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

Author

Listed:
  • Gaurav Sharma

    (University of Rajasthan
    University of Delhi)

  • Sapan Kumar Das

    (Ministry of Finance)

  • Ganesh Kumar

    (University of Rajasthan)

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.

Suggested Citation

  • Gaurav Sharma & Sapan Kumar Das & Ganesh Kumar, 2023. "Solving zero-sum two-person game with triangular fuzzy number payoffs using new fully fuzzy linear programming models," OPSEARCH, Springer;Operational Research Society of India, vol. 60(3), pages 1456-1487, September.
    • Handle: RePEc:spr:opsear:v:60:y:2023:i:3:d:10.1007_s12597-023-00642-3
    DOI: 10.1007/s12597-023-00642-3
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    References listed on IDEAS

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    1. R. E. Bellman & L. A. Zadeh, 1970. "Decision-Making in a Fuzzy Environment," Management Science, INFORMS, vol. 17(4), pages 141-164, December.
    2. Sapan Kumar Das & T. Mandal & Diptiranjan Behera, 2019. "A new approach for solving fully fuzzy linear programming problem," International Journal of Mathematics in Operational Research, Inderscience Enterprises Ltd, vol. 15(3), pages 296-309.
    3. Li, Deng-Feng, 2012. "A fast approach to compute fuzzy values of matrix games with payoffs of triangular fuzzy numbers," European Journal of Operational Research, Elsevier, vol. 223(2), pages 421-429.
    4. Ankan Bhaumik & Sankar Kumar Roy & Gerhard Wilhelm Weber, 2020. "Hesitant interval-valued intuitionistic fuzzy-linguistic term set approach in Prisoners’ dilemma game theory using TOPSIS: a case study on Human-trafficking," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 28(2), pages 797-816, June.
    5. El-Saeed Ammar & M. G. Brikaa & Entsar Abdel-Rehim, 2019. "A study on two-person zero-sum rough interval continuous differential games," OPSEARCH, Springer;Operational Research Society of India, vol. 56(3), pages 689-716, September.
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