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Presently, Artificial Intelligence (AI) has seen a significant shift in focus towards the design and development of interpretable or explainable intelligent systems. This shift was boosted by the fact that AI and especially the Machine Learning (ML) field models are, currently, more complex to understand due to the large amount of the treated data. However, the interchangeable misuse of XAI concepts mainly “interpretability” and “explainability” was a hindrance to the establishment of common grounds for them. Hence, given the importance of this domain, we present an overview on XAI, in this paper, in which we focus on clarifying its misused concepts. We also present the interpretability levels, some taxonomies of the literature on XAI techniques as well as some recent XAI applications.

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Inference systems are intelligent software performed generally to help people take appropriate decisions and solve problems in specific domains. Fuzzy inference systems are a kind of these systems that are based on fuzzy knowledge. To handle the fuzziness in the inference, the compositional rule of inference is used, which has two parameters: a t-norm and an implication operator. However, most of the combinations of t-norm/implication do not give an adequate inference result that coincides with human intuitions. This was the motivation for several works to study these combinations and to identify those that are compatible, in order to guarantee a performance close to that of humans. We are interested in this paper to a more general form of rules, which is complex rules, whose premise is a conjunction of propositions. To obtain the consequence in a fuzzy inference system using the compositional rule of inference with a complex rule, we study, in this work, Lukasiewicz t-norm which was not investigated before in this context. We combine it with known implications, and we verify the satisfaction of some criteria that model human intuitions.

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Inference systems are a well-defined technology derived from knowledge-based systems. Their main purpose is to model and manage knowledge as well as expert reasoning to insure a relevant decision making while getting close to human induction. Although handled knowledge are usually imperfect, they may be treated using a non classical logic as fuzzy logic or symbolic multi-valued logic. Nonetheless, it is required sometimes to consider both fuzzy and symbolic multi-valued knowledge within the same knowledge-based system. For that, we propose in this paper an approach that is able to standardize fuzzy and symbolic multi-valued knowledge. We intend to convert fuzzy knowledge into symbolic type by projecting them over the Y-axis of their membership functions. Consequently, it becomes feasible working under a symbolic multi-valued context. Our approach provides to the expert more flexibility in modeling their knowledge regardless of their type. A numerical study is provided to illustrate the potential application of the proposed methodology.

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In the pharmaceutical industry, the production of psychiatric drugs has been seriously disrupted since the appearance of COVID'19. For that, Demand Forecasting of psychiatric drugs is among the big challenges in this industry. The objective is to avoid an excess of stock and, at the same time, to ensure that a stock rupture does not occur. Based on analysis of psychiatric drugs data, we compare in this paper several forecasting techniques which are Exponential Smoothing, seasonal ARIMA (i.e. SARIMA), SARIMAX, enhanced with the integration of exogenous (explanatory) variables, and LSTM. Through all the done tests, we make a comparison study of the results to identify the most promising models.

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Fuzzy control is an intelligent software performed to tune a process and make it react in a desirable way. Nowadays, many researchers are interested in the Fuzzy Proportional-Integral-Derivative (FPID) controller because of its performance and simple structure. FPID controller, as fuzzy controller, is based on the Compositional Rule of Inference (CRI) that allows to infer with fuzzy data. As defined by Zadeh, the CRI contains two parameters: t-norm (T) and fuzzy implication (I). Because of the singleton representation of crisp inputs in fuzzy controllers, the t-norm is no longer considered in the CRI, which gives results based only on the fuzzy implication. In this study, we use non-singleton representation of the inputs, and we apply several implications in a fuzzy PID controller combined with the product t-norm. We study the behaviour of the fuzzy PID controller according to each combination (T,I) to evaluate its efficiency in term of quality and time of convergence. We finally compare the obtained results with the theoretical inference results and we find that they are consistent.

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In front of the continued growth of autistics number in the world, intelligent systems can be used by non-specialists such as educators or general physicians in autism screening. Moreover, it can assist psychiatrists in the diagnosis of autism to detect it as early as possible for early intervention. We propose in this chapter a tool for the diagnosis of autism: DAS-Autism. It is a knowledge-based system that handles qualitative knowledge in the multi-valued context. For this, we use our knowledge-based system shell RAMOLI, and its inference engine executes an approximate reasoning based on linguistic modifiers that we have introduced in a previous work. We have built a knowledge base that represents the domain expertise, in collaboration with a child psychiatry department of Razi hospital, the public psychiatric hospital in Tunisia. We have then conducted an experimental study in which we compared the system results to expert’s diagnoses. The results of this study were very satisfactory and promising.

