AbstractUnfolding is a semantics-preserving program transformation technique that consists in the expansion of subexpressions of a program using their own definitions. In this paper we define two unfolding-based transformation rules that extend the classical definition of the unfolding rule (for pure logic programs) to a fuzzy logic setting. We use a fuzzy variant of Prolog where each program clause can be interpreted under a different (fuzzy) logic. We adapt the concept of a computation rule, a mapping that selects the subexpression of a goal involved in a computation step, and we prove the independence of the computation rule. We also define a basic transformation system and we demonstrate its strong correctness, that is, original and transformed programs compute the same fuzzy computed answers. Finally, we prove that our transformation rules always produce an improvement in the efficiency of the residual program, by reducing the length of successful Fuzzy SLD-derivations.