Paper Info
Title
Symmetric fuzzy numbers and additive equivalence of fuzzy numbers
Abstract
To obtain the group properties of fuzzy quantities, Mareš introduced an equivalence relation between fuzzy quantities. However, the Mareš's method used to prove his main theorems demands to limit the investigation to fuzzy quantities with finite support. In this paper, we discuss the properties of symmetric fuzzy numbers, show an equivalent characterization of convex fuzzy sets, and present a way to construct a symmetric convex fuzzy set with a convex fuzzy set. Based on these results, we restrict ourselves to fuzzy numbers and prove Mareš's results without the limitation to fuzzy numbers with finite support using the refined equivalence relation due to Hong and Do. Our results prove one of Mareš's open questions in the literature.
Year
DOI
Venue
2013
10.1007/s00500-013-1000-3
Soft Computing - A Fusion of Foundations, Methodologies and Applications
Keywords
Field
DocType
additive equivalences,convex fuzzy sets,fuzzy numbers,symmetric fuzzy sets
Discrete mathematics,Defuzzification,Fuzzy classification,Fuzzy set operations,Fuzzy mathematics,Fuzzy set,Fuzzy subalgebra,Type-2 fuzzy sets and systems,Fuzzy number,Mathematics
Journal
Volume
Issue
ISSN
17
8
14337479
Citations 
PageRank 
References 
25
1.10
21
Authors
2
Name
Order
Citations
PageRank
Dong Qiu1696.38
Weiquan Zhang2606.33