• 제목/요약/키워드: Fuzzy partially ordered set

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FUZZY LATTICES AS FUZZY RELATIONS

  • CHON, INHEUNG
    • Korean Journal of Mathematics
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    • 제23권4호
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    • pp.557-569
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    • 2015
  • We dene a fuzzy lattice as a fuzzy relation, develop some basic properties of the fuzzy lattice, show that the operations of join and meet in fuzzy lattices are isotone and associative, characterize a fuzzy lattice by its level set, and show that the direct product of two fuzzy lattices is a fuzzy lattice.

Fuzzzy Functions and Fuzzy Partially Ordered Sets

  • Hur, Kul;Jung, Hyo-Mi;Lee, Wang-Ro
    • International Journal of Fuzzy Logic and Intelligent Systems
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    • 제9권4호
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    • pp.285-293
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    • 2009
  • By using the notion of fuzzy functions introduced by Dib and Youssef, we obtain fuzzy analogues of some results concerning ordinary functions. In particular, we give the denition dierent from one of invertible fuzzy function introduced by Dib and Youssef. And we show that the two denitions are equivalent. Furthermore, we introduce the concepts of fuzzy increasing functions and fuzzy isomorphisms, and we obtain fuzzy analogues of many results concerning ordinary increasing functions and isomorphisms.

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.

The Linear Discrepancy of a Fuzzy Poset

  • Cheong, Min-Seok;Chae, Gab-Byung;Kim, Sang-Mok
    • International Journal of Fuzzy Logic and Intelligent Systems
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    • 제11권1호
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    • pp.59-64
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    • 2011
  • In 2001, the notion of a fuzzy poset defined on a set X via a triplet (L, G, I) of functions with domain X ${\times}$ X and range [0, 1] satisfying a special condition L+G+I = 1 is introduced by J. Negger and Hee Sik Kim, where L is the 'less than' function, G is the 'greater than' function, and I is the 'incomparable to' function. Using this approach, we are able to define a special class of fuzzy posets, and define the 'skeleton' of a fuzzy poset in view of major relation. In this sense, we define the linear discrepancy of a fuzzy poset of size n as the minimum value of all maximum of I(x, y)${\mid}$f(x)-f(y)${\mid}$ for f ${\in}$ F and x, y ${\in}$ X with I(x, y) > $\frac{1}{2}$, where F is the set of all injective order-preserving maps from the fuzzy poset to the set of positive integers. We first show that the definition is well-defined. Then, it is shown that the optimality appears at the same injective order-preserving maps in both cases of a fuzzy poset and its skeleton if the linear discrepancy of a skeleton of a fuzzy poset is 1.