On solution of constraint matrix games under rough interval approach

Ammar, E. E.; Brikaa, M. G.

doi:10.1007/s41066-018-0123-4

Cited by 11 publications

(8 citation statements)

References 28 publications

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“…Singh et al 51 explored a study on two-stage formulation of a cost minimization solid transportation problem, where the parameters are considered as rough interval form. Ammar and Brikaa 52 considered rough interval constrained matrix games and solved such game by developing a linear programming methodology, the expected value of RIs, and the trust measure of the RIs.…”

Section: Literature Reviewmentioning

confidence: 99%

“…In the literature, we found that Ammar and Brikaa 52 proposed the linear programming technique, where the lower-lower bound, lower-upper bound, upper-lower bound, and upperupper bound of the RI value of the rough constrained matrix games are obtained by solving the derived four LPPs for each player. But there is no theoretical establishment of the methodology and the physical significance of the obtained results.…”

Section: Motivationmentioning

confidence: 99%

“…In this section, we consider a case study on the telecom market share problem and another example adapted from Li et al 41 The problems are solved with the proposed solution approaches (Approach I and Approach II). The problem is also solved using the linear programming technique described in Ammar and Brikaa 52 and obtained results are compared and analyzed.…”

Section: Numerical Illustrationsmentioning

confidence: 99%

“…In this section, the results of the case study in Section 7.1 are obtained by following the linear programming technique proposed in Ammar and Brikaa. 52 Ammar and Brikaa 52 solved constraint matrix games with rough interval pay-offs where the strategies of the players are constrained. Players have to select their mixed strategies p p p p = ( , , …, ) from convex polyhedrons, which are defined as constrained sets containing system of equations and linear inequalities.…”

Section: Comparative Analysismentioning

confidence: 99%

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Solution of matrix games with rough interval pay‐offs and its application in the telecom market share problem

Seikh

Dutta

2021

Int J Intell Syst

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Rough interval (RI) is an appropriate generalization of the crisp interval and is very much useful to express uncertain parameters or partially unknown variables when they contain dual-layer information. In real-life problems, there are many situations where players of a matrix game cannot assess their pay-offs by using fuzzy sets/intuitionistic fuzzy sets or ordinary intervals. RIs are used as an excellent tool to handle such situations. This paper explores matrix games with RI pay-offs and investigates two different solution methodologies to solve such a game. In the first approach, a pair of auxiliary linear programming problems with RI coefficients for the players has been constructed. Then each of the two auxiliary programming problems is converted into two linear programming problems with interval coefficients (LPPICs) using lower and upper approximation intervals of the RI. Finally from each LPPIC, two classical linear programming problems (LPPs) are constructed. In the second approach, the expected value technique for RI is used for transforming auxiliary mathematical programming models under the RI environment to crisp LPP. A case study on the telecom market share problem is considered to show the applicability of the proposed approaches and results are compared and analyzed with an existing method.

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Section: Literature Reviewmentioning

confidence: 99%

Section: Motivationmentioning

confidence: 99%

Section: Numerical Illustrationsmentioning

confidence: 99%

Section: Comparative Analysismentioning

confidence: 99%

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Solution of matrix games with rough interval pay‐offs and its application in the telecom market share problem

Seikh

Dutta

2021

Int J Intell Syst

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“…In recent years, many research articles examined imprecise matrix games; for example, linear programming has been adopted to solve the zero-sum two-person game with payoffs of grey numbers [14]. Ammar et al [15] studied constraint matrix games with rough interval payoffs. Bector et al [16] studied the duality fuzzy linear programming for matrix games with fuzzy payoffs and fuzzy goals.…”

Section: Introductionmentioning

confidence: 99%

Fuzzy Multi-objective Programming Approach for Constrained Matrix Games with Payoffs of Fuzzy Rough Numbers

2019

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Imprecise constrained matrix games (such as fuzzy constrained matrix games, interval-valued constrained matrix games, and rough constrained matrix games) have attracted considerable research interest. This article is concerned with developing an effective fuzzy multi-objective programming algorithm to solve constraint matrix games with payoffs of fuzzy rough numbers (FRNs). For simplicity, we refer to this problem as fuzzy rough constrained matrix games. To the best of our knowledge, there are no previous studies that solve the fuzzy rough constrained matrix games. In the proposed algorithm, it is proven that a constrained matrix game with fuzzy rough payoffs has a fuzzy rough-type game value. Moreover, this article constructs four multi-objective linear programming problems. These problems are used to obtain the lower and upper bounds of the fuzzy rough game value and the corresponding optimal strategies of each player in any fuzzy rough constrained matrix games. Finally, a real example of the market share game problem demonstrates the effectiveness and reasonableness of the proposed algorithm. Additionally, the results of the numerical example are compared with the GAMS software results. The significant contribution of this article is that it deals with constraint matrix games using two types of uncertainties, and, thus, the process of decision-making is more flexible.

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Solving zero-sum two-person game with triangular fuzzy number payoffs using new fully fuzzy linear programming models

Sharma

Das²,

Kumar

2023

OPSEARCH

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On solution of constraint matrix games under rough interval approach

Cited by 11 publications

References 28 publications

Solution of matrix games with rough interval pay‐offs and its application in the telecom market share problem

Solution of matrix games with rough interval pay‐offs and its application in the telecom market share problem

Fuzzy Multi-objective Programming Approach for Constrained Matrix Games with Payoffs of Fuzzy Rough Numbers

Solving zero-sum two-person game with triangular fuzzy number payoffs using new fully fuzzy linear programming models

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