International Journal of Fuzzy Logic and Intelligent Systems

Korean Institute of Intelligent Systems (한국지능시스템학회)
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A NEW APPROACH TO FUZZY CONGRUENCES

  • Hur, Kul (Division of Mathematics and Informational Statistics, Wonkwang University) ;
  • Jang, Su-Youn (Division of Mathematics and Informational Statistics, Wonkwang University) ;
  • Lee, Keon-Chang (Department of Computer Science, Dongshin Universuty)
  • Published : 2007.03.01
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Abstract

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.

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