Solving fuzzy fractional programming problems by VNS algorithm using modified Kerre's inequality

Here, we propose a new variable neighbourhood search (VNS) algorithm for solving fractional fuzzy number linear programming problems (FFNLPPs). We make use of modified Kerre’s inequality for comparison of LR fuzzy numbers. In our proposed algorithm, we introduced a new local search defined based on descent directions, which are found by solving four crisp mathematical programming problems. In several methods, a fuzzy fractional optimization problem is converted to a crisp problem. Still, in our proposed method, using modified Kerre’s inequality, the fuzzy optimization problem is solved directly, without changing it to a crisp program. To show the effectiveness of our method, we compare our proposed algorithm with other available methods.