Exact alternative optima for nonlinear optimization problems defined with maximum component objective function constrained by the Sugeno-Weber fuzzy relational inequalities

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 Sugeno - Weber family of t - norms is considered as fuzzy composition. Sugeno - Weber family of t - norms and t - conorms is one of the most applied one in various fuzzy modelling problems. Thi s family of t - norms and t - conorms was suggested by Weber for modeling intersection and union of fuzzy sets. Also, the t - conorms were suggested as addition rules by Sugeno for so - called - fuzzy measures. The resolution of the feasible region of the problem is firstly investigated when it is defined with max - Sugeno - Weber 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 sol ving 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.