• Title/Summary/Keyword: Informational Technology

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NEIGHBORHOOD STRUCTURES IN ORDINARY SMOOTH TOPOLOGICAL SPACES

  • Lee, Jeong Gon;Lim, Pyung Ki;Hur, Kul
    • Honam Mathematical Journal
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    • v.34 no.4
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    • pp.559-570
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    • 2012
  • We construct a new definition of a base for ordinary smooth topological spaces and introduce the concept of a neighborhood structure in ordinary smooth topological spaces. Then, we state some of their properties which are generalizations of some results in classical topological spaces.

Vague Continuous Mappings

  • Lim, Pyung-Ki;Kim, So-Ra;Hur, Kul
    • International Journal of Fuzzy Logic and Intelligent Systems
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    • v.10 no.2
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    • pp.157-164
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    • 2010
  • Up to now, in the area of fuzzy topology, almost all the researchers have investigated fuzzy continuities by using ordinary mappings. However, in this paper, we study continuities by using fuzzy mappings introduced by Demirci [2].

The Category VSet(H)

  • Lim, Pyung-Ki;Kim, So-Ra;Hur, Kul
    • International Journal of Fuzzy Logic and Intelligent Systems
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    • v.10 no.1
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    • pp.73-81
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    • 2010
  • We introduce the new category VSet(H) consisting of H-fuzzy spaces and H-fuzzy mappings between them satisfying a certain condition, and investigate VSet(H) in the sense of a topological universe. Moreover, we show that VSet(H) is Cartesian closed over Set.

Lattices of Interval-Valued Fuzzy Subgroups

  • Lee, Jeong Gon;Hur, Kul;Lim, Pyung Ki
    • International Journal of Fuzzy Logic and Intelligent Systems
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    • v.14 no.2
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    • pp.154-161
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    • 2014
  • We discuss some interesting sublattices of interval-valued fuzzy subgroups. In our main result, we consider the set of all interval-valued fuzzy normal subgroups with finite range that attain the same value at the identity element of the group. We then prove that this set forms a modular sublattice of the lattice of interval-valued fuzzy subgroups. In fact, this is an interval-valued fuzzy version of a well-known result from classical lattice theory. Finally, we employ a lattice diagram to exhibit the interrelationship among these sublattices.

INTERVAL-VALUED FUZZY GROUP CONGRUENCES

  • Lee, Jeong Gon;Hur, Kul;Lim, Pyung Ki
    • Honam Mathematical Journal
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    • v.38 no.2
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    • pp.403-423
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    • 2016
  • We introduce the concepts of interval-valued fuzzy complete inner-unitary subsemigroups and interval-valued fuzzy group congruences on a semigroup. And we investigate some of their properties. Also, we prove that there is a one to one correspondence between the interval-valued fuzzy complete inner-unitary subsemigroups and the interval-valued fuzzy group congruences on a regular semigroups.

ON INTERVAL-VALUED FUZZY LATTICES

  • LEE, JEONG GON;HUR, KUL;LIM, PYUNG KI
    • Honam Mathematical Journal
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    • v.37 no.2
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    • pp.187-205
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    • 2015
  • We discuss the relationship between interval-valued fuzzy ideals and interval-valued fuzzy congruence on a distributive lattice L and show that for a generalized Boolean algebra the lattice of interval-valued fuzzy ideals is isomorphic to the lattice of interval-valued fuzzy congruences. Finally we consider the products of interval-valued fuzzy ideals and obtain a necessary and sufficient condition for an interval-valued fuzzy ideal on the direct sum of lattices to be representable as a direct sum of interval-valued fuzzy ideals on each lattice.

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.

Fuzzy Mappings and Fuzzy Equivalence Relations

  • Lim, Pyung-Ki;Choi, Ga-Hee;Hur, Kul
    • International Journal of Fuzzy Logic and Intelligent Systems
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    • v.11 no.3
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    • pp.153-164
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    • 2011
  • Equivalence relations and mappings for crisp sets are very well known. This paper attempts an investigation of equivalence relations and mappings for fuzzy sets. We list some concepts and results related to fuzzy relations. We give some examples corresponding to the concept of fuzzy equality and fuzzy mapping introduced by Demirci [1]. In addition, we introduce the notion of preimage and quotient of fuzzy equivalence relations. Finally, we investigate relations between a fuzzy equivalence relation and a fuzzy mapping.