# Assessing the Interpretability of Fuzzy Rule Bases

Thomas Pontoizeau, Romain Caillière, Marie-Jeanne Lesot, Christophe

Marsala, Nicolas Museux, Jean-Noël Vittaut

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Thomas Pontoizeau, Romain Caillière, Marie-Jeanne Lesot, Christophe Marsala, Nicolas Museux, et al.. Assessing the Interpretability of Fuzzy Rule Bases. 2025 IEEE International Conference on Fuzzy Systems (FUZZ), Jul 2025, Reims, France. pp.1-6, 10.1109/FUZZ62266.2025.11152209 . hal-05325150

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# Assessing the Interpretability of Fuzzy Rule Bases

Thomas Pontoizeau

Sorbonne Université, CNRS, LIP6

F-75005 Paris, France

thomas.pontoizeau@lip6.fr

Romain Caillière

cortAIx Labs, Thales

Palaiseau, France

romain.cailliere@thalesgroup.com

Marie-Jeanne Lesot

Sorbonne Université, CNRS, LIP6

F-75005 Paris, France

marie-jeanne.lesot@lip6.fr

Christophe Marsala

Sorbonne Université, CNRS, LIP6

F-75005 Paris, France

christophe.marsala@lip6.fr

Nicolas Museux

cortAIx Labs, Thales

Palaiseau, France

nicolas.museux@thalesgroup.com

Jean-Noël Vittaut

Sorbonne Université, CNRS, LIP6

F-75005 Paris, France

jean-noel.vittaut@lip6.fr

**Abstract**—Fuzzy systems are valued for their ability to model complex phenomena while contributing to maintaining interpretability through natural language rules. However, this property is not inherently guaranteed by the adoption of fuzzy sets. This paper proposes both a tool, named FuzzIC, to assess the interpretability of fuzzy rule bases through the computation of various complementary criteria taken from the literature, and an empirical user study of these criteria. The latter shows that some criteria capture characteristics that significantly enhance interpretability in practical applications, while others appear less influential than anticipated.

**Index Terms**—XAI, interpretability, fuzzy rule base.

## I. INTRODUCTION

When decision systems are automatically produced with machine learning techniques, the decision performances are not the only referee, especially when they are deployed in critical systems, where the end-user inherits the responsibilities of the decision consequences: explainability, interpretability and verifiability then become as crucial as performances.

In terms of intelligibility, the evaluation of artificial intelligence systems remains an issue within the eXplainable Artificial Intelligence (XAI) community with no clear consensus yet established, see e.g. [1]–[5]. Indeed, defining a measure for the quality of an explanation is inherently challenging, as it first requires a clear definition of what constitutes a “good” explanation. The latter should ideally be evaluated by the explanation recipient, requiring to involve the user.

Human-Centred eXplainable Artificial Intelligence (HCXAI) addresses this question by focusing on user-centric development and evaluation of intelligibility methods [6], [7]. It draws on cognitive sciences or on social science studies, such as Miller’s work [8], which highlights desirable criteria for explanations. These criteria, while valuable, may be difficult to quantify and implement across all explanation forms. Among others, HCXAI recommends combining objective comprehension and subjective satisfaction evaluations to assess explanation quality effectively [9].

Approaches based on fuzzy logic are often considered natural solutions, as they are close to human reasoning and use a formalism deemed directly intelligible, see e.g. [10]. However, a nuanced analysis is necessary: as a basic example,

a fuzzy rule base with numerous rules may be too complex for a final user and not considered intelligible. As discussed in Section II, many works have been proposed on identifying properties and criteria capturing what makes fuzzy logic systems interpretable.

