Exact optimal solutions for the Latticized-Dombi FRI optimization problems

In this paper, we study a latticized optimization problem with fuzzy relational inequality constraints where the feasible region is formed as the intersection of two inequality fuzzy systems and Dombi family of t-norms is considered as fuzzy composition. Dombi family of t-norms includes a parametric family of continuous strict t-norms, whose members are increasing functions of the parameter. This family of t-norms covers the whole spectrum of t-norms when the parameter is changed from zero to infinity. The resolution of the feasible region of the problem is firstly investigated when it is defined with max-Dombi 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.

کلیدواژه ها:

Fuzzy relation ، fuzzy relational inequality ، nonlinear optimization ، fuzzy compositions and t-norms.