Paper Info
Title
Alfa-cut based linear programming methodology for constrained matrix games with payoffs of trapezoidal fuzzy numbers
Abstract
The purpose of this paper is to develop an effective methodology for solving constrained matrix games with payoffs of trapezoidal fuzzy numbers (TrFNs), which are a type of two-person non-cooperative games with payoffs expressed by TrFNs and players' strategies being constrained. In this methodology, it is proven that any Alfa-constrained matrix game has an interval-type value and hereby any constrained matrix game with payoffs of TrFNs has a TrFN-type value. The auxiliary linear programming models are derived to compute the interval-type value of any Alfa-constrained matrix game and players' optimal strategies. Thereby the TrFN-type value of any constrained matrix game with payoffs of TrFNs can be directly obtained through solving the derived four linear programming models with data taken from only 1-cut and 0-cut of TrFN-type payoffs. Validity and applicability of the models and method proposed in this paper are demonstrated with a numerical example of the market share game problem.
Year
DOI
Venue
2013
10.1007/s10700-012-9148-3
FO & DM
Keywords
Field
DocType
Fuzzy game theory,Group decision making,Interval computation,Linear programming,Algorithm
Discrete mathematics,Mathematical economics,Mathematical optimization,Linear programming,Normal-form game,Symmetric game,Interval arithmetic,Fuzzy number,Market share,Mathematics,Group decision-making,Outcome (game theory)
Journal
Volume
Issue
ISSN
12
2
1568-4539
Citations 
PageRank 
References 
4
0.44
6
Authors
2
Name
Order
Citations
PageRank
Deng-Feng Li196846.12
Fang-Xuan Hong2121.01