The Entropy of Fuzzy Dynamical Systems with Countable Partitions

In this paper, the entropy of fuzzy countable partitions is proposed. In addition, the notion of fuzzy conditional entropy, fuzzy relative entropy and entropy on a fuzzy dynamical system based on fuzzy countable partitions are introduced and some properties of these entropies are analyzed. Using the concept of fuzzy generator, it is proved that the entropy of a dynamical system is done through a fuzzy generator. Furthermore, one of the proven results in this paper is isomorphism invariant property of entropy with fuzzy countable partitions on a fuzzy dynamical system.