• International Journal of Fuzzy Logic and Intelligent Systems
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• 제10권3호
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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.

• 대한수학회지
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• 제44권6호
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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.

• Journal of applied mathematics & informatics
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• 제16권1_2호
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• pp.371-381
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• 2004

In this paper, fuzzy metric spaces are redefined, different from the previous ones in the way that fuzzy scalars instead of fuzzy numbers or real numbers are used to define fuzzy metric. It is proved that every ordinary metric space can induce a fuzzy metric space that is complete whenever the original one does. We also prove that the fuzzy topology induced by fuzzy metric spaces defined in this paper is consistent with the given one. The results provide some foundations for the research on fuzzy optimization and pattern recognition.

• International Journal of Fuzzy Logic and Intelligent Systems
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• 제9권4호
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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.

• 호남수학학술지
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• 제25권1호
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• pp.131-139
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• 2003

The notion of intuitionistic fuzzy ${\alpha}$-continuity is introduced, and its characterization is given.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제11권3호
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• pp.217-229
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• 2004

In this paper, we introduce the concepts of interior of a fuzzy set and several types of fuzzy compactness and fuzzy RS-compactness in a redefined fuzzy topological space and investigate their properties.

• 한국지능시스템학회:학술대회논문집
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• 한국퍼지및지능시스템학회 1998년도 The Third Asian Fuzzy Systems Symposium
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• pp.236-239
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• 1998

We introduce the concept of a fuzzy vietories topology and we obtain its fundamental properties.

• East Asian mathematical journal
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• 제3권
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• pp.97-111
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• 1987

• 대한수학회논문집
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• 제21권3호
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• pp.497-514
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• 2006

In this paper, we used the supra fuzzy topology which generated from a fuzzy bitopological space [1] to introduce and study the concepts of continuity (resp. openness, closeness) of mapping, separation axioms and compactness for a fuzzy bitopological spaces. Our definition preserve much of the correspondence between concepts of fuzzy bitopological spaces and the associated fuzzy topological spaces.

• 대한수학회보
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• 제39권3호
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• pp.441-453
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• 2002

We introduce the concepts of fuzzy r-regular open sets and fuzzy almost r-continuous maps in the fuzzy topology of Chat-topadhyay. Also we investigate the equivalent conditions of the fuzzy almost r-continuity.