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http://dx.doi.org/10.5391/IJFIS.2013.13.3.231

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)
Publication Information
International Journal of Fuzzy Logic and Intelligent Systems / v.13, no.3, 2013 , pp. 231-244 More about this Journal
Abstract
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.
Keywords
Interval-valued fuzzy set; Interval-valued fuzzy (normal) subgroup; Interval-valued fuzzy congruence;
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Times Cited By KSCI : 11  (Citation Analysis)
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