• The Pure and Applied Mathematics
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• v.14 no.4
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• pp.255-270
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• 2007

In this paper, we introduce the concepts of r-generalized fuzzy closed sets, r-generalized fuzzy continuous maps and several types of r-generalized compactness in fuzzy topological spaces and investigate some of their properties.

• Communications of the Korean Mathematical Society
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• v.13 no.1
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• pp.137-150
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• 1998

The purpose of this paper is to introduce and study the concept of fuzzy FC-compactness for fuzzy topological spaces.

• Communications of the Korean Mathematical Society
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• v.27 no.2
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• pp.357-368
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• 2012

We introduce the concepts of fuzzy ${\delta}$-interior and show that the set of all fuzzy ${\delta}$-open sets is also a fuzzy topology, which is called the fuzzy ${\delta}$-topology. We obtain equivalent forms of fuzzy ${\delta}$-continuity. More-over, the notions of fuzzy ${\delta}$-compactness and fuzzy locally ${\delta}$-compactness are defined and their basic properties under fuzzy ${\delta}$-continuous mappings are investigated.

• East Asian mathematical journal
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• v.23 no.2
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• pp.213-227
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• 2007

In this paper the concept of fuzzy nearly C-compactness is introduced in Generalized fuzzy topological spaces. Several characterizations and some interesting properties of these spaces in Generalized fuzzy topological spaces are discussed. The properties of fuzzy almost continuous and fuzzy almost open functions in Generalized fuzzy topological spaces are also studied.

• 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.

• Korean Journal of Mathematics
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• v.14 no.1
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• pp.101-112
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• 2006

In this paper, we introduce the concepts of weak smooth ${\alpha}$-closure and weak smooth ${\alpha}$-interior of a fuzzy set and obtain some of their structural properties. We also introduce the concepts of several types of weak quasi-smooth ${\alpha}$-compactness in terms of the concepts of weak smooth ${\alpha}$-closure and weak smooth ${\alpha}$-interior of a fuzzy set and investigate some of their properties.

• Communications of the Korean Mathematical Society
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• v.24 no.3
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• pp.433-450
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• 2009

We introduce a new concept of intuitionistic fuzzy topological subspace, which coincides with the usual concept of intuitionistic fuzzy topological subspace due to Samanta and Mondal [18] in the case that $\mu=X_A$ for A $\subseteq$ X. Also, we introduce and study some concepts such as continuity, separation axioms, compactness and connectedness in this sense.

• Journal of the Korean Institute of Intelligent Systems
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• v.21 no.1
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• pp.128-131
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• 2011

In this paper, we introduce and study the concept of fuzzy r-$M^*$ preopen mappings between fuzzy r-minimal spaces. We also investigate the relationships among fuzzy r-M precontinuous mappings, fuzzy r-$M^*$-preopen mappings and several types of fuzzy r-minimal compactness.

• 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.

• Korean Journal of Mathematics
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• v.11 no.2
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• pp.127-136
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• 2003

In this paper we obtain some properties of the weak smooth ${\alpha}$-closure and weak smooth ${\alpha}$-interior of a fuzzy set in smooth topological spaces and introduce the concepts of several types of $weak^*$ smooth compactness in smooth topological spaces and investigate some of their properties.