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Approximate reasoning is used in Fuzzy Inference Systems to handle imprecise knowledge. It aims to be close as possible to human reasoning. The main approach of approximate reasoning is the compositional rule of inference, which generates different methods by varying its parameters: a t-norm and an implication. In most cases, combinations of t-norms and implications do not fit human intuitions. Based on these methods, we suggest the use of the product t-norm in the compositional rule of inference. We combine this t-norm with different known implications. We then study these combinations and check if they give reasonable consequences.

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Nowadays, knowledge-based system has to be able to model and treat imperfect knowledge. Among the knowledge imperfection, we cite imprecision. Imprecise information are generally represented in a quantitative way using fuzzy logic or in a qualitative way using symbolic multi-valued logic. As far as we knew, no work has considered both fuzzy and symbolic multi-valued knowledge simultaneously in the same knowledge-based system. However, the user is often in need of both data types to insure a relevant decision-making. In order to improve the decision-making process performance, we propose in this paper an approach, that is able to standardize input knowledge. In fact, we propose a fuzzy-to-symbolic conversion of inputs by projecting them over the abscissa axis. We apply the proposed conversion module in symbolic inference systems. Thus, a symbolic approximate reasoning can be executed. The conversion process involves the expert by asking him to express its tolerance threshold toward handled fuzzy knowledge. Thus, a minimum of fuzzy information loss will be insured according to the expert preferences and the reasoning context. Our proposal is also useful even when the rule conclusion is originally fuzzy. In that case, a symbolic-to fuzzy conversion of the inference result is required to make the inference result more intelligible for the user and to maintain the transparency of the fuzzy-to-symbolic conversion. A numerical study is provided to illustrate the potential applications of the proposed methodology.

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When building Knowledge-Based Systems, we are often faced with vague data. The formers are generally modeled and treated using fuzzy logic, which is based on fuzzy set theory, or using symbolic multi-valued logic, which is based on multi-set theory. To provide a unified framework to handle simultaneously both types of information, we propose in this paper a new approach to translate multi-valued knowledge into fuzzy knowledge. For that purpose, we put forward a symbolic-to-fuzzy conversion method to automatically generate fuzzy sets from an initial multi-set. Once unified, handling heterogeneous knowledge become feasible. We apply our proposal in Rule-Based Systems where an approximate reasoning is required in their inference engine. Once new facts are deduced and in order to make the translation completely transparent for the user, we also provide a fuzzy-to-symbolic conversion method. Its purpose is to restore the original knowledge type if they were multi-valued. Our proposal offer a high flexibility to the user to reason regardless to the knowledge type. In addition, it is an alternative to overcome the modeling shortcoming of abstract data by taking advantage of a rigorous mathematical framework of fuzzy logic. A numerical study is finally provided to illustrate the potential application of the proposed methodology.

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Approximate reasoning aims to manage knowledge imprecision in the inference process. It is a generalization of the Modus Ponens of classical logic. Originally, it is defined in fuzzy logic context, where knowledge are modeled by a quantitative way. We are interested in this paper to approximate reasoning in the symbolic multi-valued logic context. This logic allows presenting imprecise knowledge in a qualitative way, where every predicate is modeled by a multi-set. In order to express imprecision, each multi-set is associated to a scale base of ordered symbolic degrees. In a previous work where a symbolic approximate reasoning has been defined, it has been assumed that all multi-sets of the inference schema have the same scale base. This has the disadvantage to prevent free definition of knowledge. For that, we propose in this paper a new approximate reasoning which can infer with multi-sets having different scale bases. Our solution consists of interfacing all the multi-sets in order to avoid information loss.

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Knowledge-based systems have nearly become omnipresent in various sectors to facilitate decision-making. Their aim is to get close to human induction. For that, dealing imprecise knowledge is essential since human thinks imprecisely. The principal logics that allow manipulating this kind of knowledge in intelligent systems are fuzzy logic and multi-valued logic. Up to now, according to our knowledge, knowledge-based systems manage separately either fuzzy knowledge or multi-valued knowledge. However, modeling heterogeneous knowledge (fuzzy and multi-valued) in the same inference engine should ensure more flexibility and freedom to the user. In that context, our aim is to allow the use of fuzzy and multi-valued knowledge at once. We propose a new approach to convert fuzzy knowledge into symbolic knowledge by projecting fuzzy inputs over the x-axis that corresponds to the universe of discourse of fuzzy variable. In order to demonstrate its applicability, our proposal is tested within a rule-based system. A numerical example is then provided.

