, C. A comprehensive survey evidential deep learning and its applications. arXiv preprint arXiv:2409.044 044000 2024.
Impact Statement
Geng, Y., Han, Z., Zhang, C., and Hu, Q. Uncertainty-awar multi-view representation learning. In Proceedings of the AAAI Conference on Artificial Intelligence, volume 35, pp. 7545-7553, 2021.
This paper presents work to advance the field of multi- view learning in machine learning. Our goal is to construct a trusted and reliable multi-view classification method to boost the accuracy and credibility of joint decisions in multi- view systems, lowering the potential classification errors and inaccurate uncertainty estimates of prediction. How- ever, due to the data bias in open environments, there is possibility of inevitable error when applying our method in real-world applications.
Han, Z., Zhang, C., Fu, H., and Zhou, T. Trusted multi- view classification. In International Conference on Learn- ing Representations, 2020.
Han, Z., Yang, F., Huang, J., Zhang, C., and Yao, J. Multi- modal dynamics: Dynamical fusion for trustworthy mul- timodal classification. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pp. 20707-20717, 2022a.
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Deep Fuzzy Multi-view Learning for Reliable Classification
APPENDIX
This document provides mathematical proofs, additional experimental details, additional experimental results, and limitations to support the paper:
In Appendix A, we provide mathematical proofs for all propositions presented in Section 3.3.
In Appendix B, present comprehensive experimental documentation:
Datasets Details in Appendix B.1
Baselines Details in Appendix B.2
Implementation Details in Appendix B.3
In Appendix C, conduct extensive supplementary analyses through nine investigations:
Additional Conflicting Multi-view Classification Results and Analysis in Appendix C.I Additional Uncertainty Effectiveness Analysis in Appendix C.2
Additional Multi-view Fusion Effectiveness Analysis in Appendix C.3
Additional Ablation Study Appendix C.4
Identification of Out-of-distribbttio in Appendix C.5
Parameter Analysis Appendix C.6
Challenges of DST in ECML in Appendix C.7
Conflict Visualization Appendix C.8
Adversarial Noise Effect Analysis in Appendix C.9
In Appendix D, discuss the limitations of our FUMI..
A. Proofs
A.1. Proof of Proposition 3.4
Proof. Without loss of generality, for the i-th multi-view instance, let m = [m]] mb,..., ..., m denote the sorted
memberships of clean view X² i.e., m. > m/2 2.... mag. and m [m m .... m2 denote sorted memberships of another noisy view X²2 We assume that my mi 2 mi m h = 2,3, ......K K. Therefore, we have
m + 1 - 1-mb
41
2
mi + +1
-
m
c/
2, K,
(10)
2
H mm
+ -K H miitt-mmm
2
"
K 1n2
where H(I) = --- -m)(() - (1- 1) 1n(1 (1- - 1). Because / = 0.5 is the symmetry axis of H()), we have
H( ml m
+ Σk H( ml mhimmu+t
ml
2
(11)
K In
After fusing view X7 and X22, we have
m fi m w m k = 2,3,..., K,
(12)
where mf denotes the fused memberships, and i! > 0 and w/ 0 represent the weights of view X! and X?? respectively. Therefore, we have
m m wi (m m3b) + wf (m² - m < mm - -m
(13)
m mij
w! (m) m3 + 3 (m² m2)) < m mmk
2,
k = 2. K,
12

---

Deep Fuzzy Multi-view Learning for Reliable Classification
and
mi
m22
+
mi
m22
+
H
2 >
HI
2
(14)
mi
+1
m1 mip +
H
H
) k = 2,3, 3..,.... K.
2
Therefore, have
12
+ Σx= k=
H
mik
H
m
ma
+ >k= H
m mla +1
4
(15)
K In
K In
A.2. Proof of Proposition 3.5
Proof. Without loss of generality, for the i-th multi-view instance, let m [m]] m/2 .... [ denote the memberships of a clean view X₁ and m [m m ... m denote the memberships of another clean but misaligned view X?3. We assume that the view X? is the p-th category and the view X? of the g-th category. Therefore, we can assume that
mi > mih wh # P. m >> maa: Vd + q.
(16)
m ss m
After that, for view X7 we have
mip + max 1/ + p}
ip
(17)
1 + 1 mpp
c/
2
Then,
/ ((c.p) + Enop (cth)
H( m. + max(mm) (epppt
Exep H m.) m1, +
2
(18)
K. 1n2
K 1.l2
where H(t) -t -m((t) (1 -tt) t) 1n(1 t). Because t 0.5 is the symmetry axis of (t), we have
H( m +1 max (m (1/p)
+ Ensp
H miy 1-mb
2
2
(19)
K In2
Meanwhile, for view X²2, we have
H m 1- (1l-mmxxmmm (d
+E
H 2 +1
+1- m
2
(20)
K 1n2
After fusing view X! and X?, because m. ss m² > mig. m m/ mz + p and + q. we have
H m +1 1-m
H(
my + 1- m
Σ kopp.kz H mic m
K ln
(21)
2. In + Ek
H( m m
K ln
Next, prove that uf > u.. Specifically, have
m ip
m wt (mL
mle) + wo (m2 m
(22)
13

---

Deep Fuzzy Multi-view Learning for Reliable Classification
where Wi (0, and w (0,1) represent the weights of view X² and X2, respectively. In addition, have / + +
1.
Because m m²g 2 mag my m m and # 9, deduce that
m m < map - mix < mi - mik Ak +
(23)
Therefore,
mip +
mik
mi
H
H
(24)
2
2
Then, we can deduce that
m71 ip
+ - max maxl + p}
H( 1 Inn.
H(
(25)
2
Combine Equations (19), (21), (24) and (25), we can deduce that
H miy max (ma (b
Enop H
mipt 1-mi
2-1n2 2 Ektp, H
m 1-m
2
(26)
K- 2
K In2
Similarly, u u² can also be easily proved.
B. Experimental Details
B.1. Datasets Details
The multi-view data used in this paper include:
HandWritten (HW) comprises 2000 instances of handwritten numerals ranging from '0' to '9', with 200 patterns per class, represented using six feature sets.
MSRC-VI (MSRC) (Winn & Jojic, 2005) contains 210 images. Each image includes classes. Following (Nie et al., 2017), we extract five features, including CM, HOG, GIST, CENTRIST feature, and LBP.
NUS-WIDE-OBJECT" (NUSOBJ) consists of 30,000 images of 31 classes. Each instance described as views, including Color Histogram, block-wise Color Moments, Color Correlogram, Edge Direction Histogram, and Wavelet Texture.
Fashion-MV (Fashion) (Wang et al., 2023) is an image dataset that contains 10 categories with a total of 30,000 fashion products. It has three views, each consisting of 10,000 grayscale images sampled from the same category.
Scene15 (Scene) includes 4485 images from 15 indoor and outdoor scene categories, with features extracted using GIST, PHOG, and LBP.
LandUse (Yang& & Newsam, 2010) contains 2100 satellite images with 3 views and 21 categories.
1eaves100 (Leaves) consists of 1600 leaf samples from 100 plant species. We extracted shape descriptors, fine-scale edges, and texture histograms as 3 views.
!IE!! contains 680 instances belonging to 68 classes, with intensity, LBP, and Gabor as views.
"htts://archive.iie
"https://lms.om http://lmms.coo....aa weammp.uus.ede www.edu..ppp.................uum wwtp:a/ww.gwww...ooo/ooooeee wwwppp/cootte/iiplola//////////
14

---

Deep Fuzzy Multi-view Learning for Reliable Classification
B.2. Baselines Details
We compare the proposed FUML with the following baselines:
(1) The untrusted baselines include:
DFTMC (Dynamical Fusion for Trustworthy Multimodal Classification) (Han et al., 2022a) captures both feature and modality informativeness, proposing dynamical fusion network for trustworthy multimodal classification.
DCP (Dual Contrastive Prediction) (Lin et al., 2022) Provides an information-theons framework integrating consis- tency learning and data recovery, imputing missing views by minimizing conditional entropy through dual prediction.
QMF (Quale Multimodal Fusion) (Zhang et al., 2023) improves classification accuracy and model robustness by provably robust multimodal fusion method.
PDF (Predictive Dynamic Fusion) (Cao al., 2024) reveals the multimodal fusion from a generalization perspective, improving reliability and stability.
(2) The trusted baselines include:
DUA-Nets (Dynamic Uncertainty-Awar Networks) (Geng et al., 2021) utilizes reversal networks to integrate intrinsic information from different views into unified representation.
TMC (Trusted Multi-view Classification) (Han et al., 2020) pioneers addressing the uncertainty estimation problem in multi-view classification and producing trusted classification results.
ETMC (Enhanced Trusted Multi-view Classification) (Han et al., 2022b) extends TMC by incorporating pseudo view, enabling comprehensive interaction among different views.
TMDL-OA (Trusted Multi- View Deep Learning with Opinion Aggregation) (Liu et al., 2022) proposes a consistency measure loss achieve trustworthy learning results.
UIMC (Uncertainty-induueed Incomplete Multi-View Data Classification) (Xie al., 2023) uses uncertainty-based imputation and evidence-based fusion for reliable classification of incomplete multi-view data.
ECML (Evidential Conflictive Multiview Learning) (Xu et al., 2024a) is the SOTA method for conflict multi-view classification, which proposes a new opinion aggregation strategy.
TMNR (Trusted Multi-view Learning with Label Noise) (Xu et al., 2024b) a reliable multi-view learning model under the guidance of noisy labels.
CCML (Consistent and Complementary-aware trusted Multi-view Learning) (Liu al., 2024) solves the problem of data semantic fuzziness in multi-view learning by dynamically decoupling consistency and complementary evidence, thus improving the accuracy and reliability of classification.
B.3. Implementation Details
All experiments are implemented in PyTorch and are carried out on NVIDIA Tesla V100S. During the training phase, our FUML uses Adam (Kingma& & Ba, 2015) with 31 0.9, 3, = 0.999, weight decay of 0.0001, and maximum of 500 epochs. The in Equation (3) is set to 3. For the NUSOBJ and Fashion datasets, the learning rate is set to 0.0002 and the batch size to 400, while for the remaining six datasets, the learning rate is set to 0.001 and the batch size to 100. The pseudo-code of FUML is shown Algorithm 1. In addition, for a fair comparison, we replace the backbone networks of QMF (Zhang et al., 2023) and PDF (Cao et al., 2024) with the same fully connected layer as FUML while preserving their core models and loss functions. For other baselines, we follow the settings in their source code.
15

