Latticized optimization problem subjected to the intersection oftwo fuzzy relational inequalities defined by Yager family of tnorms

In this paper, we study a latticized optimization problem with fuzzy relational inequality constraintswhere the feasible region is formed as the intersection of two inequality fuzzy systems and Yager familyof t-norms is considered as fuzzy composition. The resolution of the feasible region of the problem isfirstly investigated when it is defined with max-Yager composition and a necessary and sufficientcondition is presented for determining the feasibility. An algorithm is presented for solving this nonlinearproblem. It is proved that the algorithm can find the exact optimal solution and an example is presented toillustrate the proposed algorithm.

Keywords:

Fuzzy relation , fuzzy relational inequality , nonlinear optimization , fuzzy compositionsand t-norms.