This paper first proposes Fuzzy Interpretability Checker (FuzzIC), a tool that implements a wide range of interpretability criteria within a flexible architecture: FuzzIC allows to assess any fuzzy rule base on 18 complementary criteria taking into account different granularity levels for interpretability. In addition, the paper describes the results of a user study conducted to study empirically these criteria, considering fuzzy rule bases with different interpretability characteristics to examine user preferences. The study reveals that some criteria capture characteristics that significantly enhance the interpretability of fuzzy systems, while others seem not as influential as initially expected, which gives some new insight into interpretability of fuzzy rule bases.

The paper is organized as follows. Section II briefly summarizes existing works related to the interpretability of fuzzy rule bases. Section III presents FuzzIC, the Python framework we propose for assessing quantitatively this interpretability. Section IV presents the empirical user study of the interpretability criteria relevance. Section V concludes the paper and discusses some directions for future work.

## II. RELATED WORK

Fuzzy rule bases (FRBs) are defined as set of rules of the form "if $X_1$ is $A_1$, ..., and $X_p$ is $A_p$, then $Y$ is $B$" where the $X_i$ are data features and $A_i$ and $B$ are fuzzy modalities from linguistic variables respectively associated with the data features. Their interpretability is a critical aspect of their design, balancing the trade-off between human comprehensibility and system accuracy [11]. This section reviews key contributions to the interpretability of fuzzy rule bases in the literature.

Several studies have explored methods to simplify the structure of FRBs to enhance their interpretability, leading to several classifications of interpretability measures [12], [13]. The comprehensive taxonomy proposed by [12] distinguishes complexity and semantics. Complexity-based approaches aim
to reduce the model complexity, e.g. through the number of rules, variables or linguistic terms, without significantly compromising accuracy. Rule bases can be analysed by such complexity metrics or by visualization tools, for instance to identify redundancies and inconsistencies in rule interactions [14]. Along the same lines, there exist methods to construct interpretable rule bases by reducing dimensionality while maintaining meaningful representations [15]. On the other hand, semantic-based approaches focuses on preserving the meaning and clarity of fuzzy sets and rules. Key properties such as completeness, distinguishability, normalization or complementarity are often used to ensure that linguistic terms remain intuitive and non-overlapping [12], [16]. For example, Mencar and Fanelli [17] emphasize the importance of semantic constraints in fuzzy information granulation to maintain interpretability. Studies also highlight trade-offs between optimizing fuzzy sets for performance and preserving their semantic integrity, suggesting that excessive optimization can degrade interpretability [18].

Interpretability assessment remains a challenging task due to its subjective nature. Objective indices often focus on structural measures such as rule count or feature interactions, while subjective indices consider cognitive aspects such as user comprehension. Cointension-based methods [19] assess the alignment between explicit semantics and user expectations, providing a nuanced perspective on system interpretability. Some works propose empirical approaches based on user feedback to evaluate readability [20].

This paper focuses on the criteria collected by [13] and [21], adjusting them when necessary and proposing numerical scores to assess them, so as to allow for their implementation in the tool we propose. They are organised along four levels, distinguishing complementary sources for interpretability constraints: (1) the global set of fuzzy rules (FRB), (2) the individual rules (R) of the form illustrated at the beginning of the section, (3) the linguistic variables (LV) used in the fuzzy rules, defined as sets of fuzzy modalities, associating linguistic terms and fuzzy sets, (4) the fuzzy subsets (FS) themselves.

### III. THE PROPOSED FUZZIC FRAMEWORK

Our primary contribution is a Python framework named *Fuzzy Interpretability Checker* (FuzzIC) available on git<fnref n="1" />, designed to compute the interpretability criteria values for any fuzzy rule base. It implements 18 criteria taken from [13] and [21], at all 4 levels reminded in Section II. They are listed in Table I, and discussed in turn in the next subsections with their chosen implementation.

#### A. FuzzIC: Inputs and Outputs

FuzzIC takes as input a fuzzy rule base, defined on numerical features, accepting two representations: a classical format defined by a simple DTD and the format used in the reference tool *FisPro* [22]. FuzzIC assumes that the fuzzy sets are trapezoidal or Gaussian, which is not restrictive as these correspond to the most classic and interpretable choices.

