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Entropy of a fuzzy process. (English) Zbