• The Pure and Applied Mathematics
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• v.14 no.2 s.36
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• pp.63-70
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• 2007

In this paper, we introduce the concepts of r-gp-open map, weakly r-gp-open map, intuitionistic fuzzy r-compactness, nearly intuitionistic fuzzy r-compactness and almost intuitionistic fuzzy r-compactness defined by intuitionixtic gradations of openness, and obtain some characterizations.

• The Pure and Applied Mathematics
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• v.14 no.3
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• pp.167-189
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• 2007

In this paper we define a topology (analogous to Chang-type fuzzy topology) and a fuzzy topology (analogous to $H\"{o}hle-type$ fuzzy topology) associated with a lattice and study some of their properties.

• Honam Mathematical Journal
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• v.33 no.4
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• pp.453-465
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• 2011

Lim et al. [5] introduce the notion of ordinary smooth topologies by considering the gradation of openness[resp. closedness] of ordinary subsets of X. In this paper, we study a collection of all ordinary smooth topologies on X, say OST(X), in the sense of a lattice. And we prove that OST(X) is a complete lattice.

• International Journal of Fuzzy Logic and Intelligent Systems
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• v.12 no.1
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• pp.66-76
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• 2012

In this paper, we introduce the concept of ordinary smooth topology on a set X by considering the gradation of openness of ordinary subsets of X. And we obtain the result [Corollary 2.13] : An ordinary smooth topology is fully determined its decomposition in classical topologies. Also we introduce the notion of ordinary smooth [resp. strong and weak] continuity and study some its properties. Also we introduce the concepts of a base and a subbase in an ordinary smooth topological space and study their properties. Finally, we investigate some properties of an ordinary smooth subspace.