While fuzzy methods, and in particular fuzzy rule-based methods, have been pointed out as explainable, it is not always easy to attach a linguistic label to the conclusion provided by a rule-based system for a given observation. In this paper, we focus on the case of sparse rules, with imprecise or linguistic premises and conclusions, and their use with imprecise or linguistic observations. We explore fuzzy solutions of interpolative reasoning based on analogies, with regard to desirable mathematical properties and explainability criteria. We first recall such criteria existing in the state of the art and we analyse them in the light of explainable Artificial Intelligence (AI) requirements. We then propose a new method making easier to explain both the result of the fuzzy interpolative reasoning and the approach used to construct it. A set of experimental comparisons with some existing fuzzy interpolative reasoning approaches is presented.

Entropies and measures of information are extensively used in several domains and applications in Artificial Intelligence. Among the original quantities from Information theory and Probability theory, a lot of extensions have been introduced to take into account fuzzy sets, intuitionistic fuzzy sets and other representation models of uncertainty and imprecision. In this paper, we propose a study of the common property of monotonicity of such measures with regard to a refinement of information, showing that the main differences between these quantities come from the diversity of orders defining such a refinement. Our aim is to propose a clarification of the concept of refinement of information and the underlying monotonicity, and to illustrate this paradigm by the utilisation of such measures in Artificial Intelligence.

We consider objects associated with a fuzzy set-based representation. By using a classic method of measurement introduced by Tversky, we establish necessary and sufficient conditions for the existence of a particular class of fuzzy similarity measures, agreeing with an ordering relation among pairs of objects which express the idea that two objects are "no more similar than" two others.

Since the International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems published its first issue in 1993, it has made important contributions to the research field of computer science. In this study, based on the dataset of the publications published in this journal between 1993 and 2016 retrieved from Web of Science, a general overview of this journal is performed using bibliometric methods and visualized networks. First, the productive and influential publications, authors, institutions, countries/territories, and supraregions are analysed based on the total number of citations, publications, and different citation thresholds. Second, network visualization analysis is applied to illustrate the links and connections between terms by using the VOSviewer software. Moreover, the most cited journals and common author keywords of three continents, including North America, Europe, and Asia, are also presented. This paper will hopefully help researchers understand the research patterns of this journal.

The T-CGMP inference scheme combines the GMP principles with additional constraints to guide inference in the case where the observation does not match the rule premise. This paper studies its exploitation in the case where several rules are available, in particular considering the case of two rules: it proposes a local variant of T-CGMP and examines its behaviour in this interpolation-like framework, highlighting its specific features, in particular the original uncertain outputs it produces to keep track of shape mismatches. The resulting inference scheme can thus be seen as an intermediary between GMP and interpolation.

An important aspect of interpretability in Fuzzy Linguistic Summaries (FLS) is the absence of opposition therein, which is not guaranteed by the the current approaches used for their generation, possibly leading to confusion for the end-user. In this paper, we first introduce a 3-level hierarchy to organise the models of opposition starting from simpler sentences, then enriched with generalised quantifiers and thirdly considering the several negation operators allowed by fuzzy logic. We then introduce a general model of opposition for FLS sentences, which we propose to represent as a 4-dimensional cube. We additionally discuss the antonym property in this analysis framework and prove it for general protoforms.

The objective of any tutoring system is to provide resources to learners that are adapted to their current state of knowledge. With the availability of a large variety of online content and the disjunctive nature of results provided by traditional search engines, it becomes crucial to provide learners with adapted learning paths that propose a sequence of resources that match their learning objectives. In an ideal case, the sequence of documents provided to the learner should be such that each new document relies on concepts that have been already defined in previous documents. Thus, the problem of determining an effective learning path from a corpus of web documents depends on the accurate identification of outcome and prerequisite concepts in these documents and on their ordering according to this information. Until now, only a few works have been proposed to distinguish between prerequisite and outcome concepts, and to the best of our knowledge, no method has been introduced so far to benefit from this information to produce a meaningful learning path. To this aim, this article first describes a concept annotation method that relies on machine-learning techniques to predict the class of each concept—prerequisite or outcome—on the basis of contextual and local features. Then, this categorization is exploited to produce an automatic resource sequencing on the basis of different representations and scoring functions that transcribe the precedence relation between learning resources. Experiments conducted on a real dataset built from online resources show that our concept annotation approach outperforms the baseline method and that the learning paths automatically generated are consistent with the ground truth provided by the author of the online content.

