  This paper is a contribution to graded model theory, in the context of
mathematical fuzzy logic. We study characterizations of classes of graded
structures in terms of the syntactic form of their first-order axiomatization.
We focus on classes given by universal and universal-existential sentences. In
particular, we prove two amalgamation results using the technique of diagrams
in the setting of structures valued on a finite MTL-algebra, from which
analogues of the Los--Tarski and the Chang--Los--Suszko preservation theorems
follow.