<table><caption>TABLE I
IMPLEMENTATION OF INTERPRETABILITY CRITERIA</caption><thead><tr><th>Criterion</th><th>Param.</th><th>Output</th><th>Goal</th><th>Lvl</th></tr></thead><tbody><tr><td>Normality</td><td>no</td><td>[0,1]</td><td>max</td><td rowspan="2">FS</td></tr><tr><td>Unimodality</td><td>no</td><td>[0,1]</td><td>max</td></tr><tr><td>Relation preservation</td><td>yes</td><td>[0,1]</td><td>max</td><td rowspan="7">LV</td></tr><tr><td>Justifiable number of elements</td><td>no</td><td>integer</td><td>min</td></tr><tr><td>Distinguishability</td><td>yes</td><td>[0,1]</td><td>min</td></tr><tr><td>Coverage</td><td>yes</td><td>[0,1]</td><td>max</td></tr><tr><td>Complementarity</td><td>no</td><td>[0,1]</td><td>max</td></tr><tr><td>Uniformity</td><td>no</td><td>[0,1]</td><td>min</td></tr><tr><td>Prototype</td><td>yes</td><td>[0,1]</td><td>max</td></tr><tr><td>Extrema</td><td>no</td><td>[0,1]</td><td>max</td><td></td></tr><tr><td>Size of premises</td><td>no</td><td>integer</td><td>min</td><td rowspan="3">FR</td></tr><tr><td>Size of conclusion</td><td>no</td><td>integer</td><td>min</td></tr><tr><td>Size of rule</td><td>no</td><td>integer</td><td>min</td></tr><tr><td>Number of variables</td><td>no</td><td>integer</td><td>min</td><td rowspan="5">FRB</td></tr><tr><td>Membership functions sharing</td><td>no</td><td>[0,1]</td><td>max</td></tr><tr><td>Consistency</td><td>no</td><td>[0,1]</td><td>check</td></tr><tr><td>Number of activated rules</td><td>no</td><td>integer</td><td>min</td></tr><tr><td>Completeness</td><td>no</td><td>[0,1]</td><td>check</td></tr></tbody></table>

<table><caption>TABLE II
CONFIGURATION FILE PARAMETERS</caption><thead><tr><th>Parameter name</th><th>Role</th></tr></thead><tbody><tr><td>t-norm, t-conorm</td><td>Operators used for fuzzy logic operations</td></tr><tr><td>fuzzy set order relation</td><td>default: min value of the kernel</td></tr><tr><td>criteria_aggregator</td><td>Aggregator of several scores for one criterion</td></tr><tr><td>alphaCoverage</td><td>Minimal membership degree to be covered</td></tr><tr><td>similarity</td><td>Similarity measure between fuzzy sets</td></tr><tr><td>discretization_step</td><td>Number of inputs considered in a uniform grid within the domain of a variable</td></tr><tr><td>similar_var</td><td>List of labels of similar variables</td></tr><tr><td>activation_rule_threshold</td><td>Minimum premise truth value for a rule to be considered as activated</td></tr></tbody></table>

FuzzIC is configurable, flexible and customizable: it also takes as input a configuration file that allows users to customize the interpretability criteria implementation, as discussed in the next subsections and summarised in Table II. For ease of use, all parameters have predefined default values, to enable direct use by non-expert users.

As an output, FuzzIC provides a Json file with all criteria scores for a given fuzzy rule base, facilitating their exploitation for visualisation or comparison.