Linguistic summarization is a data mining and knowledge discovery approach to extract patterns and sum up large volume of data into simple sentences. There is a large research in generating linguistic summaries which can be used to better understand and communicate about patterns, evolution and long trends in numerical, time series or labelled data. The objective of this work is to develop a computational system capable of automatically generating linguistic descriptions of time series data of septic shock patients containing labelled data, not only of the whole series, but also on the differences between subsets of the data. This is of particular interest in septic shock, as the differences between patients are not well understood. For this purpose we propose a new type of differential summaries, based on a numerical criterion assessing the characteristics of the summary on each subset of interest. Furthermore, this paper proposes an extension of linguistic summaries to provide temporal and categorical contextualization. This is of particular interest in healthcare to detect differences related to a condition or illness as well as the effectiveness of the administered treatment.

Gradual relationship between premises and conclusions is often an underlying property of fuzzy rules. In this paper, we propose to integrate the gradual hypothesis, sometimes called monotonicity, to Generalized Modus Ponens (GMP). To achieve this objective, we defined the Gradual Generalized Modus Ponens (GGMP), based on a partioning of the universe of discourse. Moreover, we prove, for this formulation, some major preservation properties, such as for the convexity, the continuity and the normality. Finally, we show that the ordering of different fuzzy observations is conserved for the associated conclusions.

Along with the increase of the amount of data stored and to be analyzed, different techniques of data analysis have been developed over the years. One of them, the linguistic summary, aims at summing up large volume of data into simple sentences. In this paper, we present an overview of two main streams of research, namely fuzzy logic based systems and natural language generation, covering the methods designed to work with numerical data, time series, or simple labels (enumerations). We focus on the former stream and we give some hints to go further on fuzzy quantifiers.

This paper addresses the task of detecting Internet buzzes, defined as amplification phenomena, i.e. the diffusion on a very large scale of an Internet content, massively taken up within a short period of time. It proposes two approaches based on the citation graph that represents hyperlinks relation between websites. The first method detects temporal abnormalities in the number of citations of an information source, identifying information sources that undergo a surge of their direct citations. The second method exploits higher level cues, based on the definition of the dynamic cumulative visibility of an article. It captures the notion of citation cascade that is central to the specific type of buzzes related to rumour. Both detection approaches are illustrated, respectively on real data extracted from the Web and on realistic simulated data. The experimental study shows the relevance of the proposed methods and highlights their differences.

Investors are constantly confronted with deciding between a multitude of different investments. The characteristics, especially the estimated return, of each alternative is never precisely known. In this paper, we propose to use fuzzy present values to model this uncertainty. We extend previous work with the possibility to account for uncertain project durations, which become increasingly important for long-term projects. The results allowed a detailed assessment of the cost of hydrogen production using a thermo-chemical cycle which is still in the early phase of research. On the theoretical side, we propose a sound fuzzification over crisp domains, avoiding in particular the unsteady behaviour of existing approaches.

Fuzzy gradual rules of the form the more X is A, the more Y is B linguistically express information about the correlation between attributes and their co-variation. They thus provide valuable information summarizing the trends observed in a given data set. In this paper, we consider strengthened fuzzy gradual rules, i.e. gradual rules enriched with a clause introduced by the expression “all the more”: such rules of the form the more X is A, the more Y is B, all the more Z is C offer additional precisions on the relation between the attributes. We study the definition of such strengthened rules, discussing their possible semantics, considering several interpretations of fuzzy gradual rules. We then propose quality criteria as well as a mining algorithm.

