• Title/Summary/Keyword: Fuzzy semigroup

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HESITANT FUZZY SEMIGROUPS WITH TWO FRONTIERS

  • Jun, Young Bae;Lee, Kyoung Ja;Park, Chul Hwan
    • Communications of the Korean Mathematical Society
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    • v.31 no.1
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    • pp.17-25
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    • 2016
  • The notion of hesitant fuzzy semigroups with two frontiers is introduced, and related properties are investigated. Relations between a hesitant fuzzy semigroups with a frontier and a hesitant fuzzy semigroups with two frontiers are discussed. It is shown that the hesitant intersection of two hesitant fuzzy semigroups with two frontiers is a hesitant fuzzy semigroup with two frontiers. We provide an example to show that the hesitant union of two hesitant fuzzy semigroups with two frontiers may not be a hesitant fuzzy semigroup with two frontiers.

FUZZY SEMIGROUPS IN REDUCTIVE SEMIGROUPS

  • Chon, Inheung
    • Korean Journal of Mathematics
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    • v.21 no.2
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    • pp.171-180
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    • 2013
  • We consider a fuzzy semigroup S in a right (or left) reductive semigroup X such that $S(k)=1$ for some $k{\in}X$ and find a faithful representation (or anti-representation) of S by transformations of S. Also we show that a fuzzy semigroup S in a weakly reductive semigroup X such that $S(k)=1$ for some $k{\in}X$ is isomorphic to the semigroup consisting of all pairs of inner right and left translations of S and that S can be embedded into the semigroup consisting of all pairs of linked right and left translations of S with the property that S is an ideal of the semigroup.

A NEW APPROACH TO FUZZY CONGRUENCES

  • Hur, Kul;Jang, Su-Youn;Lee, Keon-Chang
    • International Journal of Fuzzy Logic and Intelligent Systems
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    • v.7 no.1
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    • pp.7-16
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    • 2007
  • First, we investigate fuzzy equivalence relations on a set X in the sense of Youssef and Dib. Second, we discuss fuzzy congruences generated by a given fuzzy relation on a fuzzy groupoid. In particular, we obtain the characterizations of ${\rho}\;o\;{\sigma}{\in}$ FC(S) for any two fuzzy congruences ${\rho}\;and\;{\sigma}$ on a fuzzy groupoid ($S,{\odot}$). Finally, we study the lattice of fuzzy equivalence relations (congruences) on a fuzzy semigroup and give certain lattice theoretic properties.

Interval-valued Fuzzy Ideals and Bi-ideals of a Semigroup

  • Cheong, Min-Seok;Hur, Kul
    • International Journal of Fuzzy Logic and Intelligent Systems
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    • v.11 no.4
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    • pp.259-266
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    • 2011
  • We apply the concept of interval-valued fuzzy sets to theory of semigroups. We give some properties of interval-valued fuzzy ideals and interval-valued fuzzy bi-ideals, and characterize which is left [right] simple, left [right] duo and a semilattice of left [right] simple semigroups or another type of semigroups in terms of interval-valued fuzzy ideals and intervalvalued fuzzy bi-ideals.

INTUITIONISTIC FUZZY IDEALS AND BI-IDEALS

  • HUR, KUL;KIM, KWANG JIN;SONG, HYEONG KEE
    • Honam Mathematical Journal
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    • v.26 no.3
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    • pp.309-330
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    • 2004
  • In this paper, we apply the concept of intuitionistic fuzzy sets to theory of semigroups. We give some properties of intuitionistic fuzzy ideals and intuitionistic fuzzy bi-ideals, and characterize which is left [right] simple, left [right] duo and a semilattice of left [right] simple semigroups or another type of semigroups in terms of intuitionistic fuzzy ideals and intuitionistic fuzzy bi-ideals.

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HESITANT FUZZY BI-IDEALS IN SEMIGROUPS

  • JUN, YOUNG BAE;LEE, KYOUNG JA;SONG, SEOK-ZUN
    • Communications of the Korean Mathematical Society
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    • v.30 no.3
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    • pp.143-154
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    • 2015
  • Characterizations of hesitant fuzzy left (right) ideals are considered. The notion of hesitant fuzzy (generalized) bi-ideals is introduced, and related properties are investigated. Relations between hesitant fuzzy generalized bi-ideals and hesitant fuzzy semigroups are discussed, and characterizations of (hesitant fuzzy) generalized bi-ideals and hesitant fuzzy bi-ideals are considered. Given a hesitant fuzzy set $\mathcal{H}$ on a semigroup S, hesitant fuzzy (generalized) bi-ideals generated by $\mathcal{H}$ are established.