Model and algorithm for bilevel linear programming with fuzzy decision variables and multiple followers

Volume 10, Issue 4, pp 2162--2170 http://dx.doi.org/10.22436/jnsa.010.04.68

Publication Date: April 20, 2017 Submission Date: July 11, 2016

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Authors

Shengyue Deng - School of Science, Hunan University of Technology, Zhuzhou, Hunan 412008, P. R. China. - Department of Mathematics and Computational Science, Xiangtan University, Xiangtan, Hunan 411105, P. R. China. Jintao Tan - School of Science, Hunan University of Technology, Zhuzhou, Hunan 412008, P. R. China. Chengjie Xu - School of Science, Hunan University of Technology, Zhuzhou, Hunan 412008, P. R. China. Xinfan Wang - School of Science, Hunan University of Technology, Zhuzhou, Hunan 412008, P. R. China.

Abstract

The bilevel linear programming with fuzzy decision variables and multiple followers model (MFFVBLP) is firstly established and investigated, and the model optimal solution is shown to be equivalent to the optimal solution of the bilevel linear programming with multiple followers by using fuzzy structured element theory in this paper. The optimal solution of this model is found out by adopting the Kuhn-Tucker approach. An illustrative example is provided to demonstrate the feasibility and efficiency of the proposed method for solving the MFFVBLP model.

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Keywords

• Bilevel linear programming
• fuzzy decision variables
• multiple followers
• fuzzy structured element.

MSC

•  90C70
•  93B40

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