Properties of $$\text{max-}*$$ fuzzy relation equations

Abstract

We extend the result of Zhang et al. (J Fuzzy Math 14:53, 2006), who discussed the finite fuzzy relation equations with max-min and max-prod composition. In this article, the max-Ã composition is used for wide family of operations Ã. In particular, families of solutions of two relation equations are compared.

The structure of solution sets of fuzzy relation equations

“…De Baets [4] determined all minimal solutions and Wang [24] gave a formula of the number of minimal solutions under the condition that all elements of its righthand side have irredundant finite join-irreducible decompositions. And many other works about solving fuzzy relation equations were published (see [1,5,8,10,12,13,14,15,16,17,19,20,22,23]). Compared with the linear algebraic systems, the main difference with fuzzy relation equations is the operations and the fundamental domain.…”