LP Problems on the max - Fuzzy o‎r inequalities systems

In this paper, optimization of a linear objective function with fuzzy relational inequality constraints is investigated whereby the feasible region is formed as the intersection of two inequality fuzzy systems and Fuzzy o‎r operator is considered as fuzzy composition. It is shown that a lower bound is always attainable for the optimal objective value. Also, it is proved that the optimal solution of the problem is always resulted from the unique maximum solution and a minimal solution of the feasible region. An algorithm is presented to solve the problem and an example is described to illustrate the algorithm.