Arithmetics of Vectors of Fuzzy Sets

Hsien-Chung Wu
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Hsien-Chung Wu: Department of Mathematics, National Kaohsiung Normal University, Kaohsiung 802, Taiwan

Mathematics, 2020, vol. 8, issue 9, 1-42

Abstract: The arithmetic operations of fuzzy sets are completely different from the arithmetic operations of vectors of fuzzy sets. In this paper, the arithmetic operations of vectors of fuzzy intervals are studied by using the extension principle and a form of decomposition theorem. These two different methodologies lead to the different types of membership functions. We establish their equivalences under some mild conditions. On the other hand, the α -level sets of addition, difference and scalar products of vectors of fuzzy intervals are also studied, which will be useful for the different usage in applications.

Keywords: decomposition theorem; extension principle; fuzzy numbers; fuzzy intervals; non-normal fuzzy sets (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
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