fuzzy sets; similarity relation, fuzzy logic, models of fuzzy logic

Let $\Omega$ be a complete residuated lattice. By $\Setf$ we denote a category of sets with similarity relations $(A,\delta)$ with values in $\Omega$. We then investigate an interpretation of a first order predicate fuzzy logic in a model based on objects of this category $\Setf$. Some properties of interpretation of formulas are proved.

Let $\Omega$ be a complete residuated lattice. By $\Setf$ we denote a category of sets with similarity relations $(A,\delta)$ with values in $\Omega$. We then investigate an interpretation of a first order predicate fuzzy logic in a model based on objects of this category $\Setf$. Some properties of interpretation of formulas are proved.