Kolmogorov - Sinaj entropy on MV-algebras

2003/04/09 by Beloslav Riecan, Beloslav Riečan, Riecan, Beloslav · 1 citation
Computer Science · Mathematics · #Advanced Algebra and Logic #Dynamical Systems (math.DS) #FOS: Mathematics #Logic, Reasoning, and Knowledge #Rough Sets and Fuzzy Logic #math.DS

paper · pdf · doi:10.48550/arxiv.math/0304123

11 pages

openalex publication_date 2003/04/09 · arxiv created 2003/09/19 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Cited by

• Study Entropy of L-algebras

Related

• Study Entropy of L-algebras
• A Construction of Dynamical Entropy on CAR Algebras
• Entropy in type I algebras
• Entropy of probability kernels from the backwards tail boundary
• Monotonicity of the Relative Entropy and the Two-sided Bogoliubov Inequality in von Neumann Algebras