To solve a fuzzy optimization problem, we need to compare fuzzy numbers. Here, we make use of our recently proposed modified Kerre’s method as an effective approach for comparison of LR fuzzy numbers. Using our new results on LR fuzzy numbers, we show that to compare two LR fuzzy numbers, we do not need to compute the fuzzy maximum of two numbers directly. We propose a new variable neighborhood search approach for solving fuzzy number quadratic programming problems by using the modified Kerre’s method. In our algorithm, a local search is performed using descent directions, found by solving five crisp mathematical programming problems. In several available methods, a fuzzy optimization problem is converted to a crisp problem, but in our proposed approach, 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 and show the effectiveness of our proposed algorithm by using the nonparametric statistical sign test.
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Ghanbari, R., Ghorbani-Moghadam, K. & Mahdavi-Amiri, N. A variables neighborhood search algorithm for solving fuzzy quadratic programming problems using modified Kerre’s method. Soft Comput 23, 12305–12315 (2019). https://doi.org/10.1007/s00500-019-03771-4
- Quadratic programming problem
- Modified Kerre’s method
- Ranking function