• 제목/요약/키워드: Join and meet preserving maps

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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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    • 제38권1_2호
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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.

L-upper Approximation Operators and Join Preserving Maps

  • Kim, Yong Chan;Kim, Young Sun
    • International Journal of Fuzzy Logic and Intelligent Systems
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    • 제14권3호
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    • pp.222-230
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    • 2014
  • In this paper, we investigate the properties of join and meet preserving maps in complete residuated lattice using Zhang's the fuzzy complete lattice which is defined by join and meet on fuzzy posets. We define L-upper (resp. L-lower) approximation operators as a generalization of fuzzy rough sets in complete residuated lattices. Moreover, we investigate the relations between L-upper (resp. L-lower) approximation operators and L-fuzzy preorders. We study various L-fuzzy preorders on $L^X$. They are considered as an important mathematical tool for algebraic structure of fuzzy contexts.

Some Properties of Alexandrov Topologies

  • Kim, Yong Chan;Kim, Young Sun
    • International Journal of Fuzzy Logic and Intelligent Systems
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    • 제15권1호
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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.