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

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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.

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  1. Department of Mathematics, National Kaohsiung Normal University, Kaohsiung, 802, Taiwan

    Hsien-Chung Wu

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Wu, HC. Applying the concept of null set to solve the fuzzy optimization problems. Fuzzy Optim Decis Making 18, 279–314 (2019). https://doi.org/10.1007/s10700-018-9299-y

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