Dynamics and topological entropy for Zadeh's extension of a compact system

In this study, we consider the dynamics of a fuzzy system extended by a crisp compact system, which has a mixing regular periodic decomposition. First, we describe the complete dynamics of Zadeh's extension of a crisp compact system, which has a mixing regular periodic decomposition, by splitting the space of fuzzy numbers on the compact space. Next, using the results obtained, we prove that the topological entropies of the crisp system and its Zadeh's extension to the space of fuzzy numbers are the same.