• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 1997.10a
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• pp.57-59
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• 1997

The concept of fuzzy sets was introduced by Zad도 in his highly influential paper [5]. Using this concept, Chang [1] introduced a notion of fuzzy topological spaces which formally is the same one as for ordinary topological spaces. Observing that with Chang's definition constant maps between fuzzy topological spaces are not necessarily continuous, Lowen [2] gave an alternative and more natural definition for a fuzzy topological spaces and characterized the fuzzy compact spaces by means of prefilters in [4]. In this paper we give new characterizations of fuzzy compact spaces introduced in [2]. These results explain more clearly fuzzy compactness in 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.

• Korean Journal of Mathematics
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• v.7 no.1
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• pp.11-25
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• 1999

We will define a smooth fuzzy closure space and a subspace of it. We will investigate relationships between smooth fuzzy closure spaces and smooth fuzzy topological spaces. In particular, we will show that a subspace of a smooth fuzzy topological space can be obtained by the subspace of the smooth fuzzy closure space induced by it.

• Journal of Applied and Pure Mathematics
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• v.4 no.1_2
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• pp.79-84
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• 2022

We have observed that there exist certain fuzzy topological spaces with no fuzzy minimal open sets. This observation motivates us to investigate fuzzy topological spaces with neither fuzzy minimal open sets nor fuzzy maximal open sets. We have observed if such fuzzy topological spaces exist and if it is connected are not fuzzy cut-point spaces. We also study and characterize certain properties of fuzzy mean open sets in fuzzy T₁-connected fuzzy topological 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.

• Journal of the Korean Institute of Intelligent Systems
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• v.8 no.3
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• pp.88-94
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• 1998

We will difine a base of a smooth fuzzy topological space and investigate some properties of bases. We will prove the existences of initial smooth fuzzy topological spaces. From this fact, we can define subspaces and products of smooth fuzzy topological spaces.

• Communications of the Korean Mathematical Society
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• v.25 no.3
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• pp.335-342
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• 2010

The structure of fuzzy topological spaces based on WFI-algebras is considered. The notions of WFI-fuzzy topological spaces and WFI-fuzzy continuous mappings are introduced, and several properties are investigated. A relation between WFI-homomorphism and WFI-fuzzy continuous mapping is given.

• International Journal of Fuzzy Logic and Intelligent Systems
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• v.3 no.2
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• pp.258-261
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• 2003

The aim of this paper is to introduce the concept $\gamma$-connectedness in fuzzy topological spaces. We also investigate some interre lations between this types of fuzzy connectedness together with the preservation properties under some types of fuzzy continuity. A comparison between some types of connectedness in fuzzy topological spaces is of interest.

• International Journal of Fuzzy Logic and Intelligent Systems
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• v.7 no.1
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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.

• Journal of the Korean Institute of Intelligent Systems
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• v.15 no.3
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• pp.389-394
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• 2005

The purpose of this paper is to introduce the notions of L-fuzzy topological towers by using a completely distributive lattic L and show that the category L-FPrTR of L-fuzzy pretopoplogical tower spaces and the category L-FPsTR of L-fuzzy pseudotopological tower spaces are extensional topological constructs. And we show that L-FPsTR is the cartesian closed topological extension of L-FPrTR. Hence we show that L-FPsTR is a topological universe.