Given the very ambiguous and imprecise nature of sentiments and of their expressions, this survey focuses on approaches making use of components of graduality in the task of automatic sentiments analysis. To that aim, we review methods taking account of intrinsic psychological models components of graduality as well as extrinsic components issued from computational intelligence approaches. In particular, beyond psychological models of sentiments that define affective states as multidimensional vectors in affective continuous spaces, we identify three components of graduality, namely composition or blending, intensity and inheritance. In our discussion, we review how fuzzy set theory as well as other gradual structures based on a vectorial representation are employed to describe affective states as complex or imprecise entities. Finally, we focus on verbal expressions of sentiments and more specifically, we discuss the use of components of graduality in order to deal with sentiments complex and subtle expressions issued from the expressive power of natural languages.

In this paper, a hierarchical model of functions is presented to study and to validate functions used in an inductive learning process as measures of discrimination. This model is a fuzzy extension of a previously introduced model based on the use of any t-norm to value the intersection of fuzzy sets. Moreover, this model is based on the classically used definition of the inclusion of fuzzy sets. By means of this model, three well-known measures used to select attributes during the construction of a fuzzy decision tree are shown well-adapted as measures of discrimination. However, it is also shown that the use of an extension of the entropy of fuzzy events based on the use of Zadeh's t-norm is not convenient for such a process.

In this paper, we address the problem of active query selection for clustering with constraints. The objective is to determine automatically a set of queries and their associated must-link and can-not link constraints to help constraints based clustering algorithms to converge. Some works on active constraints learning have already been proposed but they are only applied to K-Means like clustering algorithms which are known to be limited to spherical clusters while we are interested in constraints-based clustering algorithms that deals with clusters of arbitrary shapes and sizes (like Constrained-DBSCAN, Constrained-Hierarchical Clustering. . . ). Our novel approach relies on a k-nearest neighbors graph to estimate the dense regions of the data space and generates queries at the frontier between clusters where the cluster membership is most uncertain. Experiments show that our framework improves the performance of constraints based clustering algorithms.

K-Means algorithm is one of the most used clustering algorithm for Knowledge Discovery in Data Mining. Seed based K-Means is the integration of a small set of labeled data (called seeds) to the K-Means algorithm to improve its performances and overcome its sensitivity to initial centers. These centers are, most of the time, generated at random or they are assumed to be available for each cluster. This paper introduces a new efficient algorithm for active seeds selection which relies on a Min-Max approach that favors the coverage of the whole dataset. Experiments conducted on artificial and real datasets show that, using our active seeds selection algorithm, each cluster contains at least one seed after a very small number of queries and thus helps reducing the number of iterations until convergence which is crucial in many KDD applications.

The objective of any tutoring system is to provide a meaningful learning to the learner. Therefore an automated tutoring system should be able to know whether a concept mentioned in a document is a prerequisite for studying that document, or it can be learned from it. This paper addresses the problem of identifying defined concepts and prerequisite concepts from learning resources in html format. In this paper a supervised machine learning approach was taken to address the problem, based on linguistic features which enclose contextual information and stylistic features such as font size and font weight. This paper shows that contextual information in addition to format information can give better results when used with the SVM classifier than with the (LP)2algorithm.

The interpretability of decisions on the basis of approximate descriptions of situations is approached by means of the use of linguistic modifiers. The closeness between two descriptions is evaluated by means of the measure of their differences. An analogy based reasoning method is proposed in compatibility with fuzzy deductive reasoning, using linguistic modifiers.

This paper addresses the problem of introducing learning capabilities in industrial handcrafted automata-based Spoken Dialogue Systems, in order to help the developer to cope with his dialogue strategies design tasks. While classical reinforcement learning algorithms position their learning at the dialogue move level, the fundamental idea behind our approach is to learn at a finer internal decision level (which question, which words, which prosody, . . . ). These internal decisions are made on the basis of different (distinct or overlapping) knowledge. This paper proposes a novel reinforcement learning algorithm that can be used to make a data-driven optimisation of such handcrafted systems. An experiment shows that the convergence can be up to 20 times faster than with Q-Learning.

