Study On Smoothing Algorithm For Optimization Of Fuzzy Relation Inequality Constraint Of Max-product Operator

In this paper,the linear objective function minimization problem with fuzzy relation inequality constraint of max-product operator is investigated,which mainly includes the following two parts:1.An approximation problem is constructed by smoothing the constraint functions.We prove that the feasible region and the optimal solution of the approximation problem converge to the feasible region and the optimal solution of the original problem,respectively.2.Based on the smoothing approximation,we construct an algorithm and verify the effectiveness of the smoothing algorithm through numerical experiments.Numerical experiments show that the error of the approximate solution is within a reasonable range.At the same time,compared with the branch and bound method,the smoothing method takes much less time to calculate,especially for medium and large-scale problems.