Latticized optimization problem subjected to fuzzy relational equations defined by Einstein product

In this paper, we study a latticized optimization problem constrained by special system of fuzzy relational equations (FRE) in which fuzzy t-norms are considered as Einstein product. First, the resolution of the feasible solutions set is investigated when it is defined with max-Einstein product composition and a necessary and sufficient condition is presented for determining the feasibility. Then, based on some theoretical properties of the problem, an algorithm is presented for solving this nonlinear problem. It is proved that the algorithm can find the exact optimal solution and an example is presented to illustrate the proposed algorithm.

Keywords:

Fuzzy relational equations , nonlinear optimization , Einstein product t-norm , latticized programming.