An approach to the analysis of fuzzy systems

Abstract

This paper deals with a formal description of ill-defined processes (fuzzy systems) by the use of fuzzy relational equations. It is pointed out that fuzzy relational equations form a generalized version of the difference equations widely considered in control theory. Some equivalence between these two kinds of description is presented. Basic problems of fuzzy systems e.g. identification, prediction, sensitivity and stability are shown and numerical algorithms are given. Indices of each method are introduced (especially the degree of fuzziness, the sensitivity index) which makes it possible to express the quality of each of them.