Constructions of fuzzy logic models in categories of sets with similarities

Constructions of fuzzy logic models in two categories of sets with similarity relations (A, ) (graded in a complete residuated lattice ) are presented. For these models, a truth valuation of a fuzzy logic formula is defined as a special morphism [image omitted] in these categories, where is a biresiduation operator in . It specifies a grade [image omitted] in which is true if free variables [image omitted] are substituted by elements [image omitted]. We will introduce a notion of a model homomorphism and prove some relationships between interpretations [image omitted] and [image omitted] if there exists a model homomorphism [image omitted].