A variable neighborhood search algorithm for solving fuzzy number linear programming problems using modified Kerre’s method

Abstract

To solve a fuzzy linear program, we need to compare fuzzy numbers. Here, we make use of our recently proposed modified Kerre\\\\\\'s method for comparison of LR fuzzy numbers. We give some new results on LR fuzzy numbers and show that to compare two LR fuzzy numbers, we do not need to compute the fuzzy maximum of two numbers directly. Using the modified Kerre\\\\\\'s method, we propose a new variable neighborhood search -VNS- algorithm for solving fuzzy number linear programming problems. In our algorithm, the local search is defined based on descent directions, which are found by solving four crisp mathematical programming problems. In several methods, a fuzzy optimization problem is converted to a crisp problem but in our proposed method, using our modified Kerre\\\\\\'s method, the fuzzy optimization problem is solved directly, without changing it to a crisp program. We give some examples to compare the performance of our proposed algorithm with some available methods. We show the effectiveness of our proposed algorithm by using the non-parametric statistical sign test.