Arithmetics of Vectors of Fuzzy Sets

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 metho...

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Bibliographic Details
Published inMathematics (Basel) Vol. 8; no. 9; p. 1614
Main Author Wu, Hsien-Chung
Format Journal Article
LanguageEnglish
Published MDPI AG 01.09.2020
Subjects
decomposition theorem
extension principle
fuzzy intervals
fuzzy numbers
non-normal fuzzy sets
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Summary: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.
ISSN:2227-7390
2227-7390
DOI:10.3390/math8091614