---

Deep Fuzzy Multi-view Learning for Reliable Classification
Algorithm 1 FUML algorithm
/*Training"/
Input: the multi-view training data ( ) batch size No, maximal epoch number Ne. learning rate 7), and the multi-view model (""',0"))"""
Output: optimized network parameters {0")=z)
for .. Ne do
Randomly select N& samples from every view to construct multi view mini-batch.
Calculate the output {(a
J for all samples of the mini-batch by using their corresponding model
Calculate view-specific memberships {m") by Equation (3).
Calculate credibility degrees during training {r")
"" 1==1 by Equation (5).
Calculate category credibility during training by Equation (5) and aggregate memberships by Equation (8).
Compute Liotal according to Equation (9) minibatch.
Update FUML parameters (0') )==1 using gradient descent algorithm with learning rate 17.
end for
/"Testing"/
Calculate the view-specific memberships by the trained model.
Calculate category credibility by Equation (2) and fuse memberships by Equation (8).
C. Additional Experiments
C.1. Additional Conflicting Multi-view Classification Results and Analysis
To further assess the performance of our FUML in conflicting multi-view classification, we compare it against the three best- performing untrusted multi-view classification methods, i.e., DCP-CG, QMF, and PDF, as well as the three rest-performing trusted multi-view classification methods, i.c., UIMC, ECML, and CCML. Each method is evaluated over 10 runs, and the mean values along with standard deviations reported.
Table 9 presents the experimental results where Gaussian noise with mean of 0 and variances of 1, and 10 is randomly added to half of the views in half of the test sets. Similarly, Table 10 illustrates the results of adding Gaussian noise with a mean of 0 and a variance of I to half of the views in randomly selected 10%, 20%, 30%, 40%, and 50% of the test set. Finally, Table 11 displays the experimental results introducing unaligned views to half of the views in randomly selected 10%, 20%, 30,, 40%, and 50% of the test sets. These results indicate that our FUMI. surpasses nearly comparison methods across various conflict settings, highlighting its effectiveness in conflicting multi-view classification.
C.2. Additional Uncertainty Effectiveness Analysis
In Section 4.4 and Figure 3, we provide qualitative results on uncertainty estimation, and to complement them, we report here the quantitative results. Results are shown in Table 5, which demonstrate that our FUML more effective than ETMC and ECML in uncertainty estimation.
Table Quantitative results of uncertainty estimation. The normal test sets serve in in-distribution, while the confticting test sets out-of-distribution The evaluation metric is FPR95, where lower values indicate better performance. The best results are highlighted in boldface.
METHOD
ETMC
ECML
FUML (OurS)
DATASET
FASHION
0.930
0.967
0.510
LANDUSE
0.964
0.945
0.886
16

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Deep Fuzzy Multi-view Learning for Reliable Classification
C.3. Additional Multi-view Fusion Effectiveness Analysis
In this section, we present additional experimental results for analyzing the effectiveness of multi-view fusion. As shown in Figure 7, the prediction error of the multi-view approach is consistently lower than that of any single view in the proposed method. These results confirm that our method effectively reduces prediction error by integrating multiple views to achieve more accurate results, aligning with the observations reported in Section 4.4.
0.235
38-
View
Vie
View 1
27
View
Vieu
Vie
View
0.22
Viear 2
Viear 3
3.5-
View 4
Mult--teer
Viee 5
Vie 5
Vie 6
2.4
Wullioww
Vie
600-
View 2
View
0.08
0.315
View 3
0.550
Vicw 5
Vicw
0.54-
0.2
9.925
120
200
602
520
400
140
260
200
602
1dc
260
160
420
602
Epoch
Epoch
Epoch
Epoch
HW
(b) MSRC
(c) NUSOBJ
(d) Fashion
0.84
0--
0.8
View
View
0.7
Nultisiww
3.6-
Vaw
Error
Error
Vie 2
2.4
View
9.4
0.2
9.1
320
202
300
<2o
50c
120
202
330
420
500
120
200
300
410
500
100
203
300
420
500
Epoch
Epoch
Epoch
Epoch
(e) Scene
(f) LandUse
(g) Leaves
(h) PIE
Figure 7. Prediction error with different epnchs.
C.4. Additional Ablation Study
In this section, we report the additional ablation experimental results: (1) Results in Table 6 show that all components contribute positively to performance. Compared to Concat (i.e., concatenate all view features) and Avg (i.e., m (Ev-) mt) )/V), DRF is more effective on conflicting test sets than on normal test sets. (2) To evaluate the role of necessity, we removed the necessity in FUML and only used conflicts in the fusion process. Results in Table 7 prove that necessity can't be removed. (3) To further evaluate the role of uncertainty and conflict in DRF, we conduct more detailed ablation experiments. Results in Table 8 show that removing uncertainty (u) or conflict (c) in DRF leads to performance degradation, indicating the effectiveness of considering both uncertainty and conflict.
Table Classification accuracy (ACC), Precision (Prec.), and F-score of FUML with different combination rules the normal and conflicting test sets. All metries are expressed as percentages (%). The best results are highlighted in boldface.
DATASET
FASHION (NORMAL.)
LaNDUSE (NORMAL.)
FaShIon (CONFLICTING)
LANDUSE (CONFLICTING)
METHOD
La
RULE
ACC1
PREC. F-SCORET
ACCt
PREC.
F-SCORE"
ACCT
PREC.
F-SCORE"
ACCT|PREC.]
F-SCORE1
DRF
98.66
98.66
98.48
76.29
76.89
76.09
96.33
96.31
96.30
68.00
68.72
67.53
/
DRF
98.73
98.73
98.73
75.71
76.14
75.24
96.32
96.32
96.30
67.76
68.41
67.33
CONCAT
95.71
95.71
95.70
72.26
72.44
71.55
88,45
88.28
88.75
59.69
60.54
58.54
AVG
98.50
98.51
98.51
76.19
77.14
76.07
96.15
96.13
96.13
67.71
68.22
67.42
DRF
98.96
98.97
98.96
76.71
77.57
76.48
96.68
96.68
96.68
[6.11
70.21
69.19
17

---

Deep Fuzzy Multi-view Learning for Reliable Classification
Table Classification accuracy (%) on the normal and conflicting of the Fashion and LandUse datasets. The means and standard deviations over len runs are reported.
The best results are highlighted in boldface.
DATASET
FASHION (NORMAL)
LANDUSE (NORMAL)
FASHION (CONFLICTING)
LANDUSE (CONFLICTING)
METHOD
W/O NECESSITY
97.70=+0.41 98.96:10.25
44.64#3.65 76.71=0.46
94.91=0.47 96.68=0.32
39.00 69.14112.43
OURS
Table Classification accuracy (%) on the conflicting test set of Fashion and LandUse datasets. The means and standard deviations over ten runs are reported. The best results are highlighted in boldface.
DATASET
FASIIION
LANDUSE
METHOD
AVG 1 4
96.15=:.22
67.71
96.27+0.22
68. 1444.47
C
96.43
68.50=2.02
OURS
96.68 0.32
69.14 2.28
C.5. Identification of Out-of-distribution
This section presents distiribbititoonnnnnnn (OOD) detection results for FUML across all datasets. To validate the effectiveness of our FUML a trusted method in data noise identification, we add Gaussian noise with fixed standard deviation (8 0.1, 0.5, 1.0) to all of the test samples in the test sets, creating OOD samples. In contrast, the remaining data were treated as in-distribution (ID) samples. The results are shown in Figure 8, indicating that ID samples exhibit consistently lower uncertainty relative to OOD samples across all eight datasets. Moreover, OOD samples with greater Gaussian noise deviation generally demonstrate higher uncertainty. Additionally, datasets with higher prediction accuracy (e.g.. HW, MSRC, Fashion, Leaves, and PIE) exhibit lower overall uncertainty, whereas datasets with lower prediction accuracy, such as NUSOJB, Scene, and LandUse, tend display higher uncertainty. These results demonstrate that FUML effectively measures uncertainty, thereby ensuring the reliability of the model's decisions.
3.0
OOD(6 0.1)
p-distribulion
2.0
0OD 0.1)
In-dstribution
6-
DOO(3 = 0.1)
In-dstribtion
0OD15 0.1)
Indiisibutioon
DODI5 0.5)
OODIS 0.5)
COOYS 0.5)
OOD15
Density
1100)
Density
1.5
OODI6 - 1.0)
0O0 1.0)
Density
0OD15 1.0)
1.5
3
2.0
2-
1.5
0.5
1.0
0.5-
1-
0.5
0.0
0.0
0.0
0.0
0.6 Uncertainty
0.4
0.0
0.0
1.0
Uncertainty
Uncertainty
Uncerlainty
HW
(b) MSRC
(c) NUSOBJ
(d) Fashion
3.5
indesttbutinn
disstriiuution
17.5
indisibulion
Norma
3.0
00066 - 0.3)
2.5
0C0 0.11
OODI6 0.1)
00D(a 0.1]
00016 0.5)
OCD(3 0.5)
OODI8 0.5)
00D18 0.5)
Denat:
2.5
OODIó
Density
2.0
OCD(3
Density
12.5
OODI5
Density
4-
000(5
1.5
10.0
1.5
7.5
3-
1.0
1.0
0.5
2.5
0.0
0.8
0.0
0.0
0.2
0.4
0.8
0.8
1.0
0.0
0.6
0.0
0.2
0.1
0.8
Uncertainty
Uncertainty
Uncertainty
Uncertainty
Scene
LandUse
(g) Leaves
(h) PIE
Figure 8. Density of uncertainty.
18

