International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems

We first argue that a very important class of fuzzy functions in multivariate non-linear fuzzy regression is the multivariate fuzzy polynomials. Given some data, generated by a multivariate fuzzy function, our evolutionary algorithm searches our library of multivariate fuzzy polynomials for the one that best fits this data. Tests of our multivariate non-linear fuzzy regression package are given when the multivariate fuzzy function is a multivariate fuzzy polynomial and all the fuzzy numbers are non-negative.

In order to cope with the ambiguity of spatial relative position concepts, we propose a new definition of the relative position between two objects in a fuzzy set framework. This definition is based on a morphological and fuzzy pattern matching approach, and consists in comparing an object to a fuzzy landscape representing the degree of satisfaction of a directional relationship to a reference object. We detail its formal properties, and show that it is flexible and fits the intuition. Moreover, it applies also in 3D, and for fuzzy objects issued from images. It can be used for structural pattern recognition in images under imprecision.

This paper is devoted to the study of fuzzy weak orders, fuzzy quasi orders and fuzzy quasi-transitive relations in the context of group decision making. Transitivity is modelled by means of the minimum operator. In analogy to the numerical representation of classical weak orders, we consider a particular class of fuzzy weak orders that can be constructed from a numerical evaluation by means of Gödel implicator. We fully characterize the fuzzy relations that can be written as the intersection or union of a finite family of these so-called Gödel representable fuzzy weak orders.

This paper deals with the problem of ranking a set of alternatives, represented by triangular fuzzy numbers, in decision-making situations. A new approach is followed through the definition of some axiomatic requirements which represent the essential properties that characterize an arbitrary ranking function. A notion of degree of risk associated to every ranking function is proposed to discriminate equivalent alternatives.

Sonar sensors are widely used in mobile robots applications such as navigation, map building, and localization. The performance of these sensors is affected by the environmental phenomena, sensor design, and target characteristics. Therefore, the readings obtained from these sensors are uncertain. This uncertainity is often modeled by using Probability Theory. However, the probablistic approach is valid when the available knowledge is precise which is not the case in sonar readings. In this paper, the behavior of sonar readings reflected from walls and corners are studied, then new models of angular uncertainty and radial imprecision for sonar readings obtained from corners and walls are proposed. These models are represented by using Possibility Theory, mainly possibility distributions.

This section is maintained by Vladik Kreinovich. Please send you abstract (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.