$\epsilon$-fuzzy congruences on semigroups
Commun. Korean Math. Soc. 2008 Vol. 23, No. 4, 461-468
Printed December 1, 2008
Inheung Chon
Seoul Women's University
Abstract : We define an $\epsilon$-fuzzy congruence, which is a weakened fuzzy congruence, find the $\epsilon$-fuzzy congruence generated by the union of two $\epsilon$-fuzzy congruences on a semigroup, and characterize the $\epsilon$-fuzzy congruences generated by fuzzy relations on semigroups. We also show that the collection of all $\epsilon$-fuzzy congruences on a semigroup is a complete lattice and that the collection of $\epsilon$-fuzzy congruences under some conditions is a modular lattice.
Keywords : $\epsilon$-reflexive fuzzy relation, $\epsilon$-fuzzy equivalence relation, $\epsilon$-fuzzy congruence
MSC numbers : 3.00E+72
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