• International Journal of Fuzzy Logic and Intelligent Systems
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• v.2 no.1
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• pp.83-88
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• 2002

We study some properties of smooth uniform spaces. We investigate the relationship between smooth topological spaces and smooth uniform spaces. In particular, we define a subspace of a smooth uniform space and a product of smooth uniform spaces.

• Journal of the Korean Institute of Intelligent Systems
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• v.19 no.5
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• pp.695-698
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• 2009

In this paper, we introduce the concept of fuzzy r-generalized open sets which are generalizations of fuzzy r-open sets defined by Lee and Lee [2] and obtain some basic properties of their structures. Also we introduce and study the concepts of fuzzy r-generalized continuous mapping, fuzzy r-generalized open mapping and fuzzy r-generalized closed mapping.

• Korean Journal of Mathematics
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• v.10 no.1
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• pp.5-10
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• 2002

In this paper, we investigate the prefilter base on a fuzzy set and fuzzy net ${\varphi}$ on the fuzzy topological space (X,${\delta}$). And we show that the prefilter base $\mathcal{B}({\varphi})$ determines by the fuzzy net ${\varphi}$ converge to a fuzzy point $p$ iff the fuzzy net ${\varphi}$ converge to a fuzzy point $p$. Also we prove that if the prefilter base $\mathcal{B}$ converge to a fuzzy point $p$, then the $\mathcal{B}$ has the cluster point $p$.

• Korean Journal of Mathematics
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• v.14 no.1
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• pp.57-64
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• 2006

In this paper, we introduce the concepts of $r$-closure and $r$-interior defined by intuitionistic gradation of openness. We also introduce the concepts of $r$-gp-maps, weakly $r$-gp-maps, and obtain some characterizations in terms of $r$-closure and $r$-interior operators.

• International Journal of Fuzzy Logic and Intelligent Systems
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• v.14 no.3
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• pp.231-239
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• 2014

It presents the concepts of ordinary smooth interior and ordinary smooth closure of an ordinary subset and their structural properties. It also introduces the notion of ordinary smooth (open) preserving mapping and addresses some their properties. In addition, it develops the notions of ordinary smooth compactness, ordinary smooth almost compactness, and ordinary near compactness and discusses them in the general framework of ordinary smooth topological spaces.

• Honam Mathematical Journal
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• v.30 no.2
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• pp.283-297
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• 2008

The notion of IVF contra (${\alpha}$-)open ((${\alpha}$-)closed) mappings is introduced, and their characterizations are given. The relationship between IVF contra open (closed) mappings and IVF contra ${\alpha}$-open (${\alpha}$-closed) mappings are discussed.

• Honam Mathematical Journal
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• v.32 no.4
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• pp.711-738
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• 2010

We list two kinds of gradation of openness and we study in the sense of the followings: (i) We give the definition of IVGO of fuzzy sets and obtain some basic results. (ii) We give the definition of interval-valued gradation of clopeness and obtain some properties. (iii) We give the definition of a subspace of an interval-valued smooth topological space and obtain some properties. (iv) We investigate some properties of gradation preserving (in short, IVGP) mappings.