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[Page no. 3] "Finally (Hu et al., 2018), present a review of MAC techniques, assuming that a single clustering for a dataset can be too strict and cannot capture the diversity in some applications. In this work, the re- view is categorized into two perspectives, coupled and de-coupled methods. Also, the methods described in this work are compared based on a series of properties specifics like input parameters and the kind of subspaces considered, among other aspects. As can be seen from the reviewed literature, there are no algorithms that simultaneously consider the problem of multi-labels or MAC. 2.3. Semi-supervised learning methods (Ouali et al., 2020) present a review of the different deep semi-supervised approaches. They analyze semi-supervised learning and its applications in image classification to deep neural networks to reduce the amount of labeled data required. In the paper (van Engelen and Hoos, 2020), the authors propose a taxonomy of semi-supervised clas- sification algorithms and describe the fundamentals of the different semi-supervised learning algorithms. On the other hand (Yang et al., 2023), present a taxonomy for deep semi-supervised learning that cat- egorizes existing methods. Then they provide a review of 60 represen- tative methods and present a comparison of these methods in terms of the type of losses, architecture differences, and test performance results (Zhai et al., 2021). define a self-supervised semi-supervised learning framework for image classification. In the previous works, we can see that some are based on deep learning or are for image processing, with a high computational cost. (Huang et al., 2021) define the CAFA framework for the processing of labeled and unlabeled datasets. Particularly, CAFA uses a scoring strategy to determine the relationship between the labeled and unla- beled data to improve the semi-supervised training (Zheng et al., 2022). define SimMatch, a semi-supervised learning framework that simulta- neously"

[Page no. 3] "considers semantic similarity and instance similarity. They instantiate a labeled memory buffer to fully leverage the ground truth labels on the instance-level and bridge the gaps between the semantic and instance similarities. Finally, they propose the unfolding and ag- gregation operation which allows these two similarities to be isomor- phically transformed with each other. The paper of (Quintero and Aguilar, 2022) introduces LAMDA-HSCC, a semi-supervised learning algorithm addressing classification, clustering, or combined tasks. This algorithm allows the assignment of each individual to a single class or cluster. The algorithm includes sub-models for migration, merging, and separation to refine individual assignments. In these works, the authors develop an approach for semi-supervised context for assignment to a single class/group. Our proposal is also for a semi-supervised context but in multiclass and/or multigroup contexts. Other papers provide studies of graph-based semi-supervised learning. For example (Chong et al., 2020), define frameworks that divide the corresponding works and analyze datasets, including two face datasets and a natural image dataset. Also (Song et al., 2023), review graph-based semi-supervised learning (GSSL) methods in the literature. Their work aims to provide both researchers and practitioners with a solid and systematic understanding of relevant advances as well as the underlying connections among them. On the other hand, the paper (Sawant and Prabukumar, 2021) presents a review of graph-based learning methods for classification of the hyperspectral images (HSI, including a spectral-spatial information based graph semi-supervised classification. All of these studies are for image processing, and not for semi-labeled structural datasets, which is the focus of our proposal. Finally (Garrido et al., 2024), explore advancements in semi-supervised learning to tackle challenges posed by limited labeled data. They conduct a bibliographic review since 2013, identifying 128 new Semi-Supervised Learning for ensemble construction. The review highlights the influence of algorithms like self-training and"

[Page no. 9] "of 0.56 for MULCI. One of the limitations of our proposal is in the context of data sets with low dimensionality of data or descriptors, where determining the appropriate membership threshold can be a problem due to data scar- city. Following the above, not having an adaptive calibration of the membership threshold represents another limitation. Future work should define an adaptive method to automate the calibration process of the Gt threshold value of LAMDA-SeMLACA, in order to have a more robust algorithm. In addition, the algorithm must be tested in critical areas such as medicine and energy, among others, and the specific contribution in real contexts of a multiclassification/ clustering must be analyzed in depth. CRediT authorship contribution statement Carlos Quintero Gull: Writing – original draft, Investigation, Formal analysis, Data curation. Jose Aguilar: Writing – review & edit- ing, Validation, Supervision, Methodology, Investigation, Funding acquisition, Conceptualization. Table 9 Results for different datasets in MAC tasks. Dataset\metrics S2b S2w ρ Asymmetric 0,394 0,221 0,641 Overlap 0,284 0,542 0,344 S2 0,453 0,185 0,710 unbalance 0,487 0,124 0,797 diabetes 0,874 0,732 0,544 pendigits 0,394 0,230 0,631 smartphone 0,778 0,120 0,850 Table 10 Results for different datasets with 75% of unlabeled data in semi-supervised tasks. Dataset Sb Sw ρ ACC MULCI RLC-Index emotions 0,193 0,324 0,373 0,417 0,395 1117 amphibians 0,159 0,34 0,318 0,467 0,393 1468 genbase 0,2 0,21 0,488 0,650 0,569 1333 scene 0,112 0,345 0,245 0,678 0,462 2766 yeast 0,001 0,245 0,004 0,294 0,149 72,324 Table 11 Results for different datasets with 50% of unlabeled data in semi-supervised tasks. Dataset Sb Sw ρ ACC MULCI RLC-Index emotions 0,293 0,324 0,475 0,553 0,514 1165 amphibians 0,244 0,195 0,556 0,630 0,593 1133 genbase 0,5 0,9 0,357 0,290 0,324 0,812 scene 0,18 0,157 0,534 0,680 0,607 1273 yeast 0,021 0,345 0,057 0,203 0,130 3538 Table"

