Bernadette Bouchon-Meunier

Improving constrained clustering with active query selection

In this article, we address the problem of automatic constraint selection to improve the performance of constraint-based clustering algorithms. To this aim we propose a novel active learning algorithm that relies on a k-nearest neighbors graph and a new constraint utility function to generate queries to the human expert. This mechanism is paired with propagation and refinement processes that limit the number of constraint candidates and introduce a minimal diversity in the proposed constraints. Existing constraint selection heuristics are based on a random selection or on a min-max criterion and thus are either inefficient or more adapted to spherical clusters. Contrary to these approaches, our method is designed to be beneficial for all constraint-based clustering algorithms. Comparative experiments conducted on real datasets and with two distinct representative constraint-based clustering algorithms show that our approach significantly improves clustering quality while minimizing the number of human expert solicitations.

A comparative view of interpolation methods between sparse fuzzy rules

Several approaches have been proposed in the last few years for interpolating between sparse fuzzy rules. These proposed methods yield very different results in some cases. This is due to different views on the basic principles underlying the interpolation process. In particular, the problem can be viewed as the one of completing a partially-known mapping associating fuzzy sets with other fuzzy sets, or the one of extending the interpolation mechanism that is applicable to classical functions to fuzzily-specified ones. This paper clarifies the differences between the various methods.

Strengthening fuzzy gradual rules through “all the more” clauses

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.

Fuzzy implication operators for difference operations for fuzzy sets and cardinality-based measures of comparison

In this paper, we determine by means of fuzzy implication operators, two classes of difference operations for fuzzy sets and two classes of symmetric difference operations for fuzzy sets which preserve properties of the classical difference operation for crisp sets and the classical symmetric difference operation for crisp sets respectively. The obtained operations allow us to construct as in [B. De Baets, H. De Meyer, Transitivity-preserving fuzzification schemes for cardinality-based similarity measures, European Journal of Operational Research 160 (2005) 726–740], cardinality-based similarity measures which are reflexive, symmetric and transitive fuzzy relations and, to propose two classes of distances (metrics) which are fuzzy versions of the well-known distance of cardinality of the symmetric difference of crisp sets.

Mathematical Morphology Tools to Evaluate Periodic Linguistic Summaries

This paper considers the task of establishing periodic linguistic summaries of the form Regularly, the data take high values, enriched with an estimation of the period and a linguistic formulation. Within the framework of methods that address this task testing whether the dataset contains regularly spaced groups of high and low values with approximately constant size, it proposes a mathematical morphology MM approach based on watershed. It compares the proposed approach to other MM methods in an experimental study based on artificial data with different forms and noise types.

Modelling and management of subjective information in a fuzzy setting

Subjective information is very natural for human beings. It is an issue at the crossroad of cognition, semiotics, linguistics, and psycho-physiology. Its management requires dedicated methods, among which we point out the usefulness of fuzzy and possibilistic approaches and related methods, such as evidence theory. We distinguish three aspects of subjectivity: the first deals with perception and sensory information, including the elicitation of quality assessment and the establishment of a link between physical and perceived properties; the second is related to emotions, their fuzzy nature, and their identification; and the last aspect stems from natural language and takes into account information quality and reliability of information.

Inconsistency degree computation for possibilistic description logic: an extension of the tableau algorithm

Possibilistic description logic (PDL) is an extension of description logic based on possibilistic logic: it provides a framework to formalise knowledge allowing to encompass, model and handle uncertain information. In this paper, we consider the problem of consistency checking for PDL and propose an algorithm to compute the inconsistency degree of knowledge bases in this framework. To that aim, we present an extension of the tableau algorithm: we introduce extensions of the clash definition and completion rules to take into account the certainty associated with each formula, providing an inference procedure handling degree of certainty.

Interpretability of fuzzy linguistic summaries

This paper investigates the question of the interpretability of fuzzy linguistic summaries, both at the sentence level and at the summary level, seen as a set of sentences. The individual sentence interpretability is examined as depending both on its representativity measured by a quality degree and on its linguistic expression. Different properties at the summary level are also discussed, namely their consistency, their non-redundancy and the information they convey.

Fuzzy data mining and management of interpretable and subjective information

Fuzzy set theory offers an important contribution to data mining leading to fuzzy data mining. It enables the management of interpretable and subjective information in both input and output of the data mining process. In this paper, we discuss the notion of interpretability in fuzzy data mining and we present some references on the management of emotions as a particular kind of subjective information.

On the Paradoxical Success of Mamdani’s Minimum-Based Inference

Mamdani’s inference has an incredible success, especially in areas such as decision making and control. Yet, it is well known that it uses a min-based implication that does not verify classical boolean logic requirements.