International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems

Studying comparison methods for fuzzy sets is an essential task for the good understanding of the underlying theory in this field. Most of these tools deal with fuzzy sets from the view of similarity, order relationships and so forth. In this paper however, based on a former comparison measures introduced by the authors, the so called Coherence Measures, the extension and analysis of these tools to a measurable Lebesgue set X is carried out. Furthermore we present how coherence measures could be linked to the Fishburn-Yager's ambiguity measures. Besides, two methods for constructing coherence measures, one from ambiguity measures and another from metrics on Pf(X), the set of fuzzy sets on X, are shown and exemplified by a variety of measures and metrics. Finally some illustrative examples testing the coherence measures introduced are provided.

This paper presents a new method of estimating fuzzy multivariable linear and nonlinear regression models using triangular fuzzy numbers. This estimation method is obtained by implementing a dual version of the ridge regression procedure for linear models. It allows us to perform fuzzy nonlinear regression by constructing a fuzzy linear regression in a high dimensional feature space for the data set with crisp inputs and fuzzy output. Experimental results are then presented, which indicate the performance of this algorithm.

An assessment of a set of alternatives under certain evaluation criteria has difficulty in dealing with the priority of these alternatives, especially with a lack of precise information in an uncertain environment. Fuzzy numbers are usually applied to represent the imprecise numerical measurements of different alternatives. In this study statistical data are used to derive level (1-α,1-β) interval-valued fuzzy numbers to represent unknown alternative effectiveness scores, after which, by using the compositional rule of inference and signed distance to transform the fuzzy decision making problem into crisp one, one can conveniently obtain the order of these different alternatives and subsequently obtain the best alternative. The approach presented is computationally efficiency, and its underlying concepts are simple and comprehensible. By using this extended generalized method, two cases of an organizational type of rapid-transit-system selection problem are presented as examples to illustrate the applicability of the interval-valued fuzzy numbers and ranking system for decision making. The key contribution of the method is the seamless integration of the statistical data, interval-valued fuzzy number and signed distance to analyze multicriteria decision making problem. The innovation introduced in the model concerns interval-valued fuzzy number which is recognized as a determinant of the effectiveness score in fuzzy relation matrix.

The paper deals with division situations where individual claims can vary within closed intervals. Uncertainty of claims is removed by weighting in a consistent way the upper and lower bounds of the claim intervals. Deterministic division problems with the obtained compromise claims are then considered and classical division rules from the bankruptcy literature are used to generate several procedures leading to efficient and reasonable rules for division problems under interval uncertainty of claims.

This paper deals with the problem of establishing a new class of aggregation operators, which are close to the averaging, without being necessarily idempotent. An axiomatic approach is followed through the definition of crucial properties which characterize these aggregators, the mathematical consequences are illustrated and many examples that extend some important classical averaging operators are shown.

This paper treats the problem of fitting general aggregation operators with unfixed number of arguments to empirical data. We discuss methods applicable to associative operators (t-norms, t-conorms, uninorms and nullnorms), means and Choquet integral based operators with respect to a universal fuzzy measure. Special attention is paid to k-order additive symmetric fuzzy measures.

In this paper by using the relative fuzzy topology a new kind of dynamics is considered. A method for constructing relative semi-dynamical systems is presented. Relative fixed points and relative sinks are also studied. New results on invariant sets without any similarity in usual mathematics are deduced. Furthermore an extension of the notion of conjugate relation is presented.

We show that each fuzzy (or in general L-) topological space can be represented as a fuzzy (or an L-) Chu space. Further, this representation preserves products, coproducts, tensor products, and hom-sets (together with the structures they are enriched with).

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.