M. G. Brikaa; El-Saeed Ammar; Zhoushun Zheng

Solving Bi-matrix Games in Tourism Planning Management under Rough Interval Approach

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Author(s)

M. G. Brikaa ^1,2 El-Saeed Ammar ³ Zhoushun Zheng ¹

1. School of Mathematics and Statistics, Central South University, Changsha 410083, Hunan, PR China

2. Department of Basic Science Faculty of Computers & Informatics. Suez Canal University 41522, Ismailia, Egypt

3. Department of Mathematics Faculty of Science. Tanta University, Tanta, Egypt

* Corresponding author.

DOI: https://doi.org/10.5815/ijmsc.2019.04.05

Received: 29 May 2019 / Revised: 12 Jun. 2019 / Accepted: 13 Jul. 2019 / Published: 8 Nov. 2019

Index Terms

Rough interval, Trust measure, Bilinear programming, Bi-matrix games.

Abstract

The aim of this article is to propose a novel and simple technique for solving bi-matrix games with rough intervals payoffs. Since the payoffs of the rough bi-matrix games are rough intervals, then its value is also a rough interval. In this technique, we derived four bilinear programming problems, which are used to obtain the upper lower bound, lower lower bound, lower upper bound and upper upper bound of the rough interval values of the players in rough bi-matrix games which we called in this article as 'solution space'. Moreover, the expected value operator and trust measure of rough interval have been used to find the α-trust equilibrium strategies and the expected equilibrium strategies of rough interval bi-matrix games. Finally, numerical example of tourism planning management model is presented to illustrate the methodologies adopted and solution procedure.

Cite This Paper

M. G. Brikaa, El-Saeed Ammar, Zhoushun Zheng," Solving Bi-matrix Games in Tourism Planning Management under Rough Interval Approach", International Journal of Mathematical Sciences and Computing(IJMSC), Vol.5, No.4, pp.44-62, 2019. DOI: 10.5815/ijmsc.2019.04.05

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International Journal of Mathematical Sciences and Computing (IJMSC)