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

Document Type: Research Paper

Authors

2 Department of Statistics, Faculty of Mathematics and Computer Sciences, Shahid Bahonar University of Kerman, Kerman, Iran

3 Slovak University of Technology in Bratislava, Faculty of Civil Engineering, Radlinskeho 11, 810 05 Bratislava, Slovak Republic

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 $A \circ^{F}\textbf{x}\leq\textbf{b}$, we characterize all matrices $A^{'}$ For which the solution set of the system $A^{' } \circ^{F}\textbf{x}\leq\textbf{b}$ 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.

Keywords

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