Direct Limits and Reduced Products of Algebras with Fuzzy Equalities
We study direct limits and reduced products of algebras with fuzzy equalities. On the one hand, algebras with fuzzy equalities are natural fuzzy structures that disallow to map similar arguments to dissimilar ones. On the other hand, they are exactly the semantic structures of the equational fragment of first-order fuzzy logic. In this paper we propose generalizations of direct limits and reduced products and point out those properties which are not interesting in the classical (bivalent) case, but which seem to be of a crucial importance when considering the quasi-varieties of algebras with fuzzy equalities.