Kolmogorov - Sinaj entropy on MV-algebras

Details Kolmogorov - Sinaj entropy on MV-algebras Kolmogorov - Sinaj entropy on MV-algebras

2003-04-09

arxiv.org/abs/math/0304123v2

Mathematics

Dynamical Systems

11 pages

Scientific paper

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 $\sigma$-algebra (isomorphic to the $\sigma$-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 Mali\v{c}k\' y modification of the Kolmogorov - Sinaj entropy for fuzzy sets.

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