We study the problem of minimizing interpretations in fuzzy description logics (DLs) under the Gödel semantics by using fuzzy bisimulations. The considered logics are fuzzy extensions of the DL 𝒜ℒ𝒞reg (a variant of propositional dynamic logic) with additional features among inverse roles, nominals and the universal role. Given a fuzzy interpretation ℐ and for E being the greatest fuzzy auto-bisimulation of ℐ w.r.t. the considered DL, we define the quotient ℐ/E of ℐ w.r.t. E and prove that it is minimum w.r.t. certain criteria. Namely, ℐ/E is a minimum fuzzy interpretation that validates the same set of fuzzy terminological axioms in the considered DL as ℐ. Furthermore, if the considered DL allows the universal role, then ℐ/E is a minimum fuzzy interpretation bisimilar to ℐ, as well as a minimum fuzzy interpretation that validates the same set of fuzzy concept assertions in the considered DL as ℐ.
