Paper Info
Title
Solving constrained matrix games with payoffs of triangular fuzzy numbers
Abstract
Constrained matrix games with payoffs of triangular fuzzy numbers (TFNs) are a type of matrix games with payoffs expressed by TFNs and sets of players' strategies which are constrained. So far as we know, no study have yet been attempted for constrained matrix games with payoffs of TFNs since there is no effective way to simultaneously incorporate the payoffs' fuzziness and strategies' constraints into classical and/or fuzzy matrix game methods. The aim of this paper is to develop an effective methodology for solving constrained matrix games with payoffs of TFNs. In this methodology, we introduce the concepts of Alpha-constrained matrix games for constrained matrix games with payoffs of TFNs and the values. By the duality theorem of linear programming, it is proven that players' gain-floor and loss-ceiling always have a common interval-type value and hereby any Alpha-constrained matrix game has an interval-type value. Moreover, using the representation theorem for the fuzzy set, it is proven that any constrained matrix game with payoffs of TFNs always has a TFN-type fuzzy value. The auxiliary linear programming models are derived to compute the lower and upper bounds of the interval-type value and optimal strategies of players for any Alpha-constrained matrix game. In particular, the mean and the lower and upper limits of the TFN-type fuzzy value of any constrained matrix game with payoffs of TFNs can be directly obtained through solving the derived three linear programming models with data taken from only 1-cut and 0-cut of payoffs. Hereby the TFN-type fuzzy value of any constrained matrix game with payoffs of TFNs are easily computed. The proposed method in this paper is compared with other methods and its validity and applicability are illustrated with a numerical example.
Year
DOI
Venue
2012
10.1016/j.camwa.2011.12.009
Computers & Mathematics with Applications
Keywords
Field
DocType
alpha-constrained matrix game,fuzzy set,interval-type value,matrix game,linear programming,auxiliary linear programming model,tfn-type fuzzy value,triangular fuzzy number,common interval-type value,fuzzy matrix game method,group decision making,interval computation,algorithm
Mathematical optimization,Mathematical economics,Duality (mathematics),Fuzzy logic,Fuzzy set,Linear programming,Symmetric game,Interval arithmetic,Fuzzy number,Mathematics,Outcome (game theory)
Journal
Volume
Issue
ISSN
64
4
0898-1221
Citations 
PageRank 
References 
8
0.57
13
Authors
2
Name
Order
Citations
PageRank
Deng-feng Li1111569.00
Fang-Xuan Hong2121.01