• International Journal of Fuzzy Logic and Intelligent Systems
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• v.6 no.1
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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.

• Honam Mathematical Journal
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• v.35 no.4
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• pp.565-582
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• 2013

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

• Journal of applied mathematics & informatics
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• v.40 no.3_4
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• pp.719-727
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• 2022

In this paper, the concept of (𝛾, 𝜕)-fuzzy HX-subgroups is introduced. We present some properties of (𝛾, 𝜕)-normal fuzzy HX-subgroups and we discuss some results related to (𝛾, 𝜕)-fuzzy cosets.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 1995.10b
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• pp.335-337
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• 1995

The notion of Ap* of a fuzzy subgroup A is introduced. Using the notion, we characterize fuzzy subgroups and show that every commutative fuzzy subgroup characterized as the intersection of its all minimal fuzzy p*-subgroups.

• Communications of the Korean Mathematical Society
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• v.16 no.1
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• pp.75-83
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• 2001

The various fuzzy subgroups of a group which are admissible under operator domains are studied. In particular, the classes of all inner automorphisms, automorphisms, and endomorphisms are applied on the fuzzy subgroups of a group. As results, several theorems and examples concerning the fuzzy subgroups following from these kinds of operator domains are obtained. Moreover, we prove that a necessary condition for a fuzzy subgroup to be characteristic is that the center of the fuzzy subgroup is characteristic.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 1995.10b
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• pp.331-334
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• 1995

We redefine the sup-min product of fuzzy subsets and discuss the redefined sup-min products of fuzzy subgroupoids, fuzzy submonoids and fuzzy subgroups. And we study lattice structures of the lattices of fuzzy subgroupoids, fuzzy submonoids and fuzzy subgroups.

• 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.

• East Asian mathematical journal
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• v.14 no.1
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• pp.15-20
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• 1998

Obtained the conditions for the product UV of two fuzzy subgroups U and V to be a fuzzy subgroup. Moreover, given an example of two fuzzy subgroups U and V which their product UV does not intersect neither U nor V.

• Communications of the Korean Mathematical Society
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• v.34 no.4
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• pp.1049-1067
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• 2019

In this paper, we discuss the number of distinct fuzzy subgroups of the group ${\mathbb{Z}}_{p^n}{\times}{\mathbb{Z}}_{q^m}{\times}{\mathbb{Z}}_r$, m = 1, 2, 3 where p, q, r are distinct primes for any $n{\in}{\mathbb{Z}}^+$ using the criss-cut method that was proposed by Murali and Makamba in their study of distinct fuzzy subgroups. The criss-cut method first establishes all the maximal chains of the subgroups of a group G and then counts the distinct fuzzy subgroups contributed by each chain. In this paper, all the formulae for calculating the number of these distinct fuzzy subgroups are given in polynomial form.

• International Journal of Fuzzy Logic and Intelligent Systems
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• v.6 no.3
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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.