Abstract:

Residuated lattices play an important role in studies of fuzzy logic. First,   the notions of fuzzy ⊙-ideals in residuated lattices are introduced. Some properties of fuzzy ⊙-ideals in (regular)residuated lattices are discussed and some equivalent characterizations are given. Second, a congruence relation is structured in terms of the notion of fuzzy ⊙-ideal in regular residuated lattices. It is proved that the quotient algebra of a regular residuated lattice under a congruence relation is also a regular residuated lattice.

Key words:  fuzzy logic; (regular)residuated lattices; fuzzy ⊙-ideals; congruence relation; quotient algebra