We propose the use of a knowledge based framework for diagnosis in which the knowledge base consists of particular instances of general hierarchical disorder models. We study how to select which manifestation (symptom, malfunction) to query in order to reduce a set of competing diagnosis hypotheses (disorders), none of them completely satisfying, considering only the observed manifestations. We propose to use general information about the order in which competing disorder models should be probed first to guide us on the task of selecting which particular disorder instances to try to confirm first. We propose to then order which manifestation instances to probe, the presence or absence of which will help us to either confirm or eliminate that hypothesis, according to the principle that "(manifestation) instances that share some characteristics with the instance of manifestation that generated the whole process, but which completely disagree in relation to other characteristics" should be probed first.

We propose the use of a knowledge based framework for diagnosis in which the knowledge base consists of particular instances of general disorder models. We study how to select which manifestation (symptom, malfunction) to query in order to reduce a set of competing diagnosis hypotheses (disorders), none of them completely satisfying, considering only the observed manifestations. We propose to use similarity relations to guide us on the task of selecting which manifestations to further investigate in order to confirm or eliminate a hypothesis, as well as information about the order in which the competing hypotheses should be probed first.

We have developed an early warning prototype, based on a knowledge management approach, so as to carry out the online detection of crises. Experts, with the help of automatic tools, design an ontology describing domain-specific crisis eruption processes. Then a recognition engine performs model-based inference, in order to identify among the events feeding the system, typical sequences that might trigger a crisis. Crises are described in the ontology through the template technique which provides also mechanisms to assess the similarity between stored scenarios and event flows related to the monitored process. This technique takes into account imperfect knowledge and uncertainties: for instance, imprecise temporal constraints between events are represented by fuzzy sets.

A similarity measure between the focal elements used on a distance function of two basic belief assignments in the theory of evidence is presented, making way for the application of classical classification algorithms in this field. The properties of this measure are particular to its context, considering the characteristics of the focal elements, their relationship with each other and their proximity to the vacuous belief function that represents the state of total ignorance

In this paper, we present a new method to construct fuzzy prototypes of heterogeneous classes, in a supervised learning context. Heterogeneous classes are classes where the coexistence of far behaviours can be observed. Our approach consists in two stages. The first one enables to discover, in an original method, the different behaviours within a class by decomposing it in subclasses. In the second stage, we construct a fuzzy prototype for each subclass by using typicality degrees. Thanks to this decomposition of a class and to this characterization of typical behaviours, we propose an intuitive summarization of a class. We illustrate the advantages of our method on both artificial and real dataset.

The construction of decision trees is an efficient tool for inductive learning, and fuzzy decision trees are particularly interesting because they enable the user to take into account imprecise descriptions of the cases, or heterogeneous values (symbolic, numerical, or fuzzy). However, since the method to construct a fuzzy decision tree is not unique, in this paper, a comparative study is presented to point out differences between three methods. This study focus on differences between methods when ranking attributes during the construction of a fuzzy decision tree. The aim is to enable the reader to understand what kind of fuzzy decision tree is obtained by each method.

Natural concept modelling aims at representing numerically semantic knowledge; generally, experts are asked to provide examples of linguistic terms associated with numerical data descriptions. We propose to exploit directly non labelled databases to extract the concepts that enable a semantic description of the data. Our method consists in identifying the subgroups corresponding to the concepts and then representing them as fuzzy subsets. For the identification step, we propose an algorithm based on a conjugate iterative use of the single linkage hierarchical clustering algorithm and the fuzzy c-means, that explicitly takes into account both a separability objective and a compactness aim; the description step builds membership functions as generalized Gaussians. The adequacy of the results with spontaneous descriptions is illustrated on artificial and real databases.

