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
A
i
, 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.