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Paper Information

Journal:   IRANIAN JOURNAL OF FUZZY SYSTEMS   2012 , Volume 9 , Number 4; Page(s) 115 To 132.
 
Paper: 

L-FUZZIFYING TOPOLOGICAL GROUPS

 
 
Author(s):  ZHANG S.Y., YAN C.H.
 
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Abstract: 

The main purpose of this paper is to introduce a concept of L- fuzzifying topological groups (here L is a completely distributive lattice) and discuss some of their basic properties and the structures. We prove that its corresponding L-fuzzifying neighborhood structure is translation invariant. A characterization of such topological groups in terms of the corresponding L- fuzzifying neighborhood structure of the unit is given. It is shown that the category of L-fuzzifying topological groups L-FYTPG is topological over the category of groups GRP with respect to the forgetful functor. As an application, the conclusion that the product of L-fuzzifying topological groups is also an L-fuzzifying topological group is proved. Finally, it is proved the forgetful functor preserves the product.

 
Keyword(s): L-FUZZIFYING TOPOLOGICAL GROUPS, L-FUZZIFYING TOPOLOGY, L-FUZZIFYING NEIGHBORHOOD STRUCTURE, CATEGORY
 
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