We first introduce the fuzzy similarity measures in the context of a CBIR system. This leads to the observation of an invariance in the ranking for different similarity measures. We then propose an explanation to this phenomenon, and a larger theory about order invariance for fuzzy similarity measures. We introduce a definition for equivalence classes based on order conservation between these measures. We then study the consequences of this theory on the evaluation of document retrieval by fuzzy similarity.

This paper is concerned with methods of construction of fuzzy decision trees and the choice of such a method the user has to make. The main differences between methods lies in the choice of the measure of discrimination that enables the ranking of attributes during the construction step. In this paper, a formal study of the main differences between measures is done. The aim is to highlight the major properties of the fuzzy decision trees constructed by a particular method.

The classical interpolative reasoning has been previously extended to handle an incomplete rule base with imprecise description of variables. This extension has been done due to the assumption of gradual variations of the variables, by using a fuzzy analogical approach. In this paper, we interpret the model of analogical interpolative reasoning from the point of view of measures of comparison and generalize the interpolation method proposed by Bouchon-Meunier et al. (2000).

We propose a new way to generalize logical operations from the discrete classical logic to a continuous fuzzy logic, namely we propose to define derivatives for the discrete case, and then to use these derivatives to derive the continuous operations. We show that this natural approach leads to "algebraic" fuzzy operations a/spl middot/b and a+b-a/spl middot/b.

In this paper, we propose a new algorithm to infer automatically a fuzzy partition for the universe of a set of fuzzy values, when each of these values is associated with a class. This algorithm can be used in a fuzzy decision tree system to extract knowledge from a database and to construct a set of fuzzy rules. These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

We propose a new method to use an incomplete rule base with imprecise descriptions of variables. We extend classical interpolative reasoning to this case, under the assumption of graduality in variations of the variables, by using an analogical fuzzy approach.

Standard model of fuzzy computations is based on extension principle. It is known to work well, in practice, only for continuous fuzzy numbers, while producing unintuitive results when one or more arguments are discrete. It is also computationally cumbersome for all but linear operations. Another model was proposed for trapezoidal numbers only. Its operations amount to computing on the four vertices of the trapezoids, and then spanning a new trapezoid on the four resulting vertices. It is efficient, but produces fairly crude approximations for curvilinear fuzzy numbers; moreover, it is not applicable when discrete arguments are present. A model based on approximating fuzzy numbers, whether continuous or discrete, by multitrapezoidal curves and then performing coordinate-wise computations was proposed first by Ramer. It was applied to economical decision problems by his doctoral student James Wang. In this paper we place this computational method in context of fuzzy interpolations. We show how interpolation can bring quite disparate argument into a standardized form, thus permitting for efficient computations and avoid unintuitive results. Here we use the model of multiple trapezoids, but other classes of curves can be considered.

If we view fuzzy logic as a logic, i.e., as a particular case of a multi-valued logic, then one of the most natural questions to ask is whether the corresponding propositional logic is decidable, i.e., does there exist an algorithm that, given two propositional formulas F and G, decides whether these two formulas always have the same truth value. It is known that the simplest fuzzy logic, in which &=min and ∨=max, is decidable. In this paper, we prove a more general result: that all propositional fuzzy logics with algebraic operations are decidable. We also show that this result cannot be generalized further, e.g., no deciding algorithm is possible for logics in which operations are algebraic with constructive (nonalgebraic) coefficients. ©1999 John Wiley & Sons, Inc.14: 935–947, 1999

One of the most important parts of designing an expert system is elicitation of the expert's knowledge. This knowledge usually consists of facts and rules. Eliciting these rules and facts is relatively easy: the more complicated task is assigning weights (numerical or interval-valued degrees of belief) to different statements from the knowledge base. Experts often cannot quantify their degrees of belief, but they can order them (by suggesting which statements are more reliable). It is, therefore, reasonable to try to reconstruct the degrees of belief from such an ordering.In this paper, we analyze when such a reconstruction is possible, whether it lead to unique values of degrees of belief, and how computationally complicated the corresponding reconstruction problem can be. © 1998 John Wiley & Sons, Inc.

