• Journal of applied mathematics & informatics
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• v.9 no.1
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• pp.359-370
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• 2002

The purpose of this paper is to introduce and discuss the concept of $\beta$-compactness for L-fuzzy topological spaces.

• Bulletin of the Korean Mathematical Society
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• v.45 no.4
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• pp.749-755
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• 2008

In this paper, we introduce the relatively new notion of fuzzy ${\omega}^O$-open set. We prove that the collection of all fuzzy ${\omega}^O$-open subsets of a fuzzy topological space forms a fuzzy topology that is finer than the original one. Several characterizations and properties of this class are also given as well as connections to other well-known "fuzzy generalized open" subsets.

• The Pure and Applied Mathematics
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• v.11 no.3
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• pp.243-265
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• 2004

In this paper, we introduce the fundamental concepts of intuitionistic fuzzy Q-neighborhood, intuitionistic Q-first axiom of countability, intuitionistic first axiom of countability, intuitionistic fuzzy closure operator, intuitionistic fuzzy boundary point and intuitionistic fuzzy accumulation point and investigate some of their properties.

• Bulletin of the Korean Mathematical Society
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• v.37 no.1
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• pp.63-76
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• 2000

In this paper, we introduce the concept of intuitionistic fuzzy points and intuitionistic fuzzy neighborhoods. We investigate the properties of continuous, open and closed maps in the intuitionistic fuzzy topological spaces, and show that the category of Chang's fuzzy topological spaces is a bireflective full subcategory of that of intuitionistic fuzzy topological spaces.

• Journal of applied mathematics & informatics
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• v.13 no.1_2
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• pp.487-500
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• 2003

We investigate categorical relationships between the category of smooth fuzzy topological spaces, the category of intuitionistic fuzzy topological spaces, and the category of intuitionistic fuzzy topological spaces, and the category of intuitioistic fuzzy topological spaces in Sostak's sense.

• The Pure and Applied Mathematics
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• v.14 no.4
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• pp.255-270
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• 2007

In this paper, we introduce the concepts of r-generalized fuzzy closed sets, r-generalized fuzzy continuous maps and several types of r-generalized compactness in fuzzy topological spaces and investigate some of their properties.

• International Journal of Fuzzy Logic and Intelligent Systems
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• v.8 no.2
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• pp.111-115
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• 2008

By generalizing the definition of fuzzy weakly semicontinuous mappings by B. S. Zhong, we introduce the concept of fuzzy weakly r-semicontinuous mappings in fuzzy topology of Chattopadhyay. Then the concept introduced by B. S. Zhong becomes a special case of our definition. Also, we show that fuzzy weakly r-semicontinuity and fuzzy weakly r-continuity are independent notions.

• International Journal of Fuzzy Logic and Intelligent Systems
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• v.8 no.3
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• pp.202-206
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• 2008

We introduce the concept of interval-valued minimal structure which is an extension of the interval-valued fuzzy topology. And we introduce and study the concepts of IVF m-continuous and several types of compactness on the interval-valued fuzzy m-spaces.

• International Journal of Fuzzy Logic and Intelligent Systems
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• v.15 no.2
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• pp.137-144
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• 2015

In this paper, we obtain two types of adjoint functors between the category of intuitionistic fuzzy topological spaces in Mondal and Samanta’s sense, and the category of intuitionistic fuzzy topological spaces in Ŝostak’s sense. Also, we reveal that the category of Chang’s fuzzy topological spaces is a bireflective full subcategory of the category of intuitionistic fuzzy topological spaces in Mondal and Samanta’s sense.

• Communications of the Korean Mathematical Society
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• v.10 no.1
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• pp.175-186
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• 1995

The concept of a fuzzy set, which was introduced in [9], provides a natural framework for generalizing many of the concepts of general topology to what might be called fuzzy topological spaces. The idea of fuzzy topological spaces was introduced by Chang [2]. The idea is more or less a generalization of oridinary topological spaces.