• Title/Summary/Keyword: (fuzzy) closure spaces

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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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FUZZY CLOSURE SYSTEMS AND FUZZY CLOSURE OPERATORS

  • Kim, Yong-Chan;Ko, Jung-Mi
    • Communications of the Korean Mathematical Society
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    • v.19 no.1
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    • pp.35-51
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    • 2004
  • We introduce fuzzy closure systems and fuzzy closure operators as extensions of closure systems and closure operators. We study relationships between fuzzy closure systems and fuzzy closure spaces. In particular, two families F(S) and F(C) of fuzzy closure systems and fuzzy closure operators on X are complete lattice isomorphic.

Some properties of fuzzy closure spaces

  • Lee, Sang-Hun
    • Journal of the Korean Institute of Intelligent Systems
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    • v.9 no.4
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    • pp.404-410
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    • 1999
  • We will prove the existence of initial fuzzy closure structures. From this fact we can define subspaces and products of fuzzy closure spaces. Furthermore the family $\Delta$(X) of all fuzzy closure operators on X is a complete lattice. In particular an initial structure of fuzzy topological spaces can be obtained by the initial structure of fuzzy closure spaces induced by those. We suggest some examples of it.

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Delta Closure and Delta Interior in Intuitionistic Fuzzy Topological Spaces

  • Eom, Yeon Seok;Lee, Seok Jong
    • International Journal of Fuzzy Logic and Intelligent Systems
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    • v.12 no.4
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    • pp.290-295
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    • 2012
  • Due to importance of the concepts of ${\theta}$-closure and ${\delta}$-closure, it is natural to try for their extensions to fuzzy topological spaces. So, Ganguly and Saha introduced and investigated the concept of fuzzy ${\delta}$-closure by using the concept of quasi-coincidence in fuzzy topological spaces. In this paper, we will introduce the concept of ${\delta}$-closure in intuitionistic fuzzy topological spaces, which is a generalization of the ${\delta}$-closure by Ganguly and Saha.

Fuzzy closure spaces and fuzzy quasi-proximity spaces

  • Lee, Jong-Wan
    • Journal of the Korean Institute of Intelligent Systems
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    • v.9 no.5
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    • pp.550-554
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    • 1999
  • We will define a fuzzy quasi-proximity space and give some examples of it. We show that the family M(X, C) of all fuzzy quasi-proximities on X which induce C is nonempty. Moreover we will study the relationship between the category of fuzzy closure spaces and that of fuzzy quasi-proximity spaces.

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ON FUZZY ${T_2}$-AXIOMS

  • Cho, Sung-Ki
    • Communications of the Korean Mathematical Society
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    • v.14 no.2
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    • pp.393-403
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    • 1999
  • Some fuzzy T\ulcorner-axioms are characterized in terms of the notion of fuzzy closure and the relationship between those fuzzy T\ulcorner-axioms are obtained. Also, finite fuzzy topological spaces satisfying one of those axioms are studied.

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Final Smooth Fuzzy Topologies

  • Kim, Young-Sun
    • Journal of the Korean Institute of Intelligent Systems
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    • v.10 no.2
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    • pp.107-112
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    • 2000
  • We will prove the existence of final smooth fuzzy topological spaces and final smooth fuzzy closure spaces. From this fact we can define quotient spaces of their spaces.

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FUZZY G-CLOSURE OPERATORS

  • Kim, Yong-Chan;Ko, Jung-Mi
    • Communications of the Korean Mathematical Society
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    • v.18 no.2
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    • pp.325-340
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    • 2003
  • We introduce a fuzzy g-closure operator induced by a fuzzy topological space in view of the definition of Sostak [13]. We show that it is a fuzzy closure operator. Furthermore, it induces a fuzzy topology which is finer than a given fuzzy topology. We investigate some properties of fuzzy g-closure operators.

Fuzzy quasi extremally disconnected spaces (퍼지 준 extremally disconnected 공간)

  • Park, Jin-Han;Park, Yong-Beom;Lee, Bu-Young
    • Proceedings of the Korean Institute of Intelligent Systems Conference
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    • 2005.11a
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    • pp.209-212
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    • 2005
  • In this paper, we introduce the concept of fuzzy quasi extremally disconnectedness in fuzzy bitopological space, which is a generalization of fuzzy extremally disconnectedness due to Ghosh [5] in fuzzy topological space and investigate some of its properties using the concepts of quasi-semi-closure, quasi-$\Theta$_closure and related notions in a fuzzy bitopological setting.

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R-Fuzzy $\delta$-Closure and R-Fuzzy $\theta$-Closure Sets

  • Kim, Yong-Chan;Park, Jin-Won
    • Journal of the Korean Institute of Intelligent Systems
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    • v.10 no.6
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    • pp.557-563
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    • 2000
  • We introduce r-fuzzy $\delta$-cluster ($\theta$-cluster) points and r-fuzzy $\delta$-closure ($\theta$-closure) sets in smooth fuzzy topological spaces in a view of the definition of A.P. Sostak [13]. We study some properties of them.

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