m-Generators of Fuzzy Dynamical Systems

Year 2012, Volume: 9 Issue: 2, - , 01.04.2012

Mohammad Ebrahimi Uosef Mohamadi

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.

Keywords

Fuzzy probability space, entropy, fuzzy dynamical systems, m-equivalence, m-refinement, fuzzy m-generator

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