We analyze the influence of some usual linguistic modifiers, such as scalar product, normalization, Bouchon-Meunier modifiers, perturbation, and (weakening and reinforcement) power, in the process of approximate reasoning and clarify the difference between the conclusions of fuzzy modus ponens in which linguistic modifiers appear and do not appear in premises. © 1998 John Wiley & Sons, Inc.

Supervised classification has already been the subject of numerous studies in the fields of Statistics, Pattern Recognition and Artificial Intelligence under various appellations which include discriminant analysis, discrimination and concept learning. Many practical applications relating to this field have been developed. New methods have appeared in recent years, due to developments concerning Neural Networks and Machine Learning. These "hybrid" approaches share one common factor in that they combine symbolic and numerical aspects. The former are characterized by the representation of knowledge, the latter by the introduction of frequencies and probabilistic criteria. In the present study, we shall present a certain number of hybrid methods, conceived (or improved) by members of the SYMENU research group. These methods issue mainly from Machine Learning and from research on Classification Trees done in Statistics, and they may also be qualified as "rule-based". They shall be compared with other more classical approaches. This comparison will be based on a detailed description of each of the twelve methods envisaged, and on the results obtained concerning the "Waveform Recognition Problem" proposed by Breiman et al.,4 which is difficult for rule based approaches.

We have developed a new algorithm for the characterization of microcalcification clusters. Fuzzy logic is well suited to represent and to manipulate data and knowledge at different levels of the algorithm. Our algorithm is built in 3 steps: Detection and segmentation of the individual microcalcifications, measurements on the segmented microcalcifications (shape, contrast, relative localization), use of these measurements as inputs of a learning system which concludes if the current case is malignant or not. We first describe some aspects of the fuzzy segmentation we have implemented. Then we explain how we build fuzzy measurements from the segmented objects and how these measurements are manipulated into the fuzzy decision tree we are using. Finally, we present the preliminary results we obtained with our test database. © 1997 John Wiley & Sons, Inc.

We humans usually think in words; to represent our opinion about, e.g., the size of an object, it is sufficient to pick one of the few (say, five) words used to describe size (“tiny,” “small,” “medium,” etc.). Indicating which of 5 words we have chosen takes 3 bits. However, in the modern computer representations of uncertainty, real numbers are used to represent this “fuzziness.” A real number takes 10 times more memory to store, and therefore, processing a real number takes 10 times longer than it should. Therefore, for the computers to reach the ability of a human brain, Zadeh proposed to represent and process uncertainty in the computer by storing and processing the very words that humans use, without translating them into real numbers (he called this idea granularity). If we try to define operations with words, we run into the following problem: e.g., if we define “tiny” + “tiny” as “tiny,” then we will have to make a counter-intuitive conclusion that the sum of any number of tiny objects is also tiny. If we define “tiny” + “tiny” as “small,” we may be overestimating the size. To overcome this problem, we suggest to use nondeterministic (probabilistic) operations with words. For example, in the above case, “tiny” + “tiny” is, with some probability, equal to “tiny,” and with some other probability, equal to “small.” We also analyze the advantages and disadvantages of this approach: The main advantage is that we now have granularity and we can thus speed up processing uncertainty. The main disadvantage is that in some cases, when defining symmetric associative operations for the set of words, we must give up either symmetry, or associativity. Luckily, this necessity is not always happening: in some cases, we can define symmetric associative operations. © 1997 John Wiley & Sons, Inc.

We study knowledge-based systems using fuzzy logic and we focus on the representation of knowledge through linguistic variables characterized by means of fuzzy qualifications or labels. We study a new form of linguistic modifier which slightly changes the qualifications through either a weakening or a reinforcement. This modifier is an important tool for approximate reasoning for two reasons: its use is equivalent to a simple rule given in a symbolic way, avoiding computations and compatible with the fuzzy logic; it enables gradual rules to be used in the context of deduction rules and corresponds to the idea of gradual changing of category.