m-Generators of Fuzzy Dynamical Systems

Abstract

In this paper we prove that the entropy of a fuzzy measure preserving transformation with respect to a sub-σ-algebra having finite atoms is affine and then we extend the method of computing the entropy of a finite sub-σ-algebra to a sub-σ-algebra having countable atoms, and we investigate the ergodic properties of fuzzy probability dynamical systems. At the end by using this notion, a version of Kolmogorov-Sinai proposition [6, 9, 10] is given.