Summary: The author studies systems of equations which naturally arise in the formalization of the Port-Royal theory of concepts. An unknown quantity is a relation between objects and attributes. We study the case where the relation is fuzzy with truth values in a complete residuated lattice, covering therefore the special cases of complete Boolean algebras, Heyting algebras, MV-algebras, etc. We answer the question of solvability, structure of solutions, and show how solvability of non-solvable systems may be attained by so-called decrease of logical precision.