• Title/Summary/Keyword: Complete residuated lattice

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Fuzzy Connections and Relations in Complete Residuated Lattices

  • Kim, Yong Chan
    • International Journal of Fuzzy Logic and Intelligent Systems
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    • v.13 no.4
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    • pp.345-351
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    • 2013
  • In this paper, we investigate the properties of fuzzy Galois (dual Galois, residuated, and dual residuated) connections in a complete residuated lattice L. We give their examples. In particular, we study fuzzy Galois (dual Galois, residuated, dual residuated) connections induced by L-fuzzy relations.

TOPOLOGICAL STRUCTURES IN COMPLETE CO-RESIDUATED LATTICES

  • Kim, Young-Hee;Kim, Yong Chan
    • The Pure and Applied Mathematics
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    • v.29 no.1
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    • pp.19-29
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    • 2022
  • Information systems and decision rules with imprecision and uncertainty in data analysis are studied in complete residuated lattices. In this paper, we introduce the notions of Alexandrov pretopology (precotopology) and join-meet (meet-join) operators in complete co-residuated lattices. Moreover, their properties and examples are investigated.

Some Fundamental Concepts in (2, L)-Fuzzy Topology Based on Complete Residuated Lattice-Valued Logic

  • Zeyada, Fathei M.;Zahran, A.M.;El-Baki, S.A.Abd;Mousa, A.K.
    • International Journal of Fuzzy Logic and Intelligent Systems
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    • v.10 no.3
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    • pp.230-241
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    • 2010
  • In the present paper we introduce and study fundamental concepts in the framework of L-fuzzifying topology(so called(2,L)-fuzzy topology)as L-concepts where L is a complete residuated lattice. The concepts of (2,L)-derived, (2,L)-closure, (2,L)-interior, (2,L)-exterior and (2,L)-boundary operators are studied and some results on above concepts are obtained. Also, the concepts of an L-convergence of nets and an L-convergence of filters are introduced and some important results are obtained. Furthermore, we introduce and study bases and subbases in (2,L)-topology. As applications of our work the corresponding results(see[10-11]) are generalized and new consequences are obtained.

L-pre-separation axioms in (2, L)-topologies based on complete residuated lattice-valued logic

  • Zeyada, Fathei M.;Abd-Allahand, M. Azab;Mousa, A.K.
    • International Journal of Fuzzy Logic and Intelligent Systems
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    • v.9 no.2
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    • pp.115-127
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    • 2009
  • In the present paper we introduce and study L-pre-$T_0$-, L-pre-$T_1$-, L-pre-$T_2$ (L-pre-Hausdorff)-, L-pre-$T_3$ (L-pre-regularity)-, L-pre-$T_4$ (L-pre-normality)-, L-pre-strong-$T_3$-, L-pre-strong-$T_4$-, L-pre-$R_0$-, L-pre-$R_1$-separation axioms in (2, L)-topologies where L is a complete residuated lattice.Sometimes we need more conditions on L such as the completely distributive law or that the "$\bigwedge$" is distributive over arbitrary joins or the double negation law as we illustrate through this paper. As applications of our work the corresponding results(see[1,2]) are generalized and new consequences are obtained.

DISTANCE SPACES, ALEXANDROV PRETOPOLOGIES AND JOIN-MEET OPERATORS

  • KIM, YOUNG-HEE;KIM, YONG CHAN;CHOI, JONGSUNG
    • Journal of applied mathematics & informatics
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    • v.39 no.1_2
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    • pp.105-116
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    • 2021
  • Information systems and decision rules with imprecision and uncertainty in data analysis are studied in complete residuated lattices. In this paper, we introduce the notions of distance spaces, Alexandrov pretopology (precotopology) and join-meet (meet-join) operators in complete co-residuated lattices. We investigate their relations and properties. 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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    • v.14 no.3
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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.