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We introduce in this paper a tool for the diagnosis of autism called DASAutism. For this, we use our knowledge-based system shell RAMOLI. This system handles knowledge in the multi-valued context. Moreover, its inference engine executes an approximate reasoning based on linguistic modifiers that we have introduced in a previous work. We have built a knowledge base that represents the domain expertise, in collaboration with the child psychiatry department of Razi hospital.

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Approximate reasoning allows inferring with imperfect knowledge. It is based on a generalization of modus ponens (MP) known as generalized modus ponens (GMP). We are interested in approximate reasoning within symbolic multi-valued logic framework. In a previous work, we have proposed a new GMP based on linguistic modifiers in the multi-valued logic framework. The use of linguistic modifiers allows having a gradual reasoning; moreover, it allows checking axiomatics of approximate reasoning. In this paper, we extend our approximate reasoning to hold with complex rules, i.e., rules whose premises are conjunction or disjunction of propositions. For this purpose, we introduce a new operator that aggregates linguistic modifiers and verifies the required properties of logical connectives within the multi-valued logic framework.

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Non classical logics were introduced to allow handling imperfect concepts in intelligent systems. One of the principal non classical logic is multi-valued logic that has the particularity to support symbolic data. We introduced in a previous work an approximate reasoning in the multi-valued framework based on linguistic modifiers that checks approximate reasoning axiomatics. This paper describes the development of software model for the treatment of imperfection with our approach of approximate reasoning. It is a knowledge-based systems shell for symbolic data called RAMOLI. This shell provides simple and interactive Graphical User Interface to introduce knowledge and to infer with our approximate reasoning.

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Approximate reasoning, initially introduced in fuzzy logic context, allows reasoning with imperfect knowledge. We have proposed in a previous work an approximate reasoning based on linguistic modifiers in a symbolic context. To apply such reasoning, a base of rules is needed. We propose in this paper to use a supervised learning system named SUCRAGE, that automatically generates multi-valued classification rules. Our reasoning is used with this rule base to classify new objects. Experimental tests and comparative study with two initial reasoning modes of SUCRAGE are presented. This application of approximate reasoning based on linguistic modifiers gives satisfactory results. Besides, it provides a comfortable linguistic interpretation to the human mind thanks to the use of linguistic modifiers.

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Linguistic modifiers, defined by Zadeh in fuzzy logic context, are operators that transform a linguistic term to another linguistic term. Akdag and al. extend linguistic modifiers to symbolic multi-valued logic context, and called them Generalized Symbolic Modifiers. In this paper we propose a study which allows deepening the use of Generalized Symbolic Modifiers in soft computing applications. We focus on symbolic modifiers composition, and we give new properties. Then, we study modifiers order relation, based on a lattice that orders all the defined modifiers according to their parameters. Finally, we illustrate the utilities of our propositions, particularly in approximate reasoning based on linguistic modifiers.

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Approximate reasoning is based on a generalization of Modus Ponens, known as Generalized Modus Ponens (GMP). Its principle is that from an observation different but approximately equal to the rule premise, we can deduce a fact approximately equal to the rule conclusion. However, the deduced fact is not obtained with an arbitrary way. A set of axioms are fixed to have coherent and logic results. In this paper, we propose a new rule of GMP in the multi-valued logic framework. Our aim is to provide inference results which checks the axiomatic of approximate reasoning. We propose to use linguistic modifiers in GMP and we explain how it allows having a gradual reasoning.

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We focus in this paper on approximate reasoning in a symbolic framework, and more precisely in multi-valued logic. Approximate reasoning is based on a generalization of Modus Ponens, known as Generalized Modus Ponens (GMP). Its principle is that from an observation different but approximately equal to the rule premise, we can deduce a fact approximately equal to the rule conclusion. We propose a generalization of the approximate reasoning axiomatic introduced by Fukami, and we show the weakness of GMP approaches in the multi-valued context towards this axiomatic. Moreover, we propose two rules of symbolic GMP that check the axiomatic. One is based on the implication operator and the second on linguistic modifiers.