#### B. Criteria at the Fuzzy Set Level

At the most basic level, FuzzIC assesses the interpretability of a fuzzy rule base FRB as the aggregation of the individual properties of the fuzzy sets it contains

For the normality criterion, FuzzIC computes the proportion of fuzzy sets with height 1 among the fuzzy sets involved in the considered FRB. The unimodality criterion imposes that a fuzzy subset have a single element with maximal membership value and that any of its α-cuts be connected. Thus FuzzIC counts the proportion of triangular and Gaussian fuzzy sets of height 1. The continuity criterion is satisfied by trapezoidal and Gaussian membership functions, it is therefore not implemented in FuzzIC.

#### C. Criteria at the Linguistic Variable Level

For all LV criteria, FuzzIC aggregates, through the operator specified in the configuration file (default = maximum), the

<footnote n="1">¹https://gitlab.lip6.fr/pontoizeau/fuzzic/</footnote>
scores obtained by each linguistic variables involved in the
considered FRB.

The relation preservation criterion demands that a provided order relation on linguistic terms (e.g. small ≲ medium ≲ large) be respected by their associated membership functions. FuzzIC computes the proportion of variables that respects the order, where the order relationship and the ordering relation defined on fuzzy sets are specified in the configuration file.

The *justifiable number of elements* criterion demands that the number of modalities within a linguistic variable be small. For each linguistic variable, FuzzIC thus computes the number of fuzzy sets.

The *distinguishability* criterion imposes that any two fuzzy sets used for a given linguistic variable have distinct semantics, understood as a low overlap. FuzzIC computes the similarity, using the function given in the configuration file, between all pairs of fuzzy subsets associated to each linguistic variable.

The *coverage* criterion demands that any value of the domain on which a linguistic variable is defined belong to one of its modality. Given a discretization step and a desired minimal degree $\alpha$, FuzzIC computes the percentage of values for which there exists a fuzzy subset to which it belongs with degree greater than $\alpha$.

The *complementarity* criterion imposes that, for any value in the domain of a linguistic variable, the sum of its membership degrees to all modalities equal 1. For any linguistic variable, given a discretization step, FuzzIC returns 1 if this condition is satisfied and 0 otherwise.

The *uniformity* criterion demands that all fuzzy sets of a variable have a similar cardinality. This criterion is motivated in [23]. For any linguistic variable, FuzzIC implements this criterion by computing the ratio of the minimum cardinality to the maximum cardinality. The closer the result is to 1, the more uniform the fuzzy sets of a linguistic variable are.

For the *prototype* criterion, objects that have a specific meaning in the considered application context, called *prototypes*, must belong to a modality with degree 1. FuzzIC computes the proportion of prototypes provided in the configuration file that satisfy this condition.

The *extrema* criterion demands that the boundaries of the domain belong to at least one fuzzy set with membership degree 1. FuzzIC computes the percentage of boundaries satisfying this condition.

### D. *Criteria at the Rule Level*

The *size of premises* (resp. *conclusions, rules*) criterion requires them to be short. FuzzIC computes the number of terms they respectively contain for each rule in the rule base and aggregates the results as the maximum (by default) or average operator.

### E. *Criteria at the Rule Base Level*

First the *number of variables* that are used in the rule base should be limited. FuzzIC thus computes this value.

Then, the *membership function sharing* criterion imposes that similar features, defined on a common domain, e.g. a

normalised interval [0, 1], use the same linguistic variables, i.e. the same fuzzy sets and labels across all rules. Based on a list of similar features specified in the configuration file, FuzzIC computes the similarity between fuzzy sets with the same label and aggregates them by the chosen aggregator.

The *consistency* criterion requires that rules activated simultaneously have similar consequences for any shared feature. FuzzIC computes the similarity of the fuzzy sets associated to the same feature for rules with identical premises.

The additional criteria involve input data to which the rules are applied. The *number of activated rules* criterion demands that the number of rules activated by any input data be limited. FuzzIC computes this value for a set of representative inputs provided in the configuration file, for the specified activation parameters (t-norm for the premise conjunction and minimal membership threshold). They are aggregated by the min (by default) or average operator. Reciprocally, the *completeness* criterion imposes that any input activate at least one rule in the rule base. FuzzIC computes the percentage of the provided inputs that satisfy this condition.

