Abstract:
Abstract. In this paper we give several characterizations for fuzzy
ideals, fuzzy homomorphisms, and fuzzy congruences of an almost dis-
tributive lattice. In addition, the quotient of an almost distributive lattice
induced by a fuzzy congruence is also presented in the paper. Furthermore,
we obtain a kind of fuzzy congruences for which their quotient is a distribu-
tive lattice and for which it is not. Mainly, we construct a monomorphism
of the lattice of fuzzy ideals into the lattice of fuzzy congruences of almost
Boolean rings, and we give a necessary and su cient condition for this
monomorphism to become a lattice isomorphism.
2010 AMS Classi cation: 06D72, 06F15, 08A72
Keywords: ADLs, Fuzzy ideals, Fuzzy homomorphisms, Fuzzy congruences.
