• International Journal of Fuzzy Logic and Intelligent Systems
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• v.10 no.1
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• pp.82-88
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• 2010

In this paper we continue the study of intuitionistic fuzzy groups by introducing the notion of intuitionistic fuzzy normal subgroup based on intuitionistic fuzzy space as a generalization of fuzzy normal subgroup.

• Honam Mathematical Journal
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• v.27 no.3
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• pp.369-388
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• 2005

First, we prove a number of results about intuitionistic fuzzy groups involving the notions of intuitionistic fuzzy cosets and intuitionistic 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 intuitionistic 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 intuitionistic fuzzy normal subgroup. Finally, we show that there is a one-to-one correspondence the intuitionistic fuzzy cosets of an intuitionistic fuzzy subgroup A of a group G and the cosets of a certain subgroup H of G.

• International Journal of Fuzzy Logic and Intelligent Systems
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• v.9 no.1
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• pp.53-58
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• 2009

We unite the two con concepts - normality We unite the two con concepts - normality and congruence - in an intuitionistic fuzzy subgroup setting. In particular, we prove that every intuitionistic fuzzy congruence determines an intuitionistic fuzzy subgroup. Conversely, given an intuitionistic fuzzy normal subgroup, we can associate an intuitionistic fuzzy congruence. The association between intuitionistic fuzzy normal sbgroups and intuitionistic fuzzy congruences is bijective and unigue. This leads to a new concept of cosets and a corresponding concept of guotient.

• Journal of applied mathematics & informatics
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• v.18 no.1_2
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• pp.665-677
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• 2005

The notion of normal intuitionistic fuzzy R-subgroups in near-rings is introduced, and related properties are investigated. Characterization of an intuitionistic fuzzy R-subgroup is given. Using a collection of right R-subgroups, an intuitionistic fuzzy right R-subgroup is established. Using a chain of right R-subgroups, an intuitionistic fuzzy right R-subgroup is also established.

• Honam Mathematical Journal
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• v.28 no.1
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• pp.31-44
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• 2006

We discuss various types of sublattice of the lattice of intuitionistic fuzzy subgroups of a given group. We prove that a special class of intuitionitic fuzzy normal subgroups constitutes a modular sublattice of the lattice of intuitionistic fuzzy subgroups.

• Honam Mathematical Journal
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• v.26 no.4
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• pp.559-587
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• 2004

We study some properties of intuitionistic fuzzy normal subgroups of a group. In particular, we obtain two characterizations of intuitionistic fuzzy normal subgroups. Moreover, we introduce the concept of an intuitionistic fuzzy coset and obtain several results which are analogous of some basic theorems of group theory.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 2004.04a
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• pp.367-371
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• 2004

We study some properties of intuitionistic fuzzy normal subgroups of a group. In particular, we obtain two characterizations of intuitionistic fuzzy normal subgroups. Moreover, we introduce the concept of an intuitionistic fuzzy coset and obtain several results which are analogs of some basic theorems of group theory.

• Journal of applied mathematics & informatics
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• v.27 no.3_4
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• pp.737-748
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• 2009

Using the notion of intuitionistic fuzzy subgroups, its roughness is discussed. With respect to a congruence relation on a group, several properties about the lower and upper approximations of a subset of a group are investigated.