• International Journal of Fuzzy Logic and Intelligent Systems
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• v.13 no.3
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• pp.224-230
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• 2013

In this paper, we introduce certain types of continuous functions and intuitionistic fuzzy ${\theta}$-compactness in intuitionistic fuzzy topological spaces. We show that intuitionistic fuzzy ${\theta}$-compactness is strictly weaker than intuitionistic fuzzy compactness. Furthermore, we show that if a topological space is intuitionistic fuzzy retopologized, then intuitionistic fuzzy compactness in the new intuitionistic fuzzy topology is equivalent to intuitionistic fuzzy ${\theta}$-compactness in the original intuitionistic fuzzy topology. This characterization shows that intuitionistic fuzzy ${\theta}$-compactness can be related to an appropriated notion of intuitionistic fuzzy convergence.

• 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.27 no.4
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• pp.543-550
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• 2005

Some properties of a transitive fuzzy matrix are examined and the canonical form of the transitive fuzzy matrix is given using the properties. As a special case an open problem concerning idempotent matrices is solved. Thus we have the same result in a intuitionistic fuzzy matrix theory. In our results a nilpotent intuitionistic matrix and a symmetric intuitionistic matrix play an important role. We decompose a transitive intuitionistic fuzzy matrix into sum of a nilpotent intuitionistic matrix and a symmetric intuitionistic matrix. Then we obtain a canonical form of the transitive intuitionistic fuzzy matrix.

• Communications of the Korean Mathematical Society
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• v.20 no.4
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• pp.791-801
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• 2005

In this paper, we introduce the concepts of closure and interior defined by an intuitionistic gradation of openness. We also introduce the concepts of weakly gp-maps, gp-open maps and several types of compactness, and obtain some characterizations.

• Korean Journal of Mathematics
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• v.25 no.1
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• pp.1-18
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• 2017

In this paper, we introduce the concepts of ([r, s], [t, u])-interval-valued intuitionistic fuzzy generalized preclosed sets and ([r, s], [t, u])-interval-valued intuitionistic fuzzy generalized preopen sets in the interval-valued intuitionistic smooth topological space and ([r, s], [t, u])-interval-valued intuitionistic fuzzy generalized pre-continuous mappings and then investigate some of their properties.

• Journal of applied mathematics & informatics
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• v.27 no.5_6
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• pp.1447-1457
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• 2009

In this paper we define intuitionistic fuzzy interior ideals in ordered semigroups. We prove that in regular(resp. intra-regular and semisimple) ordered semigroups the concepts of intuitionistic fuzzy interior ideals and intuitionistic fuzzy ideals coincide. We prove that an ordered semi group is intuitionistic fuzzy simple if and only if every intutionistic fuzzy interior ideal is a constant function. We characterize intra-regular ordered semi groups in terms of interior (resp. intuitionistic fuzzy interior) ideals.

• Korean Journal of Mathematics
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• v.13 no.2
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• pp.249-254
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• 2005

In this paper, we introduce the concepts of intuitionistic fuzzy half-compactness, nearly intuitionistic fuzzy half-compactness and almost intuitionistic fuzzy half-compactness defined by intuitionistic gradations of openness, and obtain some characterizations.

• Honam Mathematical Journal
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• v.44 no.4
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• pp.535-559
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• 2022

The notions of cubic intuitionistic fuzzy set to filters and implicative filters of BE-algebras are introduced. Relations between cubic intuitionistic fuzzy filters with cubic intuitionistic fuzzy implicative filters of BE-algebras are investigated. The homomorphic image and inverse image of cubic intuitionistic fuzzy filters are studied and some related properties are investigated. Also, the product of cubic intuitionistic fuzzy subalgebras (implicative filters) of BE-algebras are investigated.

• Journal of the Chungcheong Mathematical Society
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• v.36 no.2
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• pp.135-148
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• 2023

We prove that for any preordered intuitionistic fuzzy approximation space, an intuitionistic fuzzy topology can be created, and conversely, for any intuitionistic fuzzy topology, a reflexive intuitionistic fuzzy relation can be constructed. We also show that there is a relationship, called Galois correspondence, between the functors of these categories. Additionally, by applying certain limitations on the category of intuitionistic fuzzy topological spaces, we obtain an isomorphism between these categories.

• Honam Mathematical Journal
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• v.28 no.4
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• pp.439-469
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• 2006

Intrinsic product of intuitionistic fuzzy sets are considered. Using this, characterizations of intuitionistic fuzzy subrings/ideals are discussed. The notions of intuitionistic fuzzy quasi ideals and intuitionistic fuzzy bi-ideals are introduced. Characterizations of regular rings are provided.