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Stability of multiobjective nonlinear programming problems with fuzzy parameters

Author

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  • Osman, Mohamed S.
  • El-Banna, Abou-Zaid H.

Abstract

This paper deals with multiobjective nonlinear programming problems with fuzzy parameters in the objective functions. These fuzzy parameters are characterized by fuzzy numbers. The existing results concerning the qualitative analysis of some basic notions in parametric nonlinear programming problems are reformulated to study the stability of multiobjective nonlinear programming problems under the concept of α-pareto optimality. An algorithm for obtaining any subset of the parametric space which has the same corresponding α-pareto optimal solution is also presented. An illustrative example is given to clarify the obtained results.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:matcom:v:35:y:1993:i:4:p:321-326
    DOI: 10.1016/0378-4754(93)90062-Y
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    Cited by:

    1. El-Banna, Abou-Zaid H. & Zarea, Sana’a A., 2001. "Stability of linear vector optimization problems corresponding to an efficient set," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 57(6), pages 335-345.
    2. El-Hady Kassem, Mohamed Abd, 2001. "Interactive stability of vector optimization problems," European Journal of Operational Research, Elsevier, vol. 134(3), pages 616-622, November.
    3. Hamiden Abd El-Wahed Khalifa, 2020. "Goal programming approach for solving heptagonal fuzzy transportation problem under budgetry constraint," Operations Research and Decisions, Wroclaw University of Science and Technology, Faculty of Management, vol. 30(1), pages 85-96.
    4. Li, Dengfeng & Cheng, Chuntian, 2004. "Stability on multiobjective dynamic programming problems with fuzzy parameters in the objective functions and in the constraints," European Journal of Operational Research, Elsevier, vol. 158(3), pages 678-696, November.
    5. Kassem, Mohamed Abd El-Hady, 1997. "Decomposition of the fuzzy parametric space in multiobjective nonlinear programming problems," European Journal of Operational Research, Elsevier, vol. 101(1), pages 204-219, August.
    6. 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.

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