• Title, Summary, Keyword: interval-valued fuzzy group congruence

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Interval-Valued Fuzzy Congruences on a Semigroup

  • Lee, Jeong Gon;Hur, Kul;Lim, Pyung Ki
    • International Journal of Fuzzy Logic and Intelligent Systems
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    • v.13 no.3
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    • pp.231-244
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    • 2013
  • We introduce the concept of interval-valued fuzzy congruences on a semigroup S and we obtain some important results: First, for any interval-valued fuzzy congruence $R_e$ on a group G, the interval-valued congruence class Re is an interval-valued fuzzy normal subgroup of G. Second, for any interval-valued fuzzy congruence R on a groupoid S, we show that a binary operation * an S=R is well-defined and also we obtain some results related to additional conditions for S. Also we improve that for any two interval-valued fuzzy congruences R and Q on a semigroup S such that $R{\subset}Q$, there exists a unique semigroup homomorphism g : S/R${\rightarrow}$S/G.

INTERVAL-VALUED FUZZY GROUP CONGRUENCES

  • Lee, Jeong Gon;Hur, Kul;Lim, Pyung Ki
    • Honam Mathematical Journal
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    • v.38 no.2
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    • pp.403-423
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    • 2016
  • We introduce the concepts of interval-valued fuzzy complete inner-unitary subsemigroups and interval-valued fuzzy group congruences on a semigroup. And we investigate some of their properties. Also, we prove that there is a one to one correspondence between the interval-valued fuzzy complete inner-unitary subsemigroups and the interval-valued fuzzy group congruences on a regular semigroups.