• Honam Mathematical Journal
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• v.25 no.1
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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.

• Journal of the Chungcheong Mathematical Society
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• v.22 no.2
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• pp.235-243
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• 2009

In this paper, we introduce the notion of intuitionistic fuzzy semiprimality in an ordered semigroup, which is an extension of fuzzy semiprimality and investigate some properties of intuitionistic fuzzification of the concept of several ideals.

• Journal of the Korean Institute of Intelligent Systems
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• v.15 no.6
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• pp.771-779
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• 2005

We introduce two concepts of intuitionistic fuzzy Rees congruence on a semigroup and intuitionistic fuzzy Rees con-gruence semigroup. As an important result, we prove that for a intuitionistic fuzzy Rees congruence semigroup S, the set of all intuitionistic fuzzy ideals of S and the set of all intuitionistic fuzzy congruences on S are lattice isomorphic. Moreover, we show that a homomorphic image of an intuitionistic fuzzy Rees congruence semigroup is an intuitionistic fuzzy Rees congruence semigroup.

• 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.

• 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.

• Korean Journal of Mathematics
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• v.30 no.3
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• pp.443-458
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• 2022

In this paper, we apply the concept of intuitionistic Q-fuzzy set to PMS-algebras. We study the concept of intuitionistic Q-fuzzy PMS-ideals of PMS-algebras and investigate some related properties of intuitionistic Q-fuzzy PMS-ideals of PMS-algebras. We provide the relationship between an intuitionistic Q-fuzzy PMS-subalgebra and an intuitionistic Q-fuzzy PMS-ideal of a PMS-algebra. We establish a condition for an intuitionistic Q-fuzzy set in a PMS-algebra to be an intuitionistic Q-fuzzy PMS-ideal of a PMS-algebra. Characterizations of intuitionistic Q-fuzzy PMS-ideals of PMS-algebras in terms of their level sets are given.

• Journal of applied mathematics & informatics
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• v.26 no.5_6
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• pp.1049-1056
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• 2008

Intuitionistic Fuzzifications of strong hyper K-ideals and hyper K-subalgebras in hyper K-algebras are discussed, and related properties are investigated. Relations between intuitionistic fuzzy hyper K-subalgebras, intuitionistic fuzzy weak hyper K-ideals and intuitionistic fuzzy strong hyper K-ideals are provided.

• 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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• 2005.04a
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• pp.157-160
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• 2005

In this paper, we define precompact set in intuitionistic fuzzy metric spaces and prove that any subset of an intuitionistic fuzzy metric space is compact if and only if it is precompact and complete. Also we define topologically complete intuitionistic fuzzy metrizable spaces and prove that any $G\delta$ set in a complete intuitionistic fuzzy metric spaces is a topologically complete intuitionistic fuzzy metrizable space and vice versa.

• Journal of applied mathematics & informatics
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• v.11 no.1_2
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• pp.401-412
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• 2003

Using the idea of "intuitionistic fuzzy set" [l, 2, 3], we defined the concept of intuitionistic fuzzy matrices as a natural generalization of fuzzy matrices. And we introduced and studied the determinant of square intuitionistic fuzzy matrices [4]. In this paper, we investigate the adjoint of square intuitionistic fuzzy matrices.