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Solving Fuzzy Optimization Problems Using Shapley Values and Evolutionary Algorithms

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  • Hsien-Chung Wu

    (Department of Mathematics, National Kaohsiung Normal University, Kaohsiung 802, Taiwan)

Abstract

The fusion of evolutionary algorithms and the solution concepts of cooperative game theory is proposed in this paper to solve the fuzzy optimization problems. The original fuzzy optimization problem is transformed into a scalar optimization problem by assigning some suitable coefficients. The assignment of those coefficients is frequently determined by the decision-makers via their subjectivity, which may cause some biases. In order to avoid these subjective biases, a cooperative game is formulated by considering the α -level functions of the fuzzy objective function. Using the Shapley values of this formulated cooperative game, the suitable coefficients can be reasonably set up. Under these settings, the transformed scalar optimization problem is solved to obtain the nondominated solution, which will depend on the coefficients. In other words, we shall obtain a bunch of nondominated solutions depending on the coefficients. Finally, the evolutionary algorithms are invoked to find the best nondominated solution by evolving the coefficients.

Suggested Citation

  • Hsien-Chung Wu, 2023. "Solving Fuzzy Optimization Problems Using Shapley Values and Evolutionary Algorithms," Mathematics, MDPI, vol. 11(24), pages 1-26, December.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:24:p:4871-:d:1294062
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    References listed on IDEAS

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    2. Rodica Branzei & Dinko Dimitrov & Stef Tijs, 2008. "Models in Cooperative Game Theory," Springer Books, Springer, edition 0, number 978-3-540-77954-4, July.
    3. U. M. Pirzada & V. D. Pathak, 2013. "Newton Method for Solving the Multi-Variable Fuzzy Optimization Problem," Journal of Optimization Theory and Applications, Springer, vol. 156(3), pages 867-881, March.
    4. Dipankar Chakraborty & Dipak Kumar Jana & Tapan Kumar Roy, 2016. "A new approach to solve fully fuzzy transportation problem using triangular fuzzy number," International Journal of Operational Research, Inderscience Enterprises Ltd, vol. 26(2), pages 153-179.
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