---

Deep Fuzzy Multi-view Learning for Reliable Classification
C.6. Parameter Analysis
To investigate the parameter sensitivity of our method, plot the accuracy, precision, and F-score of multi-view classification versus different p on the test sets of all the datasets shown in Figure 9. The results show that in all datasets, the accuracy, precision, and F-score all increase first and then decrease with the increase of p. In general, performance is best when p is within 2-5. In this paper, we set p to 3 on all datasets. If we adjust the p value in our model, we believe our FUML will improve over what is reported in the Table and Table 3.
Precition
Accoursry
0.998
Acccuraty
Trecation
0.45
0.989
0.9925
0.996
0.988
0.987
0.9920
0.9915
0.35
0.986
0.985
0.984
Acccuracy
0.9905
0.990
0.25
0.983
0.982
0.9900
6
10
10
10
2
10
(a) HW
(b) MSRC
(c) NUSOBJ
(d) Fashion
0.78
0.76
0.95
0.96
0.78
0.90
0.74
0.95
0.77
0.85
Accouracy
Accouracy
Accouracy
Acccuracy
0.75
Prectsion
F-scora
Precaion
F-score
0.70
Trecasoo
Facore
0.93
Precaion
Piscora
(c) Scene
(f) LandUse
(g) Leaves
(h) PIE
Figure The influence p.
C.7. Challenges of DST ECML
In evidential deep learning, the outputs of the classification neural network are modeled as evidence. Here, we define the
e The parameter of = [af...., .x]] ] of the Dirichlet distribution induced evidence vector for v-th view as e" [e,...., .r....,,lll from evidence, i.e., of = ex + 1. Then, the belief mass by and the uncertainty are computed as
c
a -1
K
50 and u
(27)
5
S"
where S" (e(+)) a. is the Dirichlet strength. Next, analyze why the decision-leve fusion in ECML (Xu al., 2024a) is order-dependent, In the ECML framework, it is established that fusing two opinions (w (b, u, a.) could be mathematically represented as averaging two pieces of evidence, using the following formula:
ur w 2 w² ...Q v..
(28)
This formula is implemented in the code snippet:
evidence_a evidences[0]
for v in range(num views):
evidence a = (evidences[i] + evidence 2
ECML essentially applies the D-S combination rule by sequentially merging evidence from different views. However, it has significant limitation: its decision-level fusion is order-dependent, where the later decision (here referring to evidence) strongly influences the final decision. As a result, ECML is sensitive to the order of conflicting views, making the final decision less reliable when contradictions arise between views. The proposed FUML uses uncertainty and conflict to calculate weights and simultaneously fuses the decision of multiple views at the decision-lever fusion, thus avoiding this problem. The results are shown in the Table 12, confirming this.
19

---

10 Deep Fuzzy Multi-view Learning for Reliable Classification
Table We add Gaussian noise on random 50% modalities of 50% random samples test set presents standard deviation.
The means and standard deviations of classification accuracies (%) over ten runs are reported. The best results are highlighted in boldface.
DATASET
METHOD
8 =
DCP-CG
99.00-10.47
98.02.0.552
96.40-1.22
93.40.1.112
QMF
98.72=0..8
94.85=0.99
77.32
1..2
PDF
98.40+0.33
95.40+0.98
78.92+1.65
73.55+1.68
HW
UIMC
98.2510.00
97.2211..13
94.70.10.24
93.42-0.233
ECML
98.72+0.39
1.75
73.03=1.51
10.18=1.21
CCML
97.60+10.63
94.05+
72.17+1.51
66.85
OURS
99.2010.336
96.78110.22
92.38-11.53
91.72:1.722
DCP-CG
95.24.1.66
79.0512..78
75.24
74.1411.44
QMF
97.86+1.22
93.57+2.62
73.33++0.60
68.57#5.19
PDF
97.14+1.78
96.43+2..44
80.71+3.22
73.81+4.64
MSRC
UIMC
98.81
97.21
94.71-11.78
93.2911.90
ECML
94.05-11.60
83.3313.53
68.33-13.38
63.95
CCML
96.90=2..39
91.90=1.90
73.33:7.559
66.4326.16
OURS
99.76:10.75
98.1012..33
95.00-12.49
94.2913.05
DCP-CG
43.65+1.10
29.11=1.28
28.73=1.13
28.67
QMF
45.41-10.43
32.9440.33
30.62-+0.39
30.25+0.43
PDF
46.78110.3
34.15+0.32
31.94-1..3
31.6910.35
NUSOBJ
UIMC
43.42+0012
40.97+0.12
36.67+0.13
35.85
ECML
42.62.10.42
31.59-10.65
30.33-10.53
29.9110.48
CCML
41.43:00.71
29.96:10.87
28.01::0.67
27.75=0.65
OURS
48.23+0042
41.49+0.49
41.20=10.54
41.16+10.55
DCP-CG
98. 98.11+0.23
86.77+2.10
82.45+2.67
82.2442.66
QMF
98.93-0.32
93.05-10.48
71.88-10.72
69.94
PDF
98.95=10.19
93.1610.59
79.83-10.81
73.2810.70
FASHION
UIMC
18.13+0.13
95.57+0.12
93.04-10.21
92.49-0.118
ECML
97.93-10.35
91.0010..70
76.76110.74
73.16100.67
CCML
95.16:10.41
91.39+10.43
78.22-10.84
72.49+0.87
OURS
98.96-10.25
95.22-+0.32
90.66+10.85
89.82+0.91
DCP-CG
1,,79+1.73
62.52
55.50=0.60
54.89+00.52
QMF
68.58+1.49
52.68
48 48.46
47.90=1.88
PDF
1..25+1.221
55.25 1.39
10.49+1.54
49.78+1.611
SCENE
UIMC
77.70110.0
72.32.0.556
66.35110.65
65.6311077
ECML
76.19-t0.12
58.08+1.34
17.66=1.86
57.09
CCML
13.87+1183
51.43442.10
1..8
1.66
OURS
1..4
70.1412.27
69.11
68.9712.25
DCP-CG
75.74
55.05
53.76
53.57
QMF
47.86+22555
35.36+2.65
33.38+2..56
33.43+2.75
PDF
45.17+2.66
36.21+2.17
34.64+1.74
34.31+1.71
LANDUSE
UIMC
57.95.10.61
53.26110.56
47.93-10.59
47.10-10.55
ECML
60.10+2.01
39.81=1.27
37.61#2.11
37.14
CCML
60.86-11.93
45.76+11.75
42.95-11.63
42.71+1.72
OURS
76.71110.46
63.8611.555
63.50
63.48
DCP-CG
98.1910.46
65.38111.22
65.31
65.2111.31
QMF
95.69+1.25
74.16+2.08
64.75+2.00
64.06+2.20
PDF
98.03-10.71
77.62+2.42
68.34+1.85
66.9442.07
LEAVES
UIMC
95.31+0.71
91.66+00.97
82.94+0.97
82.50-0093
ECML.
92.53.11.44
72.9411.89
65.78
64.8412.18
CCML
97.72110.2
60.0311.99
56.9112.34
56.6912.50
OURS
99.78+0.27
93.69+1.17
92.94+11.36
92.84+1.40
DCP-CG
90.59+1.99
61.18+3.40
61.18+3..40
61.18
QMF
92.06-11.66
75.51122.1
63.64-13.05
62.79-3.111
PDF
9..57=1.66
77.35+3.22
65.81+3.67
63.90=2.95
PIE
UIMC
91.69+2.16
89.25+22.22
84.81+2.03
83.85+2.01
ECML
94.7110.00
74.6313.21
64.85
63.3113.52
CCML
93.97+1.67
75.44+3.53
63.9742.90
62.57+3.06
OURS
96.18+1.24
89.41+1.68
88.38+2.07
88.38
20

