Fuzzy quotient algebras and fuzzy factor congruences (Q1920260)

The author defines a fuzzy quotient algebra of a universal algebra induced by a fuzzy congruence relation and establishes certain fuzzy counterparts of classical homomorphism theorems for fuzzy quotient algebras. Further, a pair of complementary fuzzy factor congruences is introduced and on this basis fuzzy factorable algebras are defined. Necessary and sufficient conditions for an algebra \(A\) to be fuzzy factorable are obtained. It is proved that, in case the lattice of fuzzy congruences of \(A=A_1 \times A_2\) is distributive, the lattice of fuzzy congruences of \(A_1 \times A_2\) is isomorphic to the direct product of the lattices of fuzzy congruences of \(A_1\) and \(A_2\).