ε-FUZZY CONGRUENCES ON SEMIGROUPS
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We define an ε-fuzzy congruence, which is a weakened fuzzy congruence, find the ε-fuzzy congruence generated by the union of two ε-fuzzy congruences on a semigroup, and characterize the ε-fuzzy congruences generated by fuzzy relations on semigroups. We also show that the collection of all ε-fuzzy congruences on a semigroup is a complete lattice and that the collection of ε-fuzzy congruences under some conditions is a modular lattice.
Abstract
We define an ε-fuzzy congruence, which is a weakened fuzzy congruence, find the ε-fuzzy congruence generated by the union of two ε-fuzzy congruences on a semigroup, and characterize the ε-fuzzy congruences generated by fuzzy relations on semigroups. We also show that the collection of all ε-fuzzy congruences on a semigroup is a complete lattice and that the collection of ε-fuzzy congruences under some conditions is a modular lattice.
참고문헌 (8)
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