Latticized-Hamacher optimization problem subject to fuzzy relational equations

Hamacher family of t-norms is a parametric family of continuous strict t-norms, whose members are decreasing functions of the parameter. 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 the members of the Hamacher family. First, the resolution of the feasible solutions set is investigated when it is defined with max-Hamacher 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 , Hamacher t-norm , Latticized programming