Interval programming models for matrix games with interval payoffs

Li, Dengfeng; Nan, Jiang-Xia; Zhang, Maojun

doi:10.1080/10556781003796622

Cited by 45 publications

(33 citation statements)

References 23 publications

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“…There exists several solution methods for them. However, in this study we use average weighted approach ( [11]) to solve equations (2) and (3) in the sense of pareto optimality. Therefore, the above two BOLPs become…”

Section: Matrix Game With Fuzzy Pay-offsmentioning

confidence: 99%

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An Alternative Approach for Solving Fuzzy Matrix Games

Seikh¹,

Nayak²,

Pal³

2015

International Journal of Mathematics and Soft Computing

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In this paper, two-person matrix games is considered whose elements of pay-off matrix are triangular fuzzy numbers (TFNs). To solve such game a new method based on α-cut of TFN is developed for each of the players. In this method, two auxiliary bi-objective linear programming (BOLP) models are derived. Then using average weighted approach these two BOLP models are decomposed into two auxiliary crisp linear programming (LP) problems. Finally, the value of the matrix game for each player is obtained by solving two corresponding auxiliary LP problems using the existing simplex method. Validity and applicability of this method are illustrated with practical example compared to existing methods.

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Section: Matrix Game With Fuzzy Pay-offsmentioning

confidence: 99%

“…Vijay et al [22,23] extended their duality results using aspiration level approach and also studied a generalized fuzzy relation approach to solve matrix games with fuzzy goals and fuzzy pay-offs. Some recent references on fuzzy matrix games are ( [14], [5], [8], [11,13]). …”

Section: Introductionmentioning

confidence: 99%

An Alternative Approach for Solving Fuzzy Matrix Games

Seikh¹,

Nayak²,

Pal³

2015

International Journal of Mathematics and Soft Computing

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“…In particular, strict competition between two parties facing interval uncertainty on outcomes or costs has generated a productive line of research in recent years. 11,[13][14][15][16]22 The paper is organized as follows. We recall in Sec.…”

Section: Introductionmentioning

confidence: 99%

Big Boss Interval Games

Gök

Brânzei

Tijs

2011

Int. J. Unc. Fuzz. Knowl. Based Syst.

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This paper introduces and studies a class of cooperative interval games suitable to model market situations with two corners where players face interval uncertainty regarding the outcome of cooperation. In one corner there is a powerful player called the big boss; the other corner contains players that need the big boss to benefit from cooperation. Various characterizations of big boss interval games are given. The interval core of a big boss interval game is explicitly described, bi-monotonic allocation schemes using interval core elements are introduced, and it is shown that each element of the interval core of a big boss interval game is extendable to such a scheme. Two value-type interval solution concepts are defined on the class of big boss interval games which generate for each such game the same interval core allocation which is extendable to a bi-monotonic interval allocation scheme.

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“…In fact, sometimes it is quite difficult for players to estimate exactly the coalition values once they form a coalition to do something together. Generally, we can use the theory and method of fuzzy games [4,5,6,7], interval games [8,9,10,11], and stochastic games [12] to deal with the lack of precision and the distortion of information.…”

Section: Introductionmentioning

confidence: 99%

Cost-Sharing of Ecological Construction Based on Trapezoidal Intuitionistic Fuzzy Cooperative Games

Liu

Zhao

2016

IJERPH

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There exist some fuzziness and uncertainty in the process of ecological construction. The aim of this paper is to develop a direct and an effective simplified method for obtaining the cost-sharing scheme when some interested parties form a cooperative coalition to improve the ecological environment of Min River together. Firstly, we propose the solution concept of the least square prenucleolus of cooperative games with coalition values expressed by trapezoidal intuitionistic fuzzy numbers. Then, based on the square of the distance in the numerical value between two trapezoidal intuitionistic fuzzy numbers, we establish a corresponding quadratic programming model to obtain the least square prenucleolus, which can effectively avoid the information distortion and uncertainty enlargement brought about by the subtraction of trapezoidal intuitionistic fuzzy numbers. Finally, we give a numerical example about the cost-sharing of ecological construction in Fujian Province in China to show the validity, applicability, and advantages of the proposed model and method.

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Interval programming models for matrix games with interval payoffs

Cited by 45 publications

References 23 publications

An Alternative Approach for Solving Fuzzy Matrix Games

An Alternative Approach for Solving Fuzzy Matrix Games

Big Boss Interval Games

Cost-Sharing of Ecological Construction Based on Trapezoidal Intuitionistic Fuzzy Cooperative Games

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