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http://dx.doi.org/10.5391/JKIIS.2012.22.5.646

Interval-Valued Fuzzy Cosets  

Lee, Keon-Chang (Department of Computer Science, Dongshin University)
Hur, Kul (Division of Mathematics and Informational Statistics, and Nanoscale Science and Technology Institute, Wonkwang University)
Lim, Pyung-Ki (Division of Mathematics and Informational Statistics, and Nanoscale Science and Technology Institute, Wonkwang University)
Publication Information
Journal of the Korean Institute of Intelligent Systems / v.22, no.5, 2012 , pp. 646-655 More about this Journal
Abstract
First, we prove a number of results about interval-valued fuzzy groups involving the notions of interval-valued fuzzy cosets and interval-valued fuzzy normal subgroups which are analogs of important results from group theory. Also, we introduce analogs of some group-theoretic concepts such as characteristic subgroup, normalizer and abelian groups. Secondly, we prove that if A is an interval-valued fuzzy subgroup of a group G such that the index of A is the smallest prime dividing the order of G, then A is an interval-valued fuzzy normal subgroup. Finally, we show that there is a one-to-one correspondence the interval-valued fuzzy cosets of an interval-valued fuzzy subgroup A of a group G and the cosets of a certain subgroup H of G.
Keywords
interval-valued fuzzy normal subgroup; interval-valued fuzzy coset; interval-valued fuzzy characteristic fuzzy subgroup; normalizer; abelian group;
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Times Cited By KSCI : 6  (Citation Analysis)
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