• International Journal of Fuzzy Logic and Intelligent Systems
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• 제6권1호
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• pp.85-93
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• 2006

We study the conditions under which a given intuitionistic fuzzy subgroup of a given group can or can not be realized as a union of two proper intuitionistic fuzzy subgroups. Moreover, we provide a simple necessary and sufficient condition for the union of an arbitrary family of intuitionistic fuzzy subgroups to be an intuitionistic fuzzy subgroup. Also we formulate the concept of intuitionistic fuzzy subgroup generated by a given intuitionistic fuzzy set by level subgroups. Furthermore we give characterizations of intuitionistic fuzzy conjugate subgroups and intuitionistic fuzzy characteristic subgroups by their level subgroups. Also we investigate the level subgroups of the homomorphic image of a given intuitionistic fuzzy subgroup.

• 호남수학학술지
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• 제27권3호
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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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• 제10권1호
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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.

• International Journal of Fuzzy Logic and Intelligent Systems
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• 제9권1호
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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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• 제18권1_2호
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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.

• International Journal of Fuzzy Logic and Intelligent Systems
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• 제6권3호
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• pp.240-246
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• 2006

We introduce the concept of level subgroups of an intuitionistic fuzzy subgroup and study some of it's properties. These level subgroups in turn play an important role in the characterization of all intuitionistic fuzzy subgroup of a prime cyclic group.

• 호남수학학술지
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• 제28권1호
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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.

• Kyungpook Mathematical Journal
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• 제45권1호
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• pp.87-87
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• 2005

Using the belongs to relation $({\in})$ and quasi-coincidence with relation (q) between intuitionistic fuzzy points and intuitionistic fuzzy sets, the concept of (${\Phi},\;{\Psi}$)-intuitionistic fuzzy subgroup where ${\Phi},\;{\Psi}$ are any two of {${\in},\;q,\;{\in}{\vee}q,\;{\in}{\wedge}q$} with ${\Phi}\;{\neq}\;{\in}{\wedge}q$ is introduced, and related properties are investigated.

• 대한수학회논문집
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• 제21권3호
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• pp.587-593
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• 2006

The notion of intuitionistic fuzzy graphs is introduced. We show how to associate an intuitionistic fuzzy sub(semi)group with an intuitionistic fuzzy graph in a natural way.

• 호남수학학술지
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• 제25권1호
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• pp.19-41
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• 2003

In this paper, we introduce the concepts of intuitionistic fuzzy subgroups and intuitionistic fuzzy subrings and investigated some of their properties.