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Deep Fuzzy Multi-view Learning for Reliable Classification
Table We Gaussian noise standard deviation on 50% modalities different proportions test sets. The means and standard deviations of classification accuracies (%) over ten runs are reported. The best results are highlighted in boldface.
DATASET
METHOD
0%
10%
20%
30%
40%
50%
DCP-CG
99.00=0.47
98.45=0.37
0..45=0.33
98.25=0.34
98.15=0.455
98.02=0.52
QMF
98.72:10.48
07.5
96.75=0.72
96.20-10.84
95.67=10.00
94.85-10.99
PDF
98.40-10.37
97.5210.55
97.22=0.64
96.6010.90
96.02-10.97
95.4010.98
HW
UIMC
98.25+00.00
98.15+0.12
97.95+0.12
97.95+0.12
97.92+0.12
97.22+00.13
ECML
98.72:0..99
16.18
93.92=0.81
92.30=0.76
91.05=1.099
1..5
CCML
97.60++0.63
96.85+0.71
96.05-00.99
95.35+1.02
94.82++1.28
94.05+1.32
OURS
0.32
98.62:10.45
98.15+0.53
97.8240.63
97.38++0.60
96.78+0.82
DCP-CG 95.24.13.69
91.4312.43
88.1042.61
84.2912.86
82.86.1..16
79.05
QMF
97.86=1.228
96,90+1.86
95.95+2.14
95.2442.13
94.76+22.08
93.5742.62
PDF
97.14+1.778
96.90+1.86
96.90+2.39
96.90-22.14
96.9+-2.1
96.43+2.44
MSRC
UIMC
98.8111.19
98.05
98.05
97.8111.19
97.8111.11
97.21
ECML
9..05=1.60
91.90#2.43
89.52+2.86
88.10+3.53
86.43+3.38
83.33+3.53
CCML
96.90+22.39
94.05+3.06
93.57+3.2
93.57-13.2
92.62++2.49
91.90+1.90
OURS
99.76.10.75
99.7610.71
9.02
98.8111.119
98.81111.19
98.1012.33
DCP-CG
43.65.11.10
41.0910.75
38.22.0.556
35.4310.52
32.62-10.56
29.11
QMF
45.41=:0.43
42.71=0.42
40.12=0.43
37.27=0.31
34.32+0.38
32.94+0.31
PDF
46.78+00.3
45.94+0.49
43.08+0.48
40.09+0.23
37.10+0.26
34.15+0.32
NUSOBJ
UIMC
43.42110.12
42.9510.13
42.3310.15
41.81
41.2710.17
40.9710.12
ECML
42.62+t0.2
40.62+0.89
38.50=0.84
37.09+0.66
35.06+0.82
31.59+00.55
CCML
41.43:10.71
38.76410.64
36.5710.79
34.33:10.67
32.0740.77
29.96:10.87
OURS
48.23:10.22
46.6610075
45.39
44.1010.558
42.78-10.56
41.4910.49
DCP-CG 98.1110.23
95.42.0.55
93.3310.89
91.0911.29
88.8711.75
86.7712.10
QMF
98.93-1032
96.8410.51
95.67-0.56
94.7111.45
93.78-0.51
93.05
PDF
98.9510.11
97.5710.36
96.6410.43
95.8210.46
95.1410.49
93.16:00.59
FASHION
UIMC
98.13+0..13
97.57+0.12
97.42+0.12
97.20+0.10
96.97+0.12
95.57+0.12
ECML
97.9310.33
96.4410.42
94.9111.44
93.48110.51
92.14.10.59
91.00100.70
CCML
95.16:10.41
94.47=0.55
93.58=0.48
92.7810..2
92.07=0.48
91.39+0.43
OURS
98.96-10.25
98.22+0.27
9.24
96.75+0.33
95.9440.28
95.22+0.32
DCP-CG
1..79+1.73
74.85+0.83
71.37=0.28
68.38+0.52
65.66+0.96
62.52
QMF
18.58:11.49
65.32
12.1
59.31
$5.89
52.68
PDF
70.25+11.21
67.2811.26
6..3
61.4610.94
58.25
15.25
SCENE
UIMC
77.70+00.0
16.104
70.95
73.43+0.54
72.93+0.54
7..32+0.56
ECML
76.19.10.12
69.94
66.7311.46
63.9211.44
60.81
58.08
CCML
73.87+1.83
6..5
11.19=1.49
58 18.06611.67
54.65#11.8
51.43+2.10
OuRS
1..4
7.85
75.47+1.95
73.77+-2.13
72.04+2.09
70.14+2.27
DCP-CG
75.7441.99
72.29+1.95
1..14
64.29+1.33
60.00++0.96
55.05+1.66
QMF
47.86:2.55
45.31
42.83
40.6941.63
38.1242.67
35.3612.66
PDF
45.17:2.66
44.7612.64
42.7942.54
40.6912.14
38.6242.13
36.21
LANDUSE
UIMC
57.95-10.61
57.0510..47
55.8110.47
55.5210.44
54.71110.44
53.26100.56
ECML
60.10+2.01
49.62+2.36
46.90=2.23
15.19
42.62-1.73
39.81
CCML
60.86:11.93
57.67
54.86:12.45
52.05:2.449
48.67-1..36
45.76
OuRS
76.71-10.46
7..2
7..07+1.83
68.88+1.71
66.38+11.83
63.86+1.55
DCP-CG
98.1911..46
91.0610.70
84.2511.06
77.8111.06
71.5611.27
65.38
QMF
95.69+1.25
91.31+1.20
8.70
82.37+1.97
78.3442.43
74.16+2.08
PDF
98.03-40.71
94.09+1.113
89.91+1.558
85.6242.22
81.4142.75
77.62+2.42
LEAVES
UIMC
95.3110.71
94.4110.83
93.8110.88
93.0310.77
92.03-1..82
91.6610.97
ECML
92.53+1.94
88.6941.18
84.03+1.65
79.62+1.30
75.34+1.89
72.94+1.89
CCML
97.72-0.922
1..6
1..6
69.72-11.3
65.13-11.82
60.0
OURS
99.7810.27
98.5910.64
97.5610.88
96.1211.02
94.88
93.69
DCP-CG
90.5911.99
83.2413.73
77.50
71.3211..8
66.18
61.18
QMF
9..06+11.64
88.75+1.95
85.22+2.04
81.62+2.42
78.46+3.19
75.51+2.61
PDF 92.57+11.66
89.71+1.83
86.32+2.19
83.38+2.55
80.07+3.13
77.35+3.229
PIE
UIMC 91.69-2.116
90.9912.16
90.49+1.93
90.4012.08
90.1812.22
89.2512.22
ECML 94.71+00.02
87.06+2.77
84.49+2.64
12.1232.33
79.49+2.43
76.63+3.21
CCML
93.97+1.67
88.5342.08
84.56=1.89
81.62+2.85
78.3143.48
75.44+3.53
OURS
96.1811.24
93.9711.27
92.7211.59
91.3211.57
90.0711.84
89.41
21

---

Deep Fuzzy Multi-view Learning for Reliable Classification
Table unaligned on 50% modalities the sets in different proportions. The means and standard deviations classification accuracies (%) over ten runs are reported. The best results are highlighted in boldface.
DATASET
METHOD
0%
10%
20%
30%
40%
50%
DCP-CG
09.00=0.477
98.45=0.37
98.35=0.34 3.
98.30=0.29
98.05=0.33
97.95+0.43
QMF
98.72-0.48
98.42-00446
98.38=0.44
98.30=:0.22
98.12:0..4
97.78+0.599
PDF
98.4010.37
97.50=0.43
96.72=0.55
95.55=0.58
94.50=0.80
93.6010.71
HW
UIMC
98.25+0.00
98.20=0.19
97.88-0.13
97.72=0.11
97.72+0.11
97.72+0.11
ECML
98.72+0.39
97.48=0.71
96.92=0.81
96.02=0.72
95.45=0.95
94.60=+0.77
CCML
97.60+0.63
96.23-0.75
95.40=1.00 1.02
94.40-t1.17
93.40+1.41
92.25++1.53
OURS
0..2
99.13-0.28
99.10-0.28
99.05+0.33
99.05+0.31
99.10+0.32
DCP-CG
95.2413.69
94.7113.50
94.71-2.78
93.29113.56
93.2913.56
92.33.14.10
QMF
9..86+1.228
97.14=1.78
96.67=2.18
95.95=2.14
95,48+1.98
95.00+22.70
PDF
97.14+1.78
95.71+1.78
94.76-2.08
92.86+2.61
92.38+3.16
91.43++3.2
MSRC
UIMC
98.8111.19
98.05=1.17
98.05-1.17
96.57+1.17
96.5711.17
91.9011.17
ECML
94.05+1.60
93.57=3.02
93.33=2.78
92.62+2.70
90.95+2.97
89.29+2.44
CCML
96.90+22.39
94.29-2.86
94.05=3.24
92.38
91.90+3.40
91.67+3.41
OuRS
99.76:10.75
99.76-0.71
99.76-0.71
99.76.10.71
99.76.1.71
99.76:10.71
DCP-CG
43.6511.11
43.22.0.95
1.05
41.9611.01
41.42.11044
40.86-11.08
QMF
45.41=0.43
45.22=0.40
45.15=0.43
44.94=0.55
44.76=0.55
44.72=t0.59
PDF
46.78+0.33
46.50=0.29
46.24-0.44
45.92+-0446
45.58+0.49
45.35+0.46
NUSOBJ
UIMC
43.42-10.12
43.14-0.15
42.76-0.19
42.62-1.11
42.2110.17
41.78110.14
ECML
42.62+00.2
41.92=0.59
41.29-0.57
41.03=0.58
40.71+0.58
40.53+0052
CCML
41.43:0.71
40.40=0.42
39.98-0.55
39.54
38.9240.64
38.43310.70
OURS
48.23110.42
47.78-0.58
47.62-0.50
47.40
47.0710.54
46.8611..49
DCP-CG
98.11110.23
96.00
94.71-1.56
93.0112.06
91.3312.58
89.93
QMF
98.93:10.32
97.77=0.32
96.63-0.24
90.48
94.34.0.42
13.16+0.399
PDF
98.95=0.11
97.17=0.23
95.50=0.36
93.77=0.54
91.8410.92
89.68+1.03
FASHION
UIMC
18.13+0.11
96.12=0.19
93.75-0.23
91.85+0.21
89.90=0.27
0..3033.33
ECML
97.93.10.35
94.43-0.32
91.20-0.39
87.9110.51
84.5810.60
81.49.10.68
CCML
95.16=0.41
92.55=0.32
89.76=0.24
86.81=0.62
84.08=0.83
81.45=1.07
OURS
98.96+0..25
98.57-0.21
98.18-0.24
97.78=0.11
97.32+0.21
96.88++0.33
DCP-CG
77.79+1.73
74.27=0.64
72.33=0.69
69.90=1.29
67.56+1.56
65.04+1.51
QMF
68.5811.49
6..8
65.22-1.11
63.57=1.01
61.6710.97
60.07-1.99
PDF
10.25
67.87=1.17
65.54=1.12
63.1420.98
60.6611.000
1..1
SCENE
UIMC
77.70+0.00
74.86=0.46
72.85-0.45
70.79+0.45
68.7440.43
16.02.4.44
ECML
16.1910.11
7..4
69.86-1.16
68.26.11.17
66.7311.116
65.3711.22
CCML
73.87+1.83
65.60=1.60
63.31=1.55
61.43=1.51
59.16=1.55
17.05
OURS
1..4
78.19-1.43
76.98-1.52
75.80+1..99
74.68+1.30
73.99+1.15
DCP-CG
75.74+0.98
73.33-2.03
69.57=1.12
66.71#1.56
63.00+1.76
59.95+1.69
QMF
47.86:12.55
46.60-2.61
45.10=2.62
44.0242.56
42.6712.118
41.38:12.12
PDF
45.1742.66
44.50=2.49
42.62-2.33
40.64=2.31
38.88
37.0742.12
LANDUSE
UIMC
57.95
56.40-0.58
53.45-0.56
51.8310.41
49.36-1.44
47.30-1063
ECML
60.10+2.00
52.17=1.18
50.79=1.58
49.62=1.69
48.00+1.38
46.76+1.89
CCML
60.86-11.93
59.29=1.87
57.80-2.29
55.48-22.96
54.1742.70
53.2113.07
OURS
76.71--0.46
1.95
73.38 1.81
72.10+1.74
7..9
69.93-11.47
DCP-CG
98.1910..46
98.19
91.0
91.19
88.00-1.884
84.6912.19
81.5612.01
QMF
95.69+1.25
91.50=1.32
87.66=1.71
83.25=1.81
79.0642.11
75.38+2.24
PDF
98.03-10.71
92.78-1.21
87.75-1.36
82.34+1.02
77.56+40.94
72.56+0.84
LEAVES
UIMC
95.3110.71
89.72-0.65
86.47_0.74
83.06-10.87
80.4111.94
77.09-0.99
ECML
92.53+1.94
89.84=1.95
86.41=1.84
83.09=1.82
79.6242.09
76.1222.25
CCML
97.72-10.92
81.09-2.22
78.06-2.01
74.5942.01
7..34
12
OURS
99.7810.27
98.94_0.72
97.84=1.14
9..7
95.81
94.69
DCP-CG
90.5911.99
3.01
81.03=2.05
76.76
72.6512.43
68.68
QMF
92.06=11.64
90.51=1.811
88.82-2.37
86.40=2.68
84.34+2.61
81.99+2.98
PDF
9..67+1..66
19.19=1.44
85.96-2.07
82.06+1.899
79.1242..4
75.00+2.81
PIE
UIMC
91.6912.116
85.96-2.40
82.72-2.33
77.06=2.79
73.0942.72
68.2412.82
ECML
94.71+0.02
88.75-2.51
86.69-2.47
84.56+2.28
82.50+1.977
15.1555.55
CCML
93.97+1.67
90.22=1.86
88.24=1.64
86.03+1.77
84.26+1.62
1.965
OURS
96.1811.24
94.93=1.37
93.38=1.95
91.47=11.2
89.85-2.13
87.9412.38
22

