International Journal of Fuzzy Logic and Intelligent Systems

  • 제13권3호
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  • Pages.231-244
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  • 2013
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  • 1598-2645(pISSN)
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  • 2093-744X(eISSN)
한국지능시스템학회 (Korean Institute of Intelligent Systems)
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Interval-Valued Fuzzy Congruences on a Semigroup

  • Lee, Jeong Gon (Division of Mathematics and Informational Statistics and Nanoscale Science and Technology Institute, Wonkwang University) ;
  • Hur, Kul (Division of Mathematics and Informational Statistics and Nanoscale Science and Technology Institute, Wonkwang University) ;
  • Lim, Pyung Ki (Division of Mathematics and Informational Statistics and Nanoscale Science and Technology Institute, Wonkwang University)
  • 투고 : 2013.01.02
  • 심사 : 2013.09.10
  • 발행 : 2013.09.25
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초록

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.

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참고문헌

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피인용 문헌

  1. INTERVAL-VALUED FUZZY GROUP CONGRUENCES vol.38, pp.2, 2016, https://doi.org/10.5831/HMJ.2016.38.2.403