On local entropy of fuzzy partitions

In this paper we will introduce a new kind of fuzzy version of the local entropy of a continuous dynamical system on a compact metric space and will prove some of its properties. Then we will define an average entropy of fuzzy partitions by integrating the local fuzzy entropy. We will also state the relationship between this entropy and the fuzzy entropy of dynamical systems based on the entropy of fuzzy partitions in the sense of Dumitrescu.