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Conditional entropy and Rokhlin metric. (English) Zbl 0949.28015
The paper is devoted to the study of some properties of systems of atoms of fuzzy sub-\(\sigma \)-algebras (in the sense of Klement). For a given fuzzy probability space \((X,\mathcal M, m)\), a pseudometric on an \(m\)-equivalence class \([\mathcal N]\) of fuzzy sub-\(\sigma \)-algebras is introduced. Applying a specific \(m\)-based equivalence, the so-called Rokhlin metric on relevant equivalence classes of a given \(m\)-equivalence class \([\mathcal N]\) is constructed. Although the paper gives no examples and it has some notational inaccuracies, it is an interesting contribution with possible applications in the entropy and other information measures domain.

28E10 Fuzzy measure theory
28D20 Entropy and other invariants
94A17 Measures of information, entropy
Full Text: EuDML
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