International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems

The concept of entropy of a discrete fuzzy measure has been recently introduced in two different ways. A first definition was proposed by Marichal in the aggregation framework, and a second one by Yager in the framework of uncertain variables. We present a comparative study between these two proposals and point out their properties. We also propose a definition for the entropy of an ordinal fuzzy measure, that is, a fuzzy measure taking its values in an ordinal scale in the sense of measurement theory.

Comparison tools for fuzzy sets are an indispensable topic. Mostly of this tools deal with fuzzy sets from the view of similarity, order and so forth. A comparison tool based on coherence intuitive concept is presented. For constructing this concept, one start from three basics properties. A development of this tool is presented, equally coherence measures are connected with Fishburn-Yager's ambiguity measures. Two methods for constructing coherence measures are shown: one from ambiguity measures and other from metrics on [0, 1]^m. Concretely, has been constructed various coherence measures from different ambiguity measures and different metrics. Equivalency between some coherence measures has been shown. This paper finish with numeric examples presented in order to check coherence measures displayed.

First a balancing property on a fuzzy measure is introduced. After that, the conditions of when an additive fuzzy measure is balanced are given and similar results are presented for 0-1 and S–decomposable fuzzy measures where S is a continuous t–conorm. Moreover, the concept of distance between two additive fuzzy measures is presented and some results related to the distance and the balancing property are developed.

In this paper we study the relations between divergence measures of two fuzzy sets and other well-known functions, namely aggregation operations and measures of fuzziness. We will show that these functions can be related. Therefore, we study some consequences of these properties as an application; indeed, we obtain some special cases of divergence measures whenever the aggregation operation fulfils some properties. Another application is the translation of some properties of divergence measures to measures of fuzziness.

The main aim of this paper is to present the properties of the (sup-)composition based on a general aggregation operator defined with the most useful conditions and analyze some properties about the pseudocomplement (associated with the aggregation) and the (inf-)composition based on it, to show that these compositions have analogous properties to the based on t-norms.

To cover almost all known Lebesgue type integrals constructed by means of pseudo-operations, the (S, U)-integral based on a t-conorm S, a uninorm (or t-norm) U and an S-measure (decomposable measure) is introduced and its properties are studied. Also its relationship to aggregation operators is discussed.

Representational issues of preferences in the framework of a possibilistic ordinal decision model under uncertainty were introduced by Dubois and Prade a few years ago. In this framework, finite, linear, commensurate uncertainty and preference scales are assumed and decisions are ranked according to their expected utility in terms of Sugeno integrals. In this paper we generalise the model by allowing (i) to measure uncertainty and preferences on finite, distributive lattices with involution, and (ii) to formulate the utility expectations in terms of generalized Sugeno integrals where t-norms and t-conorms play a role. For these generalized utility functions we provide axiomatic characterisations. Finally, we also briefly comment the case of working with belief states that may be partially inconsistent, which is usual in case-based decision making problems or when several inconsistent sources of information are available.

We introduce an objective function-based fuzzy clustering technique that assigns one influence parameter to each single data variable for each cluster. Our method is not only suited to detect structures or groups of data that are not uniformly distributed over the structure's single domains, but gives also information about the influence of individual variables on the detected groups. In addition, our approach can be seen as a generalization of the well-known fuzzy c-means clustering algorithm.

This article aims at showing that supervised and unsupervised learnings are not competitive, but complementary methods. We propose to use a fuzzy clustering method with ambiguity rejection to guide the supervised learning performed by bayesian classifiers. This method detects ambiguous or mixed areas of a learning set. The problem is seen from the multi-decision point of view (i.e. several classification modules). Each classification module is specialized on a particular region of the feature space. These regions are obtained by fuzzy clustering and constitute the original data set by union. A classifier is associated with each cluster. The training set for each classifier is then defined on the cluster and its associated ambiguous clusters. The overall system is parallel, since different classifiers work with their own training data clusters. The algorithm makes possible the adaptive classifier selection in the sense that the fuzzy clustering with ambiguity rejection gives adapted training data regions of the feature space. The decision making is the fusion of outputs from the most adapted classifiers.

This section is maintained by Vladik Kreinovich. Please send your abstracts (or copies of papers that you want to see reviewed here) to vladik@cs.utep.edu, or by regular mail to: Vladik Kreinovich, Department of Computer Science, University of Texas at El Paso, El Paso, TX 79968, USA.