• Journal of the Korean Institute of Intelligent Systems
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• v.14 no.2
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• pp.234-238
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• 2004

We introduce the concepts of fuzzy (r, s)-semiopen sets and fuzzy (r, s)-semicontinuous mappings on intuitionistic fuzzy topological spaces in Sostak's sense and then we investigate some of their characteristic properties.

• Journal of applied mathematics & informatics
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• v.13 no.1_2
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• pp.487-500
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• 2003

We investigate categorical relationships between the category of smooth fuzzy topological spaces, the category of intuitionistic fuzzy topological spaces, and the category of intuitionistic fuzzy topological spaces, and the category of intuitioistic fuzzy topological spaces in Sostak's sense.

• International Journal of Fuzzy Logic and Intelligent Systems
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• v.6 no.3
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• pp.255-263
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• 2006

In this paper, we introduce the concepts of ${\gamma}$-fuzzy feebly open and ${\gamma}$-fuzzy feebly closed sets in Sostak's fuzzy topological spaces and by using them, we explain the notions of ${\gamma}$-fuzzy F-closed spaces. Also, we give some characterization of ${\gamma}$-fuzzy F-closedness in terms of fuzzy filterbasis and ${\gamma}$-fuzzy feebly-${\theta}$-cluster points.

• International Journal of Fuzzy Logic and Intelligent Systems
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• v.5 no.1
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• pp.64-68
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• 2005

We introduce in Sostak's fuzzy topological spaces definitions of paracompactness, almost paracompactness, and near paracompactness all of which turn to be good extensions of their classical topological counterparts. Fuzzy semi-paracompact, para S-closed and weakly paracompact spaces are treated to a similar approach.

• Communications of the Korean Mathematical Society
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• v.26 no.2
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• pp.305-320
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• 2011

The relations among various types of continuity of fuzzy proper function on a fuzzy set and at fuzzy point belonging to the fuzzy set in the context of $\v{S}$ostak's I-fuzzy topological spaces are discussed. The projection maps are defined as fuzzy proper functions and their properties are proved.

• International Journal of Fuzzy Logic and Intelligent Systems
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• v.9 no.2
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• pp.83-93
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• 2009

Recently, El-Naschie has shown that the notion of fuzzy topology may be relevant to quantum paretical physics in connection with string theory and E-infinity space time theory. In this paper, we study the concepts of r-fuzzy semi-I-open, r-fuzzy pre-I-open, r-fuzzy $\alpha$-I-open and r-fuzzy $\beta$-I-open sets, which is properly placed between r-fuzzy openness and r-fuzzy $\alpha$-I-openness (r-fuzzy pre-I-openness) sets regardless the fuzzy ideal topological space in Sostak sense. Moreover, we give a decomposition of fuzzy continuity, fuzzy ideal continuity and fuzzy ideal $\alpha$-continuity, and obtain several characterization and some properties of these functions. Also, we investigate their relationship with other types of function.