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Applying the concept of null set to solve the fuzzy optimization problems

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  • Hsien-Chung Wu

    (National Kaohsiung Normal University)

Abstract

The concept of null set in the space of fuzzy numbers is introduced. Based on this concept, we can define two partial orderings according to the subtraction and Hukuhara difference between any two fuzzy numbers. These two partial orderings will be used to define the solution concepts of fuzzy optimization problems. On the other hand, we transform the fuzzy optimization problems into a conventional vector optimization problem. Under these settings, we can apply the technique of scalarization to solve this transformed vector optimization problem. Finally, we show that the optimal solution of the scalarized problem is also the optimal solution of the original fuzzy optimization problem.

Suggested Citation

  • Hsien-Chung Wu, 2019. "Applying the concept of null set to solve the fuzzy optimization problems," Fuzzy Optimization and Decision Making, Springer, vol. 18(3), pages 279-314, September.
    • Handle: RePEc:spr:fuzodm:v:18:y:2019:i:3:d:10.1007_s10700-018-9299-y
    DOI: 10.1007/s10700-018-9299-y
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    References listed on IDEAS

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    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. H. C. Wu, 2010. "Duality Theory for Optimization Problems with Interval-Valued Objective Functions," Journal of Optimization Theory and Applications, Springer, vol. 144(3), pages 615-628, March.
    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.
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    Cited by:

    1. Lifeng Li, 2023. "Optimality conditions for nonlinear optimization problems with interval-valued objective function in admissible orders," Fuzzy Optimization and Decision Making, Springer, vol. 22(2), pages 247-265, June.

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