• Title/Summary/Keyword: Fuzzy complete

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Expectations In Fuzzy Environments

  • Mordechay, Schneider;Abraham, Kandel
    • Journal of the Korean Institute of Intelligent Systems
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    • v.3 no.1
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    • pp.76-89
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    • 1993
  • The evaluation of the Fuzzy Expected Value (FEV) as a typical value requires complete knowledge about the domain of the evaluation, and the distribution of the population in that domain [1]. Since in many situations it is not possible to gather complete knowledge regarding the domain, it is necessary to relax some of the restrictions involving the evaluation of FEV. In this paper we discuss solutions to this problem by using the concept of the Fuzzy Expected Interval (FEI).

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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.

ε-FUZZY CONGRUENCES ON SEMIGROUPS

  • Chon, In-Heung
    • Communications of the Korean Mathematical Society
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    • v.23 no.4
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    • pp.461-468
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    • 2008
  • We define an $\epsilon$-fuzzy congruence, which is a weakened fuzzy congruence, find the $\epsilon$-fuzzy congruence generated by the union of two $\epsilon$-fuzzy congruences on a semigroup, and characterize the $\epsilon$-fuzzy congruences generated by fuzzy relations on semigroups. We also show that the collection of all $\epsilon$-fuzzy congruences on a semigroup is a complete lattice and that the collection of $\epsilon$-fuzzy congruences under some conditions is a modular lattice.

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.

𝛿;-FUZZY IDEALS IN PSEUDO-COMPLEMENTED DISTRIBUTIVE LATTICES

  • ALABA, BERHANU ASSAYE;NORAHUN, WONDWOSEN ZEMENE
    • Journal of applied mathematics & informatics
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    • v.37 no.5_6
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    • pp.383-397
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    • 2019
  • In this paper, we introduce ${\delta}$-fuzzy ideals in a pseudo complemented distributive lattice in terms of fuzzy filters. It is proved that the set of all ${\delta}$-fuzzy ideals forms a complete distributive lattice. The set of equivalent conditions are given for the class of all ${\delta}$-fuzzy ideals to be a sub-lattice of the fuzzy ideals of L. Moreover, ${\delta}$-fuzzy ideals are characterized in terms of fuzzy congruences.

FIXED POINT THEOREMS FOR FUZZY MAPPINGS

  • CHO SEONG-HOON
    • Journal of applied mathematics & informatics
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    • v.19 no.1_2
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    • pp.485-492
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    • 2005
  • In this paper, we obtain some common fixed point theorems for fuzzy mappings in complete metric linear spaces.