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

Hsien-Chung Wu ()
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Hsien-Chung Wu: National Kaohsiung Normal University

Fuzzy Optimization and Decision Making, 2019, vol. 18, issue 3, No 2, 279-314

Abstract: 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.

Keywords: Hukuhara difference; Minimal element; Null set; Partial ordering; Pointed cone (search for similar items in EconPapers)
Date: 2019
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DOI: 10.1007/s10700-018-9299-y

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