---

Deep Fuzzy Multi-view Learning for Reliable Classification
Table 12, Classification accuracy (%) of ECMI, and our FUMI, with varying noise views on the PIF: dataset. FCMI. fuses views the first view, making it sensitive to the order of the noisy views.
METHODS
NOISE VIEW
1+2+3
1+3+2
2+1+3
2+3+1
3+1+2
3+2+1
4%
87.13
81.69
87.13
76.91
81.76
77.21
10.22
ECML
2
91.18
82.13
90.96
91.25
82.06
91.25
9.19
3
86.76
88.97
86.54
90.81
88.90
91.10
4.56
93.24
OURS
2
96.18
92.65
C.8. Conflict Visualization
Figure 10 presents the conflict the HandWritten dataset with six views. To introduce conflicts, we modify the content in the third view to other categories, resulting in misalignment with the other views. The Figure 10 (a) and (b) depict the conflict normal and conflicting instances, respectively. The results show that FUML effectively captures and quantifies conflict between views, further validating its reliability.
1.0
1.0
1
0.00
0.31
0.00
0.27
0.00
0.28
1
0.00
0.31
1.00
0.27
0.00
0.28
0.8
0.8
2
0.31
0.00
0.31
0.00
0.31
0.01
2
0.31
0.00
0.98
0.00
0.31
0.01
View
3
0.00
0.27
0.6
View
3
1.00
1.00
1.00
1.00
0.6
4
0.4
4
0.4
0.00
0.31
0.00
0.27
0.00
0.28
0.00
0.31
1.00
0.27
0.00
0.28
0.2
0.2
6
0.28
0.01
0.28
0.01
0.28
0.00
6
0.28
0.01
1.00
0.01
0.28
0.00
0.0
0.0
2
3
4
5
1
4
5
View
View
(a) Normal instance
(b) Conflcting instance
Figure 10. Conflict visualization.
C.9. Adversarial Noise Effect Analysis
In this section, present additional experimental results under adversarial noise attacks. First, evaluate the performance of our FUML under adversarial noise, add projected gradient descent (PGD) adversarial noise attacks (Madry et al., 2018) with different maximum perturbation magnitudes (eps) to the test set of the Fashion dataset. The results in Table 13 show FUML's superior resistance to adversarial noise attacks. Second, to further evaluate the effectiveness of the uncertainty estimation mechanism of FUML under adversarial noise, we perform an OOD task on the Fashion dataset, using normal test sets as ID and PGD-attacked sets (eps=0. 10) as OOD. Evaluated by FPR95 (lower better), FUML achieved 0.68, outperforming ETMC and ECML (both 1.00). To sum up. under adversarial noise, the proposed FUML is superior both classification accuracy and uncertainty estimation.
D. Limitations
Even though the proposed FUML outperforms existing multi-view classification methods in terms of both performance and reliability, there are still some potential limitations, For instance, FUML's multi-view fusion weights incorporate both uncertainty and conflict through multiplication. Although extensive experiments have demonstrated the effectiveness of this
23

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Deep Fuzzy Multi-view Learning for Reliable Classification
Table 13. Classification accuracy (%) PDE; ECMI., and our FUMI. under PGD adversarial noise attacks with different eps on the Fashion dataset. The best results highlighted in boldface.
EPS
0.05
0.10
METHOD
PDF
98.95 0.19
22.07 0.90
13.54 + 0.89
ECML
97.93 + 0.35
52.58 0.51
42.74 + 1.35
OURS
98.9610.25
94.4510.18
93.4010.19
technique, it lacks corresponding theoretical guarantees. Therefore, is crucial explore new multi-view fusion techniques based uncertainty and conflict from theoretical standpoint. We hope that our study serve valuable baseline for future research in multi-view learning and uncertainty estimation.
24


