Three new cut sets of fuzzy sets and new theories of fuzzy sets

Three new cut sets are introduced from the view points of neighborhood and Q -neighborhood in fuzzy topology and their properties are discussed. By the use of these cut sets, new decomposition theorems, new representation theorems, new extension principles and new fuzzy linear mappings are obtained....

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Bibliographic Details
Published in:Computers & mathematics with applications (1987) 2009-03, Vol.57 (5), p.691-701
Main Authors: Yuan, Xue-hai, Li, Hongxing, Lee, E. Stanley
Format: Article
Language:English
Subjects:
Category
Cut set
Decomposition theorem
Descriptions
Extension principle
Fuzzy
Fuzzy linear mapping
Fuzzy logic
Fuzzy set theory
Mathematical models
Order set embedding
Representation theorem
Representations
Set embedding
Theorems
Topology
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Summary:Three new cut sets are introduced from the view points of neighborhood and Q -neighborhood in fuzzy topology and their properties are discussed. By the use of these cut sets, new decomposition theorems, new representation theorems, new extension principles and new fuzzy linear mappings are obtained. Then inner project of fuzzy relations, generalized extension principle and new composition rule of fuzzy relations are given. In the end, we present axiomatic descriptions for different cut sets and show the three most intrinsic properties for each cut set.
ISSN:0898-1221
1873-7668
DOI:10.1016/j.camwa.2008.05.044