## IV. EMPIRICAL USER STUDY

This section presents the human-centered study of the interpretability criteria we conducted to determine whether they influence the user preferences.

### A. *Experimental Set Up*

1) *Built Questionnaire:* The experiment consists in a multiple-choice questionnaire of 20 questions. A tutorial is provided at the beginning of the questionnaire for basic fuzzy set graph reading. Then, for each interpretability criterion (or group of criteria), multiple configurations are presented to the participant. The displayed configurations differ only by that specific criterion (or group of criteria). The participant is then asked to indicate which configuration they find most relevant, the results are analysed under the assumption that their preferences constitute a proxy for the tested configuration interpretability perception.

The questionnaire has been designed to avoid evaluating participants based on their technical expertise: assessing preferences or opinions regarding a fuzzy rule base on a technical subject could introduce biases related to the participant's level of knowledge. Therefore, easily understandable contexts, related to everyday life issues, are considered. Moreover, in order to study their possible influence, two contexts are selected for the linguistic variable level: the speed of a car on a highway (named car context in the following) and the age of a residence in Paris (named housing context). Regarding the rule and rule base levels, the criteria are evaluated in a typically subjective situation: participants are asked to assess their understanding of the food preferences of a fictional character named Joséphine. This approach ensures that the evaluation is based on subjective interpretation rather than technical knowledge, thus minimizing potential biases.

For the questions related to fuzzy sets and linguistic variables, preliminary technical questions (Q1, Q2, Q4 and Q5) are
<table><caption>TABLE III
GOAL OF EACH QUESTION OF THE QUESTIONNAIRE</caption><thead><tr><th>Question</th><th>What is the question checking ?</th></tr></thead><tbody><tr><td>Questions 1, 2, 4, 5</td><td>technical check</td></tr><tr><td>Question 3</td><td>normality, unimodality</td></tr><tr><td>Question 6</td><td>complementarity, distinguishability, coverage</td></tr><tr><td>Question 7</td><td>size of partition</td></tr><tr><td>Question 8</td><td>uniformity</td></tr><tr><td>Question 9</td><td>extrema</td></tr><tr><td>Question 10</td><td>prototype</td></tr><tr><td>Question 11</td><td>membership functions sharing</td></tr><tr><td>Question 12</td><td>number of variables</td></tr><tr><td>Question 14</td><td>completeness</td></tr><tr><td>Question 16</td><td>number of activated rules</td></tr><tr><td>Question 18</td><td>size of rule</td></tr><tr><td>Q13, 15, 17, 19</td><td>difficulty degree of respective previous questions</td></tr><tr><td>Question 20</td><td>expertise level on fuzzy logic and interpretable AI</td></tr></tbody></table>

included to verify that participants understand the subsequent interpretability questions and to ensure that their preference responses are relevant: answers for participants who failed these technical questions are excluded from the analysis.

Table III provides the correspondence between questions and the interpretability criteria (group of criteria) they test.

2) *Participant Recruitment:* We recruited a total of 49 participants, comprising 14 members from an academic fuzzy logic research team, 19 AI master students, and 16 computer science engineers who are familiar with AI topics (but not fuzzy logic for most of them). The questionnaires were distributed among the participants: 50% on Car, 50% on Housing, 100% on Joséphine, but the students that had not access to the Car questionnaire (100% on Housing).

3) *Study Procedure and Data Analysis:* The questionnaire was administered without a time limit, and participants typically completed it in approximately 30 minutes. 6 out of 49 participants are not included in the results at the fuzzy set and the linguistic variable level since they failed the technical questions. For each question, the participants could add a comment about why they chose their answer. On a 0-10 scale, the self-assessed expertise score for the participants was 4.8 (± 2.4) in fuzzy logic, and 4.4 (± 2.8) in interpretable AI.

