Solution of Interval-valued Matrix Games Using Intuitionistic Fuzzy Optimization Technique: An Effective Approach

Seikh, Mijanur Rahaman; Dutta, Shibaji

doi:10.1504/ijmor.2020.10032648

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“…Malhotra et al 43 proposed a methodology to find the saddle point and the optimal value of a non-cooperative 2-player zero-sum interval-valued 2-tuple fuzzy linguistic matrix game. Very recently, Seikh and Dutta 44 developed an effective approach to solve interval-valued matrix games using intuitionistic fuzzy optimization technique by considering nonlinear membership and nonmembership functions. Verma and Kumar 45 pointed out flaws in the methods discussed in References [39,41,42,46,47] and resolved the flaws by introducing a new method, named by Gaurika method.…”

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confidence: 99%

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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