Reviews:
[{"review_id": "N0VmKS9cTa", "reviewer": "Reviewer_Ffiy", "summary": "This paper proposes a deep fuzzy multi-view learning method (FUML) to classify conflicting multi-view instances and precisely estimate intrinsic uncertainty. Specifically, FUML models logits as fuzzy memberships, employs Shannon's entropy to estimate uncertainty, and utilizes the cosine metric to measure the conflict degree between views. These factors are then combined to perform weighted fusion for multi-view classification.", "questions": "", "limitations": "", "rating": 3, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "We sincerely appreciate your valuable feedback. Below are our point-to-point responses:\n\n**Q1: Concern 1**\n\n**R1**: In fact, we don't only use Shannon’s entropy for OOD detection. The uncertainty estimation mechanism of FUML includes the following steps: We first calculate the category credibility based on fuzzy membership. The category credibility contains possibility and necessity information, thereby alleviating overconfidence. Then we use Shannon’s entropy of category credibility to estimate uncertainty.  The closer the category credibility is to 0.5, the greater the entropy, indicating that the model is less able to make decisions. As can be seen in Figure 8, the uncertainty increases with the increase of noise intensity, which proves the effectiveness of our FUML for OOD detection. \n\n**Q2: Concern 2**\n\n**R2**: 1) In fact, rather than overestimating the conflict between two views, our approach correctly reflects subtle semantic differences. Specifically, the difference in lower-ranked class distributions represents the unique characteristics and information captured by each view. For instance, in Figure 1(a), despite both the RGB and text views being classified as “bathroom”, the RGB view includes additional semantics like “toilet paper” and “toilet”, which the text view lacks.  2) We are confused about your intentions. This paper considers multi-view fusion and doesn't take into account the long-tail distribution.\n\n**Q3: Concern 3**\n\n**R3**: 1) Our assumption that uncertainty and conflict should jointly determine fusion weights is well-founded: Either higher uncertainty or conflict will reduce its reliability, and it is reliable only if both are low. Specifically, high uncertainty reflects the inherent unreliability of predictions from the corresponding view, while high conflict indicates inconsistencies between decisions from different views, both of which lead to unreliable fusion outcomes. Thus, we use uncertainty and conflict together to compute the fusion weights, so as to more accurately reflect the reliability of the corresponding views. 2) When fusing two uncertainly identical and conflicting views, it is impossible to make a correct decision from a human perspective, and therefore our FUML can't either.\n\n**Q4: Concern 4**\n\n**R4**: Although the computational complexity is $O(V^2)$, the number of views is small (usually $V < 10$) in MVC, so the extra computational overhead is negligible. Our experiments indicate that our method exhibits no significant increase in inference time compared to baselines, with an approximate increase of $8\\\\%$ (i.e., 0.0231s vs. 0.0215s)\n\n**Q5: Concern 5**\n\n**R5**: 1) We conduct ablation experiments on the conflicting test sets. The classification accuracy below shows that removing $u_i^v$ or $o_i^v$ leads to performance degradation, indicating the effectiveness of considering both uncertainty and conflict.\n\n|         | AVG              | $1-u^v_i$        | $1-o^v_i$        | Ours             |\n| ------- | ---------------- | ---------------- | ---------------- | ---------------- |\n| Fashion | $96.15 \\pm 0.22$ | $96.27 \\pm 0.22$ | $96.43 \\pm 0.32$ | $96.68 \\pm 0.32$ |\n| LandUse | $67.71 \\pm 2.30$ | $68.14 \\pm 2.47$ | $68.50 \\pm 2.02$ | $69.14 \\pm 2.28$ |\n\n2)Since LGG is unavailable, we substitute it with Prokaryotic[1]. The experimental results below demonstrate the superior performance of our FUML. On the NYUD2 dataset with Gaussian noise (mean=0, variance=5), FUML demonstrates superior performance, achieving a classification accuracy of $61.44\\pm1.84$ compared to baseline methods (TMC: $59.12\\pm1.98$, QMF: $60.32\\pm2.63$, PDF: $61.83\\pm1.78$).  \n\n|             | PDF            | ECML           | CCML           | Ours           |\n| ----------- | -------------- | -------------- | -------------- | -------------- |\n| BRCA        | $82.40\\pm1.27$ | $81.49\\pm0.86$ | $79.66\\pm1.86$ | $81.78\\pm1.24$ |\n| Prokaryotic | $70.18\\pm4.79$ | $55.05\\pm5.23$ | $54.95\\pm5.18$ | $73.15\\pm4.90$ |\n\n3)Due to the unavailable source code for \"Navigating Conflicting Views: Harnessing Trust for Learning\", we compared our FUML with another latest work, TUNED (AAAI 2025)[4], as shown blow, demonstrating the superiority of our method. \n\n|       | HW               | NUSOBJ           | Fashion          | Scene            | LandUse          |\n| ----- | ---------------- | ---------------- | ---------------- | ---------------- | ---------------- |\n| THNED | $96.75 \\pm 0.55$ | $34.09 \\pm 0.14$ | $86.99 \\pm 0.75$ | $67.22 \\pm 0.58$ | $46.64 \\pm 2.10$ |\n| Ours  | $98.78 \\pm 0.36$ | $47.08 \\pm 0.32$ | $96.68 \\pm 0.32$ | $72.71 \\pm 1.75$ | $69.14 \\pm 2.43$ |\n\n**Q6: Concern 6**\n\n**R6**: We will correct Eq.(1) and thoroughly proofread the paper for any remaining errors in the next version.\n\n[1]The landscape of microbial phenotypic traits and associated genes.\n\n[2]Trusted Unified Feature-Neighborhood Dynamics for Multi-View Classification.", "claims_and_evidence": "Yes", "methods_and_evaluation_criteria": "Yes, the proposed method and evaluation criteria make sense for the multi-view classification.", "theoretical_claims": "I have checked all Theoretical Claims.", "experimental_designs_or_analyses": "I have checked all the experiments in the experimental section.", "relation_to_broader_scientific_literature": "The paper is closely related to multi-view learning and uncertainty estimation. It makes improvement to conflicting multi-view fusion.", "essential_references_not_discussed": "The paper has included the main related works that are crucial for understanding the context.", "other_strengths_and_weaknesses": "Strengths\n1. The topic of this paper is interesting as it addresses conflict-aware multi-view fusion.\n2. The writing of the paper is clear and well-structured.\n\nAfter carefully reviewing this paper, I have the following concerns:\n\n(1) Concerns about uncertainty estimation\n\nThis paper uses Shannon's entropy to estimate the uncertainty of multi-view results. However, entropy primarily measures the uniformity of category distributions, making it unreliable for distinguishing between hard-to-classify in-distribution (ID) samples and true out-of-distribution (OOD) samples, as both may exhibit high entropy. Additionally, deep neural networks often suffer from overconfidence, and without proper uncertainty calibration, OOD samples may be assigned artificially low entropy when misclassified with high confidence. It remains unclear why Shannon's entropy alone is used as an uncertainty measure for noisy or OOD detection tasks, as demonstrated in C.5.\n\n(2) Concerns about conflict measurement\n\nThe paper uses cosine similarity to estimate the conflict degree among multiple views. However, this approach may overestimate conflicts in cases where two views share the same most probable class but differ in lower-ranked class distributions. This can lead to unnecessary penalization of views that are actually aligned in their final decision. Additionally, the method does not account for the varying importance of different categories, which may result in suboptimal weighting in the fusion process.\n\n(3) Concerns about the fusion method\n\n1. The current fusion method employs an exponential weighting mechanism based on the product of uncertainty and conflict degree. While this approach effectively suppresses highly uncertain and highly conflicting views, it may introduce a notable limitation: i.e., low uncertainty inherently diminishes the impact of conflict degree. This issue arises due to the multiplicative interaction between uncertainty and conflict, which implicitly assumes that both factors should jointly determine reliability in a symmetric manner.\n\n2. This method finds it difficult to address conflicts when fusing only two views with the same uncertainty degree due to the symmetry of cosine similarity.\n\n(4)  Concerns about computational complexity\n\nThis method uses Eq.(7) to measure the conflict degree, introducing a quadratic computational complexity ($O(V^2)$) for pairwise conflict computation, which raises scalability concerns for high-dimensional multi-view data.\n\n(5)  Concerns about experiments\n\nIt is suggested to add an ablation study to analyze the effects of uncertainty and conflict separately in multi-view fusion. Furthermore, as this paper is evaluated on feature-based multi-view datasets, it is recommended to conduct experiments on multi-modal datasets, such as BRCA, LGG, and NYUD2, to enhance the evaluation. Moreover, it is recommended to compare some of the latest methods for conflicting view fusion, e.g., [1].\n\n(6) Minor Issues\n\nThe paper should be carefully double-checked, as there are some errors. For example, it should be $m_{il}^v$ in Eq.(1), and $k$ should be italicized in Line 211.\n\n[1] Navigating Conflicting Views: Harnessing Trust for Learning.", "other_comments_or_suggestions": "See Weaknesses.", "questions_for_authors": "Overall, considering the points raised in the Major Weaknesses section, I have assigned the current rating accordingly. I am open to further discussion with the authors if there are any misunderstandings in my review. I will make the final decision based on the authors' responses.", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "i7LDcKzKyh", "reviewer": "Reviewer_8eiq", "summary": "The paper introduces FUML, a novel multi-view classification framework that explicitly addresses the uncertainty caused by conflicting information across views. By leveraging Fuzzy Set Theory, the authors model the outputs of deep classifiers as fuzzy memberships, capturing both possibility and necessity. A tailored loss function (i.e., the category credibility learning loss) is proposed to guide the optimization of these fuzzy outputs. In addition, a Dual-reliable Fusion (DRF) strategy is designed to weight each view based on its estimated uncertainty and inter-view conflict, ensuring that noisy or misaligned views contribute less to the final decision. Extensive experiments on eight public datasets demonstrate that FUML not only improves classification accuracy over 13 state-of-the-art baselines but also provides more robust uncertainty estimates, particularly in scenarios with conflicting view information.", "questions": "", "limitations": "", "rating": 5, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "We appreciate your valuable comments. Below is our point-by-point response.\n\n**Q1: Weaknesses (1)**\n\n**R1**: 1) In the next version, we will provide a clearer explanation of the theoretical components. 2) An intuitive discussion of the loss function is as follows: Directly aligning category credibility $(m^j_{ik} + 1 - \\max\\{m_{il}^j \\mid l \\neq k \\})/2$ with the label $y^j_{ik}$ will lead to local optima. Specifically, when $y^j_{ik} = 0$ and $y^j_{il} = 0 (l \\neq k)$, minimizing $(1 - \\max \\\\{m_{il}^j \\mid l \\neq k \\\\} )$ drives $m_{il}^j$ toward 1 instead of 0, leading to incorrect optimization. To address this, the loss function (Eq.(4)) replaces $(m^j_{ik} + 1 - \\max\\\\{m_{il}^j \\mid l \\neq k \\\\})/2$  with $(m^j_{ik} + 1 - m^j_{il})/2$  when $y^j_{ik} = 0$, ensuring correct optimization. We will clarify this in the next version.