Parameterized bilinear programming methodology for solving triangular intuitionistic fuzzy number bimatrix games

Article type: Research Article

Authors: Yang, Jie^a | Li, Deng-Feng^{b; *} | Lai, Li-Bang^{c; *}

Affiliations: [a] College of Management, Fujian Agriculture and Forestry University, Fuzhou, China | [b] School of Economics and Management, Fuzhou University, Fuzhou, Fujian, China | [c] Fujian Chuanzheng Communications College, Fuzhou, China

Correspondence: [*] Corresponding author. Deng-Feng Li, School of Economics and Management, Fuzhou University, Fuzhou, Fujian 350108, China. Tel./Fax: +86 0591 83768427; E-mail: lidengfeng@fzu.edu.cn.

Correspondence: [*] Corresponding author, Li-Bang Lai, Fujian Chuanzheng Communications College, Fuzhou 350007, China. Tel.: +86 13599057876; E-mail: lailibang@126.com.

Abstract: The aim of this paper is to develop a new methodology for solving bimatrix games with payoffs of triangular intuitionistic fuzzy numbers (TIFNs), which are called TIFN bimatrix games for short. In this methodology, we define the concepts of the value-index and ambiguity-index and hereby develop a difference-index based ranking method, which is proven to be a total order. The parameterized bilinear programming models are derived from a pair of auxiliary TIFN mathematical programming models, which are used to determine solutions of TIFN bimatrix games. Validity and applicability of the models and method proposed in this paper are illustrated with a practical example.

Keywords: Bimatrix games, triangular intuitionistic fuzzy numbers, ranking, bilinear programming, fuzzy set

DOI: 10.3233/IFS-162125

Journal: Journal of Intelligent & Fuzzy Systems, vol. 31, no. 1, pp. 115-125, 2016