Kolmogorov - Sinaj entropy on MV-algebras

Abstract

There is given a construction of the entropy of a dynamical system on arbitrary MV-algebra $M$. If $M$ is the MV-algebra of characteristic functions of a $σ$-algebra (isomorphic to the $σ$-algebra), then the construction leads to the Kolmogorov - Sinaj entropy. If $M$ is the MV-algebra (tribe) of fuzzy sets, then the construction coincides with the Maličk\' y modification of the Kolmogorov - Sinaj entropy for fuzzy sets.