## B. Results for Criteria at the Fuzzy Set Level

Q3 studies users' preference between a non-normalized non-unimodal fuzzy set and a normal unimodal fuzzy set, respectively shown as *A* and *B* in Fig. 1 for the linguistic labels *recent* in the housing context (left) and *moderate* for the car speed context (right). The asked question is "Which fuzzy set do you think is the most relevant to describe a recent home in Paris?". Fig. 2 shows the distribution of the obtained answers. As a result, the normality criterion clearly seems important for the car context participants. In particular, this criterion is explicitly cited in five comments. The responses are more dispersed for the housing context. This may be due to a mismatch between the chosen linguistic term and fuzzy set: as mentioned in 10 comments, *recent* applies in common sense to housing built after 1990, whereas the considered membership function's core equals [1980, 1990].

<figure><img src="image_2.png" /><figcaption>Fig. 1. Fuzzy sets *A* and *B* displayed for Q3: (left) housing context, (right) car context.</figcaption></figure>

<figure><img src="image_3.png" /><figcaption>Fig. 2. Q3 results (left) housing context, (right) car context. Numbers in the pie chart indicates the number of occurrences for each answer.</figcaption></figure>

## C. Results for Criteria at the Linguistic Variable Level

Fig. 3 shows the results obtained for Q6 to Q10.

Q6 examines interpretability with regard to complementarity, distinguishability and coverage. Three partitions are proposed, each of them optimizing one of the criteria. The results show that complementarity is the most important factor for participants in both contexts (respectively 70% and 69.2%), whereas it seems that there is no significant preference between coverage and distinguishability criteria.

Q7 assesses the fuzzy set partition size impact, considering partitions with less than 7 modalities, i.e. satisfying Miller's criterion [24]. Results differ depending on the context: in the car case, a majority of participants prefer 5 fuzzy subsets; in the housing case, no consensus emerges. This may lead to consider that the ideal size for a partition to be interpretable depends on the context.

Q8 assesses the importance of the uniformity of the fuzzy subset sizes: two partitions with three modalities are compared, a uniform one and one with a larger middle fuzzy set. The participants show no consensus in their preferences. Some comments explicitly mention that a larger fuzzy set for the medium modality is more suitable, in particular in the car context, where the non-uniform partition (46.2%) is preferred to the uniform one (23.1%). This leads to the conclusion that uniformity is not necessarily a crucial criterion when designing an interpretable linguistic variable.

Q9 studies the extrema criterion: it compares a partition whose extreme modalities are associated with semi-trapezoids and a partition with regular trapezoids, in which the domain
<figure><img src="image_4.png" /><figcaption>Fig. 3. Results for the criteria associated to the linguistic variables, (left) housing context, (right) car context. Numbers in the pie chart indicates the number of occurrences for each answer.</figcaption></figure>

extreme values have 0 membership degree to all modalities. The results show that this criterion is required by almost all participants. In particular, 18 participants explicitly comment that the lack of information for extreme values is irrelevant.

Q10 studies whether a prototype value needs to have mem-
bership degree 1. In both contexts, the majority of participants
favour the partition satisfying this criterion and 11 participants
explicitly express this need in a comment. On the other hand,
4 feel at ease with a partition that does not satisfy it, since the
judgement of “typical” is considered subjective. There is thus
no consensus on this criterion.

D. Results for the Fuzzy Rule and Fuzzy Rule Base Criteria

Questions 11 to 18 study the interpretability criteria for rules
and rule bases related to the culinary tastes of the fictional
character Joséphine. Results are shown on Fig. 4.

Q11 deals with the membership function sharing criterion.
It compares 4 rule bases, each containing 2 rules: one with no
membership function sharing, two with partial sharing, and
one with full sharing. No consensus can be observed, neither

in the answers, nor in the comments: some of the latter express
a slight preference for all variables to share labels, others
express that natural language is easier to understand. Thus,
this criterion seems to be a matter of subjective preference.

