SOLUTION-SET INVARIANT MATRICES AND VECTORS IN FUZZY RELATION INEQUALITIES BASED ON MAX-AGGREGATION FUNCTION COMPOSITION

Abstract

Fuzzy relation inequalities based on max-F composition are discussed, where F is a binary aggregation on [0,1]. For a fixed fuzzy relation inequalities system $ A circ^{F}textbf{x}leqtextbf{b}$, we characterize all matrices $ A^{'} $ For which the solution set of the system $ A^{' } circ^{F}textbf{x}leqtextbf{b}$ is the same as the original solution set. Similarly, for a fixed matrix $ A $, the possible perturbations $ b^{'} $ of the right-hand side vector $ b $ not modifying the original solution set are determined. Several illustrative examples are included to clarify the results of the paper.