Recently the logical entropy was suggested by D. Ellerman (2013) as a new information measure. The present paper deals with studying logical entropy and logical mutual information and their properties in a fuzzy probability space. In particular, chain rules for logical entropy and for logical mutual information of fuzzy partitions are established. Using the concept of logical entropy of fuzzy partition we define the logical entropy of fuzzy dynamical systems. Finally, it is proved that the logical entropy of fuzzy dynamical systems is invariant under isomorphism of fuzzy dynamical systems.