• Title/Summary/Keyword: smooth fuzzy topological space

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SMOOTH FUZZY CLOSURE AND TOPOLOGICAL SPACES

  • Kim, Yong Chan
    • Korean Journal of Mathematics
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    • v.7 no.1
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    • pp.11-25
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    • 1999
  • We will define a smooth fuzzy closure space and a subspace of it. We will investigate relationships between smooth fuzzy closure spaces and smooth fuzzy topological spaces. In particular, we will show that a subspace of a smooth fuzzy topological space can be obtained by the subspace of the smooth fuzzy closure space induced by it.

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Initial smooth Fuzzy Topological Spaces

  • 김용찬
    • Journal of the Korean Institute of Intelligent Systems
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    • v.8 no.3
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    • pp.88-94
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    • 1998
  • We will difine a base of a smooth fuzzy topological space and investigate some properties of bases. We will prove the existences of initial smooth fuzzy topological spaces. From this fact, we can define subspaces and products of smooth fuzzy topological spaces.

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([r, s], [t, u])-INTERVAL-VALUED INTUITIONISTIC FUZZY GENERALIZED PRECONTINUOUS MAPPINGS

  • Park, Chun-Kee
    • Korean Journal of Mathematics
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    • v.25 no.1
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    • pp.1-18
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    • 2017
  • In this paper, we introduce the concepts of ([r, s], [t, u])-interval-valued intuitionistic fuzzy generalized preclosed sets and ([r, s], [t, u])-interval-valued intuitionistic fuzzy generalized preopen sets in the interval-valued intuitionistic smooth topological space and ([r, s], [t, u])-interval-valued intuitionistic fuzzy generalized pre-continuous mappings and then investigate some of their properties.

([r, s], [t, u])-INTERVAL-VALUED INTUITIONISTIC FUZZY ALPHA GENERALIZED CONTINUOUS MAPPINGS

  • Park, Chun-Kee
    • Korean Journal of Mathematics
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    • v.25 no.2
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    • pp.261-278
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    • 2017
  • In this paper, we introduce the concepts of ([r, s], [t, u])-interval-valued intuitionistic fuzzy alpha generalized closed and open sets in the interval-valued intuitionistic smooth topological space and ([r, s], [t, u])-interval-valued intuitionistic fuzzy alpha generalized continuous mappings and then investigate some of their properties.

Ordinary Smooth Topological Spaces

  • Lim, Pyung-Ki;Ryoo, Byeong-Guk;Hur, Kul
    • 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.

Smooth uniform spaces

  • Ramadan, A.A.;El-Dardery, M.;Kim, Y.C.
    • 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.

Intuitionistic Smooth Topological Spaces

  • Lim, Pyung-Ki;Kim, So-Ra;Hur, Kul
    • Journal of the Korean Institute of Intelligent Systems
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    • v.20 no.6
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    • pp.875-883
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    • 2010
  • We introduce the concept of intuitionistic smooth topology in Lowen's sense and we prove that the family IST(X) of all intuitionistic smooth topologies on a set is a meet complete lattice with least element and the greatest element [Proposition 3.6]. Also we introduce the notion of level fuzzy topology on a set X with respect to an intuitionistic smooth topology and we obtain the relation between the intuitionistic smooth topology $\tau$ and the intuitionistic smooth topology $\eta$ generated by level fuzzy topologies with respect to $\tau$ [Theorem 3.10].

Closure, Interior and Compactness in Ordinary Smooth Topological Spaces

  • Lee, Jeong Gon;Hur, Kul;Lim, Pyung Ki
    • 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.

INTERVAL-VALUED SMOOTH TOPOLOGICAL SPACES

  • Choi, Jeong-Yeol;Kim, So-Ra;Hur, Kul
    • 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.