Fuzzy linear optimization in the presence of the fuzzy relation inequality constraints with max–min composition

In this paper, we study the new linear objective function optimization with respect to the fuzzy relational inequalities defined by max–min composition in which fuzzy inequality replaces ordinary inequality in the constraints. Fuzzy inequalities enable us to attain the optimal points that are better solutions than those resulting from the resolution of the similar problems with Ordinary Inequality constraints (denoted by xOIxOI in this paper). We have presented an algorithm to generate such optimal solutions. Also two examples are given to illustrate the algorithm presented and some real application of this work.