• Journal of the Korean Institute of Intelligent Systems
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• v.13 no.5
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• pp.614-620
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• 2003

The aim of this paper is to introduce good definitions of compactness, almost compactness, near compactness, weak compactness, and S-closedness in fuzzy topological spaces in Sostak s sense. These compactness related concepts are defined for arbitrary fuzzy sets and some of their properties studied.

• 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.

• 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.

• Korean Journal of Mathematics
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• v.13 no.2
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• pp.223-234
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• 2005

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 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.19 no.1
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• pp.143-153
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• 2004

In [3] and [6] the concepts of smooth closure, smooth interior, smooth ${\alpha}-closure$ and smooth ${\alpha}-interior$ of a fuzzy set were introduced and some of their properties were obtained. In this paper, we introduce the concepts of several types of weak smooth compactness and weak smooth ${\alpha}-compactness$ in terms of these concepts introduced in [3] and [61 and investigate some of their properties.

• Korean Journal of Mathematics
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• v.14 no.2
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• pp.233-240
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• 2006

In this paper we 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 in smooth topological spaces and investigate some of their properties.