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We formulate and prove logical characterizations of crisp simulations andcrisp directed simulations between fuzzy labeled transition systems withrespect to fuzzy modal logics that use a general t-norm-based semantics. Theconsidered logics are fragments of the fuzzy propositional dynamic logic withthe Baaz projection operator. The logical characterizations concernpreservation of positive existential (respectively, positive) modal formulasunder crisp simulations (respectively, crisp directed simulations), as well asthe Hennessy-Milner property of such simulations.

Characterizing Crisp Simulations and Crisp Directed Simulations between Fuzzy Labeled Transition Systems by Using Fuzzy Modal Logics