Symmetric Difference Operators Derived from Overlap and Grouping Functions

This paper introduces the concept of symmetric difference operators in terms of overlap and grouping functions, for which the associativity property is not strongly required. These symmetric difference operators are weaker than symmetric difference operators in terms of positive and continuous t-nor...

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Bibliographic Details
Published in:Symmetry (Basel) 2023-08, Vol.15 (8), p.1569
Main Authors: Hu, Bo, He, Di, Dai, Songsong
Format: Article
Language:English
Subjects:
Associativity
Finite differences
Fuzzy sets
grouping functions
Norms
Operators (mathematics)
overlap functions
Set theory
symmetric difference
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Summary:This paper introduces the concept of symmetric difference operators in terms of overlap and grouping functions, for which the associativity property is not strongly required. These symmetric difference operators are weaker than symmetric difference operators in terms of positive and continuous t-norms and t-conorms. Therefore, in the sense of the characters of mathematics, these operators do not necessarily satisfy certain properties, such as associativity and the neutrality principle. We analyze several related important properties based on two models of symmetric differences.
ISSN:2073-8994
2073-8994
DOI:10.3390/sym15081569