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Enhancing Decomposition Approach for Solving Multi-Objective Dynamic Non-Linear Programming Problems Involving Fuzziness

Author

Listed:
  • Pavan Kumar

    (School of Advanced Science and Languages, VIT Bhopal University, Sehore 466116, India)

  • Hamiden Abd El-Wahed Khalifa

    (Department of Mathematics, College of Science and Arts, Qassim University, Al-Badaya 51951, Saudi Arabia
    Department of Operations and Management Research, Faculty of Graduate Studies for Statistical Research, Cairo University, Giza 12613, Egypt)

Abstract

In real-life scenarios, there are many mathematical tools to handle incomplete and imprecise data. One of them is the fuzzy approach. The main issue with addressing nonlinear interval programming (NIP) problems is that the optimal solution to the problem is a decision made under uncertainty that has a risk of not satisfying the feasibility and optimality criteria. Some strategies handle this kind of problem using classical terminology such as optimal solution and feasible solution. These strategies are insufficient for efficient analysis since the properties of the solution in an uncertain environment are ignored. Therefore, in the proposed approach, more suitable terminologies were suggested for the analysis process. In addition, it combines parametric treatment and interactive methodology. This article aims to contribute to the literature of fuzzy multi-objective dynamic programming (MODP) issues involving the fuzzy objective functions. The piecewise quadratic fuzzy numbers characterize these fuzzy parameters. Some basic notions in the problem under the α -pareto optimal solution concept is redefined and analyzed to study the stability of the problem. Furthermore, a technique, named the decomposition approach (DP), is presented for achieving a subset for the parametric space that contains the same α -pareto optimal solution. For a better understanding of the suggested concept, a numerical example is provided.

Suggested Citation

  • Pavan Kumar & Hamiden Abd El-Wahed Khalifa, 2023. "Enhancing Decomposition Approach for Solving Multi-Objective Dynamic Non-Linear Programming Problems Involving Fuzziness," Mathematics, MDPI, vol. 11(14), pages 1-16, July.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:14:p:3123-:d:1194581
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    References listed on IDEAS

    as
    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. Carraway, Robert L. & Morin, Thomas L. & Moskowitz, Herbert, 1990. "Generalized dynamic programming for multicriteria optimization," European Journal of Operational Research, Elsevier, vol. 44(1), pages 95-104, January.
    3. Cinthia Peraza & Fevrier Valdez & Juan R. Castro & Oscar Castillo, 2018. "Fuzzy Dynamic Parameter Adaptation in the Harmony Search Algorithm for the Optimization of the Ball and Beam Controller," Advances in Operations Research, Hindawi, vol. 2018, pages 1-16, August.
    4. Abo-Sinna, Mahmoud A. & Hussein, Mohammad L., 1994. "An algorithm for decomposing the parametric space in multiobjective dynamic programming problems," European Journal of Operational Research, Elsevier, vol. 73(3), pages 532-538, March.
    5. Abo-Sinna, Mahmoud A. & Hussein, Mohammad L., 1995. "An algorithm for generating efficient solutions of multiobjective dynamic programming problems," European Journal of Operational Research, Elsevier, vol. 80(1), pages 156-165, January.
    6. Hamiden Abd El-Wahed Khalifa & Pavan Kumar, 2023. "Multi-objective optimisation for solving cooperative continuous static games using Karush-Kuhn-Tucker conditions," International Journal of Operational Research, Inderscience Enterprises Ltd, vol. 46(1), pages 133-147.
    7. Osman, Mohamed S. & El-Banna, Abou-Zaid H., 1993. "Stability of multiobjective nonlinear programming problems with fuzzy parameters," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 35(4), pages 321-326.
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