• Journal of applied mathematics & informatics
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• 제13권1_2호
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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.

• 한국지능시스템학회논문지
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• 제19권5호
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• pp.725-729
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• 2009

intuitionistic fuzzy generalized topological space와 intuitionistic gradation of generalized openness의 개념을 소개한다. 한편 IFG-mapping, weak IFG-mapping과 IFG-open mapping의 개념을 소개하며 특성을 조사한다.

• International Journal of Fuzzy Logic and Intelligent Systems
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• 제3권2호
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• pp.200-205
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• 2003

In this paper, we generally introduce some of the terminology of Yalvac [10] and Azad [4] in intuitionistic fuzzy topological spaces. In addition to the fundamental concepts of intuitionistic fuzzy sets, we emphasize the usefulness of the concepts of intuitionistic fuzzy points intuitionistic fuzzy elementhood. Mainly, this paper is devoted to the study of intuitionistic fuzzy topological spaces with specific attention to the weaker forms of fuzzy continuity.

• 대한수학회보
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• 제37권1호
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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.

• International Journal of Fuzzy Logic and Intelligent Systems
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• 제15권2호
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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.

• 한국지능시스템학회:학술대회논문집
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• 한국퍼지및지능시스템학회 1998년도 The Third Asian Fuzzy Systems Symposium
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• pp.225-230
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• 1998

In this paper, we introduce the concepts of intuitionistic fuzzy points and intuitionistic fuzzy neighborhoods. We investigate 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 topogical spaces.

• 한국지능시스템학회논문지
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• 제22권1호
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• pp.126-134
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• 2012

By using the concept of intuitionistic interval-valued fuzzy sets, we introduce the notion of intuitionistic interval-valued fuzzy topology. And we study some fundamental properties of intuitionistic interval-valued fuzzy topological spaces: First, we obtain analogues[see Theorem 3.11 and 3.12] of neighborhood systems in ordinary topological spaces. Second, we obtain the result[see Theorem 4.9] corresponding to "the 14-set Theorem" in ordinary topological spaces. Finally, we give the initial structure on intuitionistic interval-valued fuzzy topologies[see Theorem 5.9].

• International Journal of Fuzzy Logic and Intelligent Systems
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• 제7권1호
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• pp.49-57
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• 2007

Using the idea of degree of openness and degree of nonopenness, Coker and Demirci [5] defined intuitionistic fuzzy topological spaces in Sostak's sense as a generalization of smooth topological spaces and intuitionistic fuzzy topological spaces. M. N. Mukherjee and S. P. Sinha [10] introduced the concept of fuzzy irresolute maps on Chang's fuzzy topological spaces. In this paper, we introduce the concepts of fuzzy (r,s)-irresolute, fuzzy (r,s)-presemiopen, fuzzy almost (r,s)-open, and fuzzy weakly (r,s)-continuous maps on intuitionistic fuzzy topological spaces in Sostak's sense. Using the notions of fuzzy (r,s)-neighborhoods and fuzzy (r,s)-semineighborhoods of a given intuitionistic fuzzy points, characterizations of fuzzy (r,s)-irresolute maps are displayed. The relations among fuzzy (r,s)-irresolute maps, fuzzy (r,s)-continuous maps, fuzzy almost (r,s)-continuous maps, and fuzzy weakly (r,s)-cotinuous maps are discussed.

• Korean Journal of Mathematics
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• 제24권4호
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• pp.663-679
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• 2016

In this paper, we introduce the concepts of several types of interval-valued intuitionistic fuzzy mappings and several types of interval-valued intuitionistic fuzzy compactness in interval-valued intuitionistic smooth topological spaces and then investigate their properties.

• 대한수학회논문집
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• 제20권1호
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• pp.117-134
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• 2005

We introduce the notion of (r,s)-connected sets in intuitionistic fuzzy topological spaces and investigate some properties of them. In particular, we show that every (r,s)-component in an intuitionistic fuzzy topological space is (r,s)-component in the stratification of it.