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Credibility equilibrium strategy for matrix games with payoffs of triangular dense fuzzy lock sets

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Abstract

Dense fuzzy lock set (DFLS) is one of the special extensions of fuzzy sets. It includes learning frequencies that have a significant function to reduce the fuzziness of information. In a matrix game, occasionally the players are urged to change their strategies to manage the circumstances. In such a situation, players may estimate the payoff values as DFLSs to make the problem more realistic. Here our prime intent is to find the credibility equilibrium strategies of matrix games with payoffs of triangular dense fuzzy lock sets (TDFLSs). To do this, we define the possibility, necessity, and credibility measures of TDFLSs along with their properties. Then we introduce the possibility, necessity, and credibility expectations of TDFLSs. Utilizing the credibility expectation we develop two linear programming models to find the credibility equilibrium strategies for the players, and the value of the game. One remarkable point of this methodology is that with the increment of the player’s learning frequencies the value of the game rises gradually. Finally, two real-world problems: a market share problem and strike policy problem are illustrated to verify the cogency and applicability of the rendered methodology.

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Acknowledgements

The authors would like to thank the anonymous scholarly reviewers for their earnest support, active opinions, and productive suggestions, which have been crucial to building a better version of the present article.

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Authors and Affiliations

  1. Department of Mathematics, Kazi Nazrul University, Asansol, 713 340, India

    Mijanur Rahaman Seikh & Shuvasree Karmakar

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  1. Mijanur Rahaman Seikh
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  2. Shuvasree Karmakar
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Correspondence to Mijanur Rahaman Seikh.

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Seikh, M.R., Karmakar, S. Credibility equilibrium strategy for matrix games with payoffs of triangular dense fuzzy lock sets. Sādhanā 46, 158 (2021). https://doi.org/10.1007/s12046-021-01666-5

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  • DOI: https://doi.org/10.1007/s12046-021-01666-5

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