Solving the fully fuzzy bilevel linear programming problem through deviation degree measures and a ranking function method
type: Item
instance of: scholarly article
title: Solving the fully fuzzy bilevel linear programming problem through deviation degree measures and a ranking function method
zbMATH Open document ID: 1400.90321
DOI: 10.1155/2016/7069804
author: Aihong Ren
published in: Mathematical Problems in Engineering
publication date: 2018-10-12T00:00:00Z
review text: Summary: This paper is concerned with a class of fully fuzzy bilevel linear programming problems where all the coefficients and decision variables of both objective functions and the constraints are fuzzy numbers. A new approach based on deviation degree measures and a ranking function method is proposed to solve these problems. We first introduce concepts of the feasible region and the fuzzy optimal solution of a fully fuzzy bilevel linear programming problem. In order to obtain a fuzzy optimal solution of the problem, we apply deviation degree measures to deal with the fuzzy constraints and use a ranking function method of fuzzy numbers to rank the upper and lower level fuzzy objective functions. Then the fully fuzzy bilevel linear programming problem can be transformed into a deterministic bilevel programming problem. Considering the overall balance between improving objective function values and decreasing allowed deviation degrees, the computational procedure for finding a fuzzy optimal solution is proposed. Finally, a numerical example is provided to illustrate the proposed approach. The results indicate that the proposed approach gives a better optimal solution in comparison with the existing method.
Mathematics Subject Classification ID: 90C70
zbMATH DE Number: 6953502
MaRDI profile type: Publication
Wikidata QID: Q59141133
full work available at URL: https://doi.org/10.1155/2016/7069804
OpenAlex ID: W2338717834
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description: scientific article; zbMATH DE number 6953502