Constrained Optimization With Max-Average Fuzzy Relational Inequality

This paper mainly studies the constrained optimization problem of fuzzy relation inequalities with max-average composition.The optimizations of quadratic objective function under the constraint of such fuzzy relation inequalities are considered.To our best knowledge,most methods for solving this kind of problems are heuristic algorithms,by which the solutions may not the optimal ones for the original problem.In this paper,based on the smoothing of the constraint function with max-average operator,an approximate function of the constraint function is constructed according to the maximum entropy method,and an approximation problem of the original problem is established.The convergences of feasible domain,optimal value solved by the new approximation algorithm to that of the original problem are proved.Finally,the feasibility and effectiveness of the algorithm are verified by examples and numerical experiments.