Q12 assesses the impact of the number of variables, com-
paring a rule base with 7 variables and one with 4, i.e. both
satisfying Miller's criterion [24]. Observations show no sig-
nificant difference in the participants' perceptions. Participants
rate the complexity of response at 5.5 (± 2.7).

Q14 assesses whether completeness is important for the
interpretability of a rule base: an incomplete rule base is
presented to the participants, together with an input that does
not activate any rule. It is thus not possible to infer the output
simply by applying a usual fuzzy logic inference system.
47.9% of participants declare that the rule base does not allow
them to conclude, certainly because they observe that the rule
base is not complete. On the other hand, half of the partic-
ipants (50%) infer the “medium” answer, which shows that
incompleteness does not prevent them from inferring a plau-
sible output. Besides, the ”medium” response is unanimous
among these participants. In addition, among the participants
who answer “cannot conclude”, two of them comment that
they think the answer should probably be “medium”. These
observations lead us to conclude that completeness is not
essential for participants to make inferences. Participants rate
the complexity of response (Q15) at 3.7 (± 2.2).

Q16 aims to evaluate the impact of the number of rules
activated by an input on the interpretability of the rule base:
the proposed input activates 6 rules, among which 4 leads
to “medium” as a conclusion, and the two others to ”low”.
A majority of participants (52.1%) consider that the rule
base does not allow them to conclude. The interpretation of
this assessment is similar to the results of Q14. Similarly,
a significant proportion of participants (45.8%) answers that
Joséphine has “medium” or “low” satisfaction. Depending on
the exact values of the input and the way in which the fuzzy
subsets of each variable are defined, it is possible to infer both
“medium” and “low” satisfaction using classic fuzzy logic
rules. These results lead us to think that the activation of
several fuzzy rules may lower the interpretability of the rule
base, but does not necessarily prevent it. Again, the number
of activated rules satisfies Miller’s criterion, higher values
would probably lower the interpretability of the fuzzy rule
base. Participants rate this question as more complex than the
previous ones, as 6.2 (± 2.5), which shows that such a question
was not easy (and thus interpretable) to apprehend.

Q18 assesses the impact of rule size on interpretability.
It proposes 4 rules satisfying Miller's criterion, with sizes
from 3 to 7. 52.1% of the participants prefer the shortest one.
However, 29.2% of them express indifference. Similar to Q7, it
may be necessary to increase the size of the proposed rules in
a future study, to determine whether there is an identifiable
limit in terms of interpretability. In this respect, some of
the participants comment that the 4 rules are not difficult to
understand, and some others point out that the rules are not
long enough for this to affect comprehension. Participants rate
<figure><img src="image_5.png" /><figcaption>Fig. 4. Results for questions about Joséphine's culinary taste. Numbers in the pie chart indicates the number of occurrences for each answer.</figcaption></figure>

the complexity of response (Q19) at 3.1 (± 2.3).

## V. CONCLUSION AND FUTURE WORK

In this paper, we propose FuzzIC a tool to assess the interpretability of fuzzy rule bases according to many complementary numerical criteria. It takes as input classical formats for fuzzy rule base representation and it offers a flexible framework through a simple configuration file, allowing for easy comparison of fuzzy rule bases. In addition, we conduct an empirical user study of these interpretability criteria. In particular, it shows that, as expected, normality, complementarity, extrema and prototype are essential criteria, whereas others as uniformity, a justifiable number of elements are not important or actually even lower interpretability for users.

These results need to be confirmed through additional experiments, increasing the number of participants as well as including other application contexts. Another direction for further user studies aims at enlarging the range of the considered values, such as the partition or rule sizes, to determine whether there is an identifiable limit in terms of interpretability.

## VI. ACKNOWLEDGEMENTS

This work has been funded by ANR-22-ASTR-0032.

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