Conditional fuzzy entropy of fuzzy dynamical systems

Entropy of fuzzy dynamical systems has been investigated as an isomorphism invariant in Dumitrescu (1995) [13]. In this paper, we will introduce a new invariant called the conditional fuzzy entropy of fuzzy dynamical systems with respect to a finite fuzzy partition and an invariant sub-σ-algebra, which is an extension of fuzzy entropy on fuzzy dynamical systems. This new invariant possesses some basic properties, such as power rule, fuzzy version of Abramov-Rokhlin entropy additive formula and generating sequence.