• 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.

• Honam Mathematical Journal
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• v.33 no.1
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• pp.27-41
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• 2011

This paper studies the relationship between L-fuzzy proximities and L-fuzzy topologies by topological fuzzy remote neigh-borhood systems. We will prove that the category of L-fuzzy topo- logical spaces can be embedded in the category of L-fuzzy quasi-proximity spaces as a core ective full subcategory.

• International Journal of Fuzzy Logic and Intelligent Systems
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• v.11 no.1
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• pp.54-58
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• 2011

In this paper, we use L-fuzzy preopen operator to introduce the degree of pre-separatedness and the degree of preconnectedness in L-fuzzy topological spaces. Many characterizations of the degree of preconnectedness are presented in L-fuzzy topological spaces.

• The Pure and Applied Mathematics
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• v.13 no.1 s.31
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• pp.47-69
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• 2006

In this paper, an idea of graded fuzzy net is introduced; its convergence is studied; Relations between g-net and g-filter are established in L-fuzzy setting.

• 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.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 1998.06a
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• pp.219-224
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• 1998

We introduce the notion of ${\gamma}$-fuzzy filter and ${\gamma}$-limit structure to L-fuzzy point. We show that the category ${\gamma}$Lim of ${\gamma}$-limit spaces is a cartesian closed topological construct containing the category LFTop of stratified L-fuzzy topological spaces as a bireflective subcategory.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 1997.10a
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• pp.367-369
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• 1997

We introduce a notion of fuzzy L-convergence of filters and show that the collection of fuzzy L-convergence spaces forms a cartesian closed topological category.

• Journal of the Korean Mathematical Society
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• v.44 no.6
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• pp.1383-1396
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• 2007

The aim of this paper is to study L-fuzzy uniformizable spaces. A new kind of topological fuzzy remote neighborhood system is defined and used for investigating the relationship between L-fuzzy co-topology and L-fuzzy (quasi-)uniformity. It is showed that this fuzzy remote neighborhood system is different from that in [23] when $\mathcal{U}$ is an L-fuzzy quasi-uniformity and they will be coincident when $\mathcal{U}$ is an L-fuzzy uniformity. It is also showed that each L-fuzzy co-topological space is L-fuzzy quasi-uniformizable.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 1998.06a
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• pp.95-100
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• 1998

A notion of 'fuzzy' convergence of filters on a set is introduced. We show that the collection of fuzzy L-limit spaces forms a cartesian closed topological category and obtain an interesting relationship between the notions of 'fuzzy' convergence structure and convergence approach spaces.

• International Journal of Fuzzy Logic and Intelligent Systems
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• v.10 no.4
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• pp.296-302
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• 2010

This paper considers fuzzifying topologies, a special case of I-fuzzy topologies (bifuzzy topologies) introduced by Ying [16, (I)]. It investigates topological notions defined by means of regular open sets when these are planted into the frame-work of Ying's fuzzifying topological spaces (in ${\L}$ukasiewwicz fuzzy logic). The concept of fuzzifying nearly compact spaces is introduced and some of its properties are obtained. We use the finite intersection property to give a characterization of fuzzifying nearly compact spaces. Furthermore, we study the image of fuzzifying nearly compact spaces under fuzzifying completely continuous functions, fuzzifying almost continuity and fuzzifying R-map.