## An Algorithm for Solving Fuzzy Relation Programming with the Max-T Composition Operator

## An Algorithm for Solving Fuzzy Relation Programming with the Max-T Composition Operator

##
*A. A. Molai*

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## Abstract

This paper studies the problem of minimizing a linear objective function subject to max-T fuzzy relation equation constraints where T is a special class of pseudo-t-norms. Some suﬃcient conditions are presented for determination of its optimal so¬lutions. Some procedures are also suggested to simplify the original problem. Some suﬃcient conditions are given for uniqueness of its optimal solution. Finally, an algo¬rithm is proposed to ﬁnd its optimal solution.

## Keywords

Fuzzy relation equations; Max-T composition; Maximum solution; Minimal solution; Fuzzy optimization; Optimal solution.