A revised simplex method of solving degenerate fuzzy number linear programming problems

Article type: Research Article

Authors: Zhong, Yi-hua^a | Jia, Yan-lin^{a; b; *} | Zhao, Jiao^a | Lin, Xu-xu^a | Yang, Yan^a

Affiliations: [a] School of Science, Southwest Petroleum University, Chengdu, Sichuan, China | [b] Department of Genenal Education, Chengdu Neusoft University, Chengdu, Sichuan, China

Correspondence: [*] Corresponding author. Yan-lin Jia, Department of Genenal Education, Chengdu Neusoft University, Chengdu, Sichuan 611844, China. Tel.: +86 028 64888454; E-mail: [email protected].

Abstract: The focus of this paper is on solving degenerate fuzzy number linear programming problems. A revised fuzzy simplex method is proposed, which can deal with this issue. First, the degenerate fuzzy number linear programming is defined and a new problem related to the original problem is constructed. Then, combined with the ranking function, some relationships between the optimal solution of the new problem and that of the original problem are given and proved. Furthermore, we propose a revised fuzzy simplex method through improving the method of selecting the leaving basic variable, which can successfully find the optimal solution of the original degenerate problem. Finally, to compare the existing method and illustrate our method, we solve one numerical example.

Keywords: Fuzzy number linear programming, fuzzy simplex method, degeneracy, ranking function, trapezoidal fuzzy number

DOI: 10.3233/IFS-151689

Journal: Journal of Intelligent & Fuzzy Systems, vol. 29, no. 5, pp. 2139-2146, 2015