Some theoretical aspects of fuzzy-relation equations describing fuzzy systems

Abstract This paper contains some theoretical results on fuzzy-relation equations and applications to analysis of fuzzy systems as well as identification and control problems. If Ai, 1 ⩽ i ⩽ k, are fuzzy inputs, B is a fuzzy output, and R is a fuzzy relation describing the system, the above problems are illustrated by means of a max-min multidimensional equation of type B = A 1 … A k R . Furthermore, we investigate some properties of fuzzy systems described by fuzzy-relation equations, focusing our attention on energy and entropy measures of fuzziness of solutions of the class of equations under discussion.