• Journal of applied mathematics & informatics
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• v.15 no.1_2
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• pp.323-331
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• 2004

A new topology in terms of order on fuzzy sets, revealing better the relationship between smooth topology and Chang's fuzzy topology, is presented in the paper. Some basic properties are discussed.

• The Pure and Applied Mathematics
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• v.12 no.1
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• pp.75-91
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• 2005

The main objective of this paper is to introduce the gradation of neigh-bourhoodness in L-fuzzy topology and to introduce the fuzziness in the concept of convergence of L-fuzzy nets.

• International Journal of Fuzzy Logic and Intelligent Systems
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• v.10 no.3
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• pp.230-241
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• 2010

In the present paper we introduce and study fundamental concepts in the framework of L-fuzzifying topology(so called(2,L)-fuzzy topology)as L-concepts where L is a complete residuated lattice. The concepts of (2,L)-derived, (2,L)-closure, (2,L)-interior, (2,L)-exterior and (2,L)-boundary operators are studied and some results on above concepts are obtained. Also, the concepts of an L-convergence of nets and an L-convergence of filters are introduced and some important results are obtained. Furthermore, we introduce and study bases and subbases in (2,L)-topology. As applications of our work the corresponding results(see[10-11]) are generalized and new consequences are obtained.

• 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.

• 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.

• International Journal of Fuzzy Logic and Intelligent Systems
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• v.9 no.4
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• pp.261-268
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• 2009

In this paper we introduce stronger form of the notion of cover so-called p-cover which is more appropriate. According to this cover we introduce and study another type of compactness in L-fuzzy topology so-called $C^*$-compact and study some of its properties with some interrelation.

• 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.

• 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.

• Journal of the Korean Institute of Intelligent Systems
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• v.11 no.7
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• pp.649-652
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• 2001

In this paper, we introduce neighborhood systems in an L-fuzzy topology using complete MV-algebras. We investigate the relationship between L-fuzzy topologies and the neighborhood systems. We study the properties of neighborhood system.

• 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.