A Smoothing Approach for Minimizing A Linear Function Subject to Fuzzy Relation Inequalities with Addition–Min Composition

Abstract

This paper mainly focuses on minimizing a linear function subject to fuzzy relation inequalities with addition–min composition. Although the problem has been proved to be equivalent to a linear programming, it is still difficult to efficiently solve when the numbers of constrains and variables come to about 200. In this paper, we devotes to constructing a smoothing approach for solving approximate solutions of the problem. Utilizing maximum entropy method, we approximate the constraints by continuously differentiable functions and prove that any cluster of an approximate solution sequence is an optimal point of the original problem. Numerical experiments show that the error of the approximate solutions is within a reasonable range. At the same time, compared to the linear programming approach, the smoothing approach costs much less computation time, especially for large-scale problems.