• Title/Summary/Keyword: Alexandrov topologies

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Some Properties of Alexandrov Topologies

  • Kim, Yong Chan;Kim, Young Sun
    • International Journal of Fuzzy Logic and Intelligent Systems
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    • v.15 no.1
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    • pp.72-78
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    • 2015
  • Alexandrov topologies are the topologies induced by relations. This paper addresses the properties of Alexandrov topologies as the extensions of strong topologies and strong cotopologies in complete residuated lattices. With the concepts of Zhang's completeness, the notions are discussed as extensions of interior and closure operators in a sense as Pawlak's the rough set theory. It is shown that interior operators are meet preserving maps and closure operators are join preserving maps in the perspective of Zhang's definition.

THE PROPERTIES OF RESIDUATED CONNECTIONS AND ALEXANDROV TOPOLOGIES

  • Oh, Ju-Mok;Kim, Yong Chan
    • Korean Journal of Mathematics
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    • v.28 no.2
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    • pp.311-321
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    • 2020
  • In this paper, we investigate the properties of residuated connections and Alexandrov topologies based on [0, ∞]. Under various relations, we investigate the residuated and dual residuated connections on Alexandrov toplogies. Moreover, we study their properties and give their examples.

ALEXANDROV TOPOLOGIES AND NON-SYMMETRIC PSEUDO-METRICS

  • Oh, Ju-mok;Kim, Yong Chan
    • The Pure and Applied Mathematics
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    • v.27 no.3
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    • pp.125-135
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    • 2020
  • In this paper, we investigate the properties of Alexandrov topologies, non-symmetric pseudo-metrics and lower approximation operators on [0, ∞]. Moreover, we investigate the relations among Alexandrov topologies, non-symmetric pseudo-metrics and lower approximation operators. We give their examples.

FUZZY JOIN AND MEET PRESERVING MAPS ON ALEXANDROV L-PRETOPOLOGIES

  • KO, JUNG MI;KIM, YONG CHAN
    • Journal of applied mathematics & informatics
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    • v.38 no.1_2
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    • pp.79-89
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    • 2020
  • We introduce the concepts of fuzzy join-complete lattices and Alexandrov L-pre-topologies in complete residuated lattices. We investigate the properties of fuzzy join-complete lattices on Alexandrov L-pre-topologies and fuzzy meet-complete lattices on Alexandrov L-pre-cotopologies. Moreover, we give their examples.

RESIDUATED CONNECTIONS INDUCED BY RESIDUATED FRAMES

  • KO, JUNG MI;KIM, YONG CHAN
    • Journal of applied mathematics & informatics
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    • v.38 no.5_6
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    • pp.547-557
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    • 2020
  • In this paper, we introduce the notions of (dual) residuated frames for a fuzzy logic as an extension of residuated frames for classical relational semantics. We investigate the relations between residuated connections and residuated frames on Alexandrov topologies based on [0, ∞]. Moreover, we study their properties and give their examples.

The Properties of L-lower Approximation Operators

  • Kim, Yong Chan
    • International Journal of Fuzzy Logic and Intelligent Systems
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    • v.14 no.1
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    • pp.57-65
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    • 2014
  • In this paper, we investigate the properties of L-lower approximation operators as a generalization of fuzzy rough set in complete residuated lattices. We study relations lower (upper, join meet, meet join) approximation operators and Alexandrov L-topologies. Moreover, we give their examples as approximation operators induced by various L-fuzzy relations.

APPROXIMATION OPERATORS AND FUZZY ROUGH SETS IN CO-RESIDUATED LATTICES

  • Oh, Ju-Mok;Kim, Yong Chan
    • Korean Journal of Mathematics
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    • v.29 no.1
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    • pp.81-89
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    • 2021
  • In this paper, we introduce the notions of a distance function, Alexandrov topology and ⊖-upper (⊕-lower) approximation operator based on complete co-residuated lattices. Under various relations, we define (⊕, ⊖)-fuzzy rough set on complete co-residuated lattices. Moreover, we study their properties and give their examples.