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Bimatrix games under dense fuzzy environment and its application to natural disaster management

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Abstract

The concept of dense fuzzy sets instigates decision-makers to reduce the fuzziness of information. Occasionally, players are bound to change their predefined strategies as per the requirements of the circumstances in bimatrix game problems. Such irregular incidents provoke decision-makers to modify the payoffs of a bimatrix game. So, to deal with such irregularities, in this paper, we consider the payoffs of a bimatrix game in the form of dense fuzzy lock sets. Initially, considering players’ confidence level towards the information, we define a new defuzzification function, viz., weighted average defuzzification function (WADF). Later, we execute an auxiliary dense fuzzy non-linear programming problem to find the nash equilibrium strategies along with the value of the game for each player. Utilizing the proposed WADF, we transform the dense fuzzy non-linear programming problem into an equivalent crisp non-linear programming problem. Then we solve the reduced problem for different trials using the software MATHEMATICA 9.0. There are two vital observations of the present problem. One of them is the gradual increment of the value of the game with the increment of players’ confidence level towards the information at a fixed trial. Another fact is the significant changes in the value of the game occurred with the number of trials at a certain confidence level. Finally, to check the efficacy and the cogency of the methodology, we discuss the natural disaster management problem in the dense fuzzy scenario.

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Acknowledgements

The authors would like to acknowledge the Editor-in-Chief Prof. Derong Liu, and the anonymous learned reviewers for their constructive criticisms, invaluable suggestions, and cordial supports, which have been helpful to generate a better version of the present work.

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

    Shuvasree Karmakar & Mijanur Rahaman Seikh

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

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Karmakar, S., Seikh, M.R. Bimatrix games under dense fuzzy environment and its application to natural disaster management. Artif Intell Rev 56, 2241–2278 (2023). https://doi.org/10.1007/s10462-022-10220-6

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