\n\n**Q2: Weaknesses (3)**\n\n**R2**:  Adverse weather conditions and data communication issues often introduce noise and misalignment in multi-view data. Existing EDL-based TMVC methods struggle with accurate classification under such conflicts and may underestimate classification uncertainty. In the next version, we will include this discussion in the Introduction Section.\n\n**Q3**: Other Comments Or Suggestions (1). \n\n**R3**: 1) In medical diagnosis, integrating multiple medical images (e.g., CT, MRI) and genetic data is crucial for disease classification. However, noise or pathological differences between imaging devices would cause inconsistencies, necessitating accurate uncertainty estimation about the classification results for doctors (e.g., ``classified as a malignant tumor, but MRI and CT conflict'') to assist in risk assessment. 2) Our FUML exhibits limited effectiveness in two-view data scenarios. These discussions will be included in the next version.\n\n**Q4: Other Comments Or Suggestions (2)**\n\n**R4**: Appendix Tables 7–9 show FUML achieving top or near-top performance in conflicting MVC across eight datasets with diverse noise and misalignment. Notably, FUML significantly outperforms other baselines on unaligned datasets. Overall, FUML demonstrates robustness in handling noisy and unaligned multi-view data, particularly in unaligned cases. This discussion will be incorporated into Appendix C.1 in the next version.\n\n**Q5: Questions For Authors (1)**\n\n**R5**: 1) Environmental factors often cause conflicts, which can mislead classification decisions. To mitigate this, we propose fusing only clear (low-uncertainty) and well-aligned (low-conflict) views. Consequently, we employ $(1−u_i^v)(1−o_i^v)$. 2) No, other combinations fail to improve performance. The table below proves this.\n\n|                             | Fashion         | LandUse         |\n| --------------------------- | --------------- | --------------- |\n| $0.5(1-u^v_i)+0.5(1-o^v_i)$ | $96.22\\pm0.26$  | $39.36\\pm5.82$  |\n| $0.8(1-u^v_i)+0.2(1-o^v_i)$ | $95.97\\pm 0.31$ | $48.71\\pm11.16$ |\n| $0.2(1-u^v_i)+0.8(1-o^v_i)$ | $96.30\\pm 0.54$ | $59.26\\pm 5.16$ |\n| Ours                        | $96.68\\pm0.32$  | $69.14\\pm2.43$  |\n\n**Q6: Questions For Authors (2)**\n\n**R6**: Regarding normalization, Appendix C.6 details the impact of the normalization parameter p on performance. The results show that FUML generally achieves optimal performance when p is between 2 and 5. As for activation functions, ReLU is essential for quantizing membership. Using alternative functions (exp or softplus) would yield outputs outside the $[0,1]$, violating fuzzy set theory's membership definition and precluding subsequent category credibility modeling and uncertainty estimation.\n\n**Q7: Weaknesses (2) & Questions For Authors (3)**\n\n**R7**:  Although the computational complexity is $O(V^2)$, the number of views in multi-view classification (MVC) is typically small ($V < 10$), making the additional computational overhead negligible.  Our experiments demonstrate that our method exhibits no significant increase in inference time compared to baselines, approximately by less than $8\\\\%$ (i.e., 0.0231s vs. 0.0215s).\n\n**Q8: Questions For Authors (4)**\n\n**R8**: 1)We add PGD adversarial noise attacks with different maximum perturbation magnitudes (eps) to the test set of the Fashion dataset. The results below show FUML's superior resistance to adversarial noise attacks. 2)We perform an OOD task on the Fashion dataset, using normal test sets as ID and PGD-attacked sets (eps=0.10) as OOD. Evaluated by FPR95 (lower is better), FUML achieved 0.68, outperforming ETMC and ECML (both 1.00).\n\n|            | 0               | 0.05            | 0.10           |\n| ---------- | --------------- | --------------- | -------------- |\n| PDF        | $98.95\\pm0.19$  | $22.07\\pm0.90$  | $13.54\\pm0.89$ |\n| ECML       | $97.93\\pm 0.35$ | $52.58\\pm 0.51$ | $42.74\\pm1.35$ |\n| FUML(Ours) | $98.96\\pm0.25$  | $94.45\\pm0.18$  | $93.40\\pm0.19$ |", "claims_and_evidence": "The primary claims of the paper are that:\n1.FUML achieves state-of-the-art classification accuracy while providing reliable uncertainty quantification.\n2.The integration of fuzzy memberships (combining possibility and necessity) offers a more reliable decision credibility measure than existing evidential approaches.\n3.The DRF strategy effectively mitigates the adverse effects of conflicting views.\n\nThese claims are supported by comprehensive experimental results comparing FUML with both “untrusted” and “trusted” baselines on standard as well as deliberately corrupted (conflicting) test sets. The inclusion of ablation studies and additional analyses (in the supplementary materials) further substantiates the advantages claimed by the authors.", "methods_and_evaluation_criteria": "The methodology is built upon a solid foundation of Fuzzy Set Theory. Modeling the classifier outputs as fuzzy memberships is an innovative approach that enables the joint estimation of possibility (likelihood) and necessity (exclusion of other classes). The loss function is carefully designed to ensure that the network learns to align its predictions with the ground truth while avoiding over-optimization issues in the unmatched categories.\nEvaluation is conducted on eight diverse datasets using standard metrics (accuracy, precision, F-score) and by reporting improvements over baselines. Moreover, the study uses both normal and synthetically corrupted testing sets to assess the robustness of the proposed uncertainty estimation and fusion strategy.", "theoretical_claims": "The paper presents two theoretical propositions (Propositions 3.4 and 3.5) which state that fusing a clean view with a conflicting view increases the overall uncertainty, which is a desirable property for flagging unreliable decisions. The proofs and reasoning are convincing.", "experimental_designs_or_analyses": "The experimental design is thorough, incorporating experiments on eight public benchmarks with a mix of standard and conflicting instances. The authors report results over multiple random seeds to capture variability, and ablation studies are conducted to isolate the contribution of each component of FUML.", "relation_to_broader_scientific_literature": "FUML is positioned well within the existing body of work on multi-view learning and uncertainty estimation. It builds upon and extends previous methods such as Evidential Deep Learning-based approaches (e.g., ETMC, TMC, ECML) and Dempster-Shafer theory, while introducing the use of fuzzy set theory, which is a perspective that has been underexplored in this context. The paper also clearly outlines how its contributions differentiate from prior works by addressing the limitation of underestimating uncertainty in conflicting instances.", "essential_references_not_discussed": "This paper has provides essential related works to understanding the key contributions of the work.", "other_strengths_and_weaknesses": "Strengths:\n1.Novel use of Fuzzy Set Theory to model classifier outputs, resulting in a richer representation of decision credibility.\n2.A well-motivated fusion strategy (DRF) that explicitly accounts for view-specific uncertainty and conflict.\n3.Comprehensive experiments and ablation studies demonstrating both accuracy gains and improved uncertainty estimates.\n\nWeaknesses:\n1.Clearer explanations of the theoretical components and a more intuitive discussion of the loss function behavior are encouraged.\n2.Details on computational complexity and hyperparameter sensitivity are limited.\n3.Additional discussion on limitations and potential failure cases in real-world noisy environments would be useful.", "other_comments_or_suggestions": "1.It may be helpful to include a discussion on potential real-world applications where the robust uncertainty estimation could be critical, as well as scenarios where the method might struggle.\n1.A more detailed error analysis could provide insights into the types of conflicting instances where FUML offers the greatest advantage.", "questions_for_authors": "1. Why do you use $(1 - u_i^v)(1 - o_i^v)$? Would other combinations (e.g., weighted sum) improve performance?\n2. How sensitive is the performance of FUML to the choice of the normalization and activation functions in mapping logits to fuzzy memberships? Could alternative functions affect the uncertainty estimation?\n3. Can you provide further insight into the computational complexity of the DRF strategy compared to conventional fusion methods?\n4. Could you discuss on the robustness of FUML in the presence of adversarial noise, and whether the uncertainty estimation mechanism is capable of flagging such instances effectively?", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "20iXwRlIN1", "reviewer": "Reviewer_hton", "summary": "This paper proposes a novel multi-view classification method based on Fuzzy Set Theory, which models classification outputs as fuzzy memberships. After that, authors introduces a category credibility learning loss and a Dual-reliable Fusion (DRF) strategy to manage conflicting views and improve uncertainty estimation over Evidential Deep Learning. Adequate experiments and analysis demonstrate FUML's superior performance in accuracy and reliability over existing methods.", "questions": "", "limitations": "", "rating": 4, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "We appreciate your detailed comments. We believe the following point-to-point response can address all the concerns:\n\n**Q1: There are some grammatical errors in the writing.**\n\n**R1**: Thanks. We will correct these grammatical errors you raise and carefully review the manuscript to ensure no other grammatical errors remain.\n\n**Q2: Can the ReLU function be replaced by other functions?**\n\n**R2**: No. To map the logits of a neural network as memberships, the process involves two key steps: First, $L_p$-normalization is applied to constrain the logits within the range $[-1, 1]$. Then, a ReLU activation function is employed to further restrict the outputs to the interval $[0, 1]$. The resulting values can be interpreted as memberships for their respective categories. Therefore, both ReLU and $L_p$ normalization are essential parts to qualify membership. If ReLU is replaced by exp or softplus used in the Evidential Deep Learning, the output value will not be in the range of $[0,1]$, which undoubtedly violates the definition of membership.\n\n**Q3**: In Eq. 8, the exp function is selected as g(). Why not use other monotonically increasing functions, such as ReLU and sigmoid?\n\n**R3**: The choice of exp is an empirical result: The performance comparison of ReLU, Sigmoid, and the exp function is shown in the following table. From these results, we can find that exp has the best or second-best performance. Therefore, we leverage exp function as g().\n\n|           | Fashion(Normal) | LandUse(Normal) | Fashion(Conflict) | LandUse(Conflict) |\n| --------- | --------------- | --------------- | ----------------- | ----------------- |\n| ReLU      | $98.81\\pm0.26$  | $76.75\\pm0.56$  | $96.51\\pm0.29$    | $68.80\\pm2.49$    |\n| Sigmoid   | $98.75\\pm0.27$  | $76.34\\pm0.78$  | $96.57\\pm0.29$    | $68.94\\pm1.89$    |\n| exp(Ours) | $98.96\\pm0.25$  | $76.71\\pm0.46$  | $96.68\\pm0.32$    | $69.14\\pm2.43$    |\n\n**Q4**: Why not use Euclidean distance or Dot Product Similarity? What is the advantage of cosine similarity?\n\n**R4**: Compared with Euclidean distance and dot product similarity, cosine similarity only evaluates the consistency of decisions through the angle between memberships, avoiding the sensitivity of Euclidean distance and dot product similarity to vector length, thereby more accurately measuring decision conflicts.", "claims_and_evidence": "Yes, this paper is supported by clear and convincing evidence.", "methods_and_evaluation_criteria": "Yes, the proposed method and evaluation criteria make sense.", "theoretical_claims": "Yes, I checked the theoretical proof section of this paper in the appendix.", "experimental_designs_or_analyses": "Yes, I checked the soundness and validity of all experimental designs and analyses in this paper.", "relation_to_broader_scientific_literature": "This paper introduces a novel trusted multi-view classification method, which is based on fuzzy set theory and can accurately classify conflicting multi-view instances and precisely estimate classification uncertainty. This work builds on the work of “Trusted Multi-View Classification with  Dynamic Evidential Fusion” which first proposed trusted multi-view classification based on evidential deep learning (EDL), and “Reliable Conflictive Multi-view Learning”, which first proposed conflictive multi-view learning. Its contributions extend beyond multi-view classification, offering new angles for single-view, multimodal classification and out-of-distribution detection.", "essential_references_not_discussed": "No.", "other_strengths_and_weaknesses": "Strengths:\n\nS1. This paper has a clear motivation and a novel perspective and effectively solves the problems of existing EDL-based TMVC methods being sensitive to conflicts and inaccurate uncertainty estimation of conflicting multi-view samples.\n\nS2. This paper is well-written and clearly presented. As far as I know, the use of fuzzy set theory to introduce output uncertainty in multi-view classification is novel.\n\nS3. The proposed Dual-reliable Multi-view Fusion is quite neat and effective.\n\nS4. The author conducted a large number of experiments to verify the effectiveness of their FUML, including both qualitative results (such as Figure 3-10) and quantitative results (such as Table 2-10). In addition, as shown in Table 2, in the case of conflicting multi-view classification, its performance far exceeds the best baselines, especially on the Leaves dataset.\n\n\nWeaknesses:\n\nW1. There are some grammatical errors in the writing: line 057:  “... have be proposed to ...” should be “... have been proposed to ...”. Line 072: “global conflicts among views overly emphasizes dominant evidence” should be “global conflicts among views overly and emphasizes dominant evidence”. Line 179: \" Thirdly the weights ...” should be “ Thirdly, the weights ...”. \n\nW2. The choice of activation function in Eq. 3 warrants further discussion. Specifically, it is unclear whether other activation functions, such as those used in Evidential Deep Learning, could be applied and whether they would offer comparable or improved effectiveness.\n\nW3. In Eq. 8, the exp function is selected as g(). Why not use other monotonically increasing functions, such as ReLU and sigmoid? This deserves further discussion.\n\nW4. In Definition 3.3, the authors used cosine distance to measure the distance between memberships, thereby measuring the conflict between views. Why not use Euclidean distance or Dot Product Similarity?", "other_comments_or_suggestions": "See the weaknesses.", "questions_for_authors": "Q1. In this paper, the authors pointed out that the norm is first used, and then the ReLU function is used to model the membership in the fuzzy set theory. Can the ReLU function be replaced by other functions?\n\nQ2. In Eq. 8, the exp function is selected as g(). Why not use other monotonically increasing functions?\n\nQ3. In Definition 3.3, the authors used cosine distance to measure the distance between memberships from different views. Why not use Euclidean distance or Dot Product Similarity? What is the advantage of cosine similarity?", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "7qFKVgOYdA", "reviewer": "Reviewer_PsMz", "summary": "This paper introduces FUML, a novel multi-view classification framework using Fuzzy Set Theory to handle conflicting views and improve uncertainty estimation. It employs a Dual-reliable Multi-view Fusion (DRF) strategy and entropy-based uncertainty quantification, achieving robust classification and reliability. Experiments show superior performance over existing methods.", "questions": "", "limitations": "", "rating": 4, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "We appreciate the identification of our novelty and the positive comments. Below are our point-by-point responses to your concerns:\n\n**Q1: In the Experimental Setup section, the author doesn’t provide details on the noise intensity and noise ratio of the added Gaussian noise.**\n\n**R1**: To create a test set with conflicting instances, following the methodology outlined in (Xu, Cai, et al. \"Reliable conflictive multi-view learning.\"), we apply two transformations: 1)We add Gaussian noise with mean 0 and variance 0.5 to $10\\%$ of the instances in the test set. 2)We randomly changed the view information of $50\\%$ of the instances in the test set, making the labels of some views inconsistent with the other views. We will clarify this in the next version.\n\n**Q2: In the experiments, the authors include some multimodal classification methods, such as PDF and QMF, in the comparison. Is this fair?**\n\n**R2**: Yes, it is fair. To ensure a fair comparison, we replace the backbone networks of QMF and PDF with the same fully connected layer as FUML while preserving their core models and loss functions. These experimental details can be found in Appendix B.3.\n\n**Q3: Concerns about the uncertainty estimation results of Handwritten or MSRC.**\n\n**R3**: We compare our FUML with ETMC and ECML on the Handwritten and MSRC datasets for the OOD task. The normal test sets serve as in-distribution, while the conflicting test sets serve as OOD. The evaluation metric is FPR95, with lower values indicating better performance. The results below demonstrate the superiority of FUML.\n\n|      | ETMC  | ECML  | FUML(Ours) |\n| ---- | ----- | ----- | ---------- |\n| HW   | 0.920 | 0.950 | 0.845      |\n| MSRC | 0.952 | 0.974 | 0.926      |\n\n**Q4: The motivation for necessity is unclear, and its impact on performance is unexplained. Why introduce it? Relevant experiments are needed.**\n\n**R4**: In Fuzzy Set Theory, necessity is introduced to quantify the certainty that a sample does not belong to other categories, as membership alone cannot capture between-class relationships. To evaluate the role of necessity, we removed the necessity in FUML and only used conflicts in the fusion process. The experimental results in the table below prove that necessity can’t be removed.\n\n|               | Fashion(Normal) | LandUse(Normal) | Fashion (Conflict) | LandUse(Conflict) |\n| ------------- | --------------- | --------------- | ------------------ | ----------------- |\n| w/o Necessity | $97.70\\pm0.41$  | $44.64\\pm3.65$  | $94.91\\pm0.47$     | $39.00\\pm3.29$    |\n| Ours          | $98.96\\pm0.25$  | $76.71\\pm0.46$  | $96.68\\pm0.32$     | $69.14\\pm2.43$    |\n\n**Q5: Can FUML be applied to multimodal classification tasks? If so, what adjustments are needed?**\n\n**R5**: Yes, our FUML framework exhibits strong generalizability and can be readily adapted to various multimodal classification tasks. The primary adjustments required involve replacing the feature extraction backbones to accommodate different data modalities. Specifically, Vision Transformer (ViT) can be employed for image feature extraction, wav2vec for audio processing, TimeSformer for video analysis, and word2vec for textual feature representation.", "claims_and_evidence": "Yes, this paper is supported by clear and convincing evidence.", "methods_and_evaluation_criteria": "Yes, the proposed method and evaluation criteria make sense.", "theoretical_claims": "Yes, I have checked the theoretical part in this paper.", "experimental_designs_or_analyses": "Yes, I checked the soundness and validity of all experimental designs and analyses in this paper.", "relation_to_broader_scientific_literature": "The key contributions of this paper are closely related to the broader scientific literature in multi-view learning, uncertainty estimation and Fuzzy Set Theroy. Specifically, this paper compares prior work in trusted multi-view classification based on Evidential Theory (Including TMC, ETMC, UMIC, and ECML) . Besides, this paper is related to and based on uncertainty estimation andfuzzy theory, and adopts fuzzy modeling, providing new ideas on how to apply fuzzy set theory to multi-view learning.", "essential_references_not_discussed": "No", "other_strengths_and_weaknesses": "Strengths:\n\n1. This paper effectively clarifies its research motivation with the aid of Figure 1 and introduces a novel approach to integrating fuzzy set theory into multi-view learning.\n\n2. This paper innovatively proposes a TMVC method based on the fuzzy set theory, avoiding the problem of EDL-based TMVC methods being sensitive to conflicts and inaccurate uncertainty estimation. The proposed FUML is simple but effective.\n\n3. The paper has sufficient experiments, for example, comparative experiments with 13 latest baselines (including five untrusted MVC baselines and eight trusted MVC baselines) on eight public datasets. In addition, including the appendix, there are 11 types of experiments, which fully demonstrate the effectiveness of the proposed method.\n\n4. The proposed method achieves significant improvements over the best baseline, especially on the conflict test set. For example, the accuracy is improved by 4.83%, 7.31% and 14.6% on Scene, LandUse and Leaves datasets respectively. \n\nWeaknesses:\n\n1. In the Experimental Setup section, the author mentioned the method of adding conflict samples, but did not provide details on the noise intensity and noise ratio of the added Gaussian noise. Please add relevant description.\n\n2. In the experiments, the authors include some multimodal classification methods such as PDF and QMF in the comparison, while this paper mainly focuses on multi-view classification. Is this fair?\n\n3. In Figure 3, the uncertainty effectiveness Analysis is only performed on Fashion and LandUse dataset which only has three views. I am concerned about the results of other datasets, such as Handwritten or MSRC, which have six views. Because as shown in Table 2, for such datasets with many views, conflicting views often don’t cause a significant drop in accuracy, but should cause an increase in uncertainty.\n\n4. The motivation for introducing necessity is unclear. Nor does authors explain the impact of necessity on performance.", "other_comments_or_suggestions": "N/A", "questions_for_authors": "1. The FUML method in this paper is mainly used for multi-view classification. Can it be applied to other multimodal classification tasks?If so, what adjustments are needed?\n\n2. Why should necessity be introduced? Corresponding experiments should be supplemented.\n\n\nBesides, please answer the questions in the weaknesses.", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}]

Author rebuttal:

Meta-review: This paper proposes a novel deep fuzzy multi-view learning method called FUML. This method leverages fuzzy set theory to model the outputs of a classification neural network as fuzzy memberships, incorporating both possibility and necessity measures to quantify category credibility, optimized by a tailored loss function. To further enhance uncertainty estimation, this paper proposes an entropy-based uncertainty estimation method leveraging category credibility, and develops a dual reliable multi-view fusion strategy that accounts for both view-specific uncertainty and inter-view conflict to mitigate the influence of conflicting views in multi-view fusion. Extensive experiments demonstrate that the proposed method achieves SOTA performance in terms of both accuracy and reliability.

After the rebuttal process, this paper finally receives 1 weak accept, 2 accept, 1 strong accept. All the reviewers reach an agreement that this paper can be accepted. So I recommend accepting this paper.
Decision: Accept (poster)