[Page no. 3] "co-training on current developments, alongside innovative ensemble learning techniques. It also underscores the need for further research into intrinsically semi-supervised and unsupervised pre-processing methods. Similarly, the paper (Han et al., 2024) delves into the potential of deep learning in medical image analysis, where labeled datasets are often limited. It explores different semi-supervised learning approaches to deep medical image segmentation. These literature reviews confirm that the use of semi-supervised learning is only for assignment to a single class or cluster. As we can see, there are no works that analyze the problem of semi- labeled structured datasets, nor semi-supervised methods for simulta- neously multi-label classification and MAC problems. There are also no techniques based on fuzzy logic that allow managing uncertainty during the analysis process of semi-labeled data. Furthermore, many of the previous works are aimed at images and not structured data. All these gaps try to be filled with our approach. 3. Fundamentals of the LAMDA algorithm This work defines LAMDA-SeMLACA, a semi-supervised algorithm for Multi-label and Multi-cluster problems. In the Multi-label context, each individual can be simultaneously assigned to several classes; on the other hand, in the Multi-cluster context, each individual can be simul- taneously assigned to several clusters. This section describes the fun- damentals of LAMDA-HAD for the Multi-label context, and next, LAMDA-RD for the Multi-cluster context. LAMDA is founded on the fuzzy theory that allocates individuals to a class (in this paper, using LAMDA-HAD) or to a cluster (in this paper, using LAMDA-RD), using the Global Adequacy Degree. In LAMDA, a data-vector X with n features is defined as: X = [ x1; x2; . . . ; xj ; . . . ; xn ] Where xj is the feature/descriptor/variable j of the object X. For in- dividuals with labels, X is X = { x1,x2,…..xj,…..xn,cl"

[Page no. 10] "of linguistic descriptors of concepts. In: Approximate Reasoning in Decision Analysis. North-Holland, pp. 165–175. Alonso, J., Paredes, R., Rosso, P., 2017. Feature representation for social circles detection using MAC. Neural Comput. Appl. 28 (9), 2395–2402. Bedoya, C., Villanova, J., Narvaez, C., 2014. Yager–Rybalov Triple Π operator as a means of reducing the number of generated clusters in unsupervised anuran vocalization recognition. In: Proceeding Mexican International Conference on Artificial Intelligence, pp. 382–391. Botía, J., Botía, D., 2018. On LAMDA clustering method based on typicality degree and intuitionistic fuzzy sets. Expert Syst. Appl. 107, 196–221. Carvalho, T., Soares, F., Vita, R., Francisco, R., Basto, J., Alcal´a, S., 2019. A systematic literature review of machine learning methods applied to predictive maintenance. Comput. Ind. Eng. 137, 106024. Cerrada, M., Aguilar, J., Altamiranda, J., S´anchez, R., 2019. A hybrid heuristic algorithm for evolving models in simultaneous scenarios of classification and clustering. Knowl. Inf. Syst. 61 (2), 755–798. Chong, Y., Ding, Y., Yan, Q., Pan, 2020. Graph-based semi-supervised learning: a review. Neurocomputing 408, 216–230. Cui, J., Ding, Z., Fan, P., Al-Dhahir, N., 2018. Unsupervised machine learning-based user clustering in millimeter-wave-NOMA systems. IEEE Trans. Wireless Commun. 17 (11), 7425–7440. F¨anti, P., Sieranoja, S., 2018. K-means properties on six clustering benchmark datasets. Appl. Intell. 48 (12), 4743–4759. http://cs.joensuu.fi/sipu/datasets/. Garrido, L., Serrano, M., Maudes, R., Rodríguez, García, O., 2024. Ensemble methods and semi-supervised learning for information fusion: a review and future research irections. Inf. Fusion, 102310. Han, K., Sheng, V., Song, Y., Liu, Y., Qiu, C., Ma, S., Liu, Z., 2024. Deep semi-supervised learning for medical image segmentation: a review. Expert Syst. Appl., 123052 Huang, Z., Xue, C., Han, B., Jian, C. Chen G., 2021. Universal semi-supervised learning. In: Ranzato, M., Beygelzimer, A., Dauphin, Y., Liang, P.S., Wortman Vaughan, J. (Eds.), Advances in Neural Information Processing Systems. Curran Associates,"

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