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

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Abstract

Many situations involve uncertainty, which we can handle with the help of triangular fuzzy numbers (TFNs). Many scenarios arise in which players in a matrix game cannot reliably estimate their payoffs using crisp numbers, as in real-world scenarios. In these circumstances, TFNs are helpful in game theory. Solving a zero-sum two-player game when all the decision variables and parameters are fuzzy is a worldwide topic of interest to scholars. This article presents a novel solution methodology to solve the zero-sum two-person fully fuzzy matrix game. The payoff matrix, decision variables, and strategies are all taken as TFNs. Two subsidiaries’ fully fuzzy linear programming problem (FFLPP) models for both players have been developed to achieve the objective. These two FFLPP models are converted into crisp linear programming problems (LPPs). This procedure uses a ranking approach to the objective function and introduces fuzzy surplus and fuzzy slack variables in constraints. These crisp LPPs are then solved using TORA software (2.0 version) to get optimal strategies and results. The proposed solution methodology in the paper is followed by a real-world example, ‘Plastic Ban Problem’, and two other examples to prove its applicability and validity.

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Authors and Affiliations

  1. Department of Mathematics, University of Rajasthan, Jaipur, 302004, India

    Gaurav Sharma & Ganesh Kumar

  2. Department of Revenue, Ministry of Finance, New Delhi, India

    Sapan Kumar Das

  3. Department of Mathematics, Acharya Narendra Dev College, University of Delhi, New Delhi, 110007, India

    Gaurav Sharma

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  1. Gaurav Sharma
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  2. Sapan Kumar Das
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  3. Ganesh Kumar
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Correspondence to Ganesh Kumar.

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Sharma, G., Das, S.K. & Kumar, G. Solving zero-sum two-person game with triangular fuzzy number payoffs using new fully fuzzy linear programming models. OPSEARCH 60, 1456–1487 (2023). https://doi.org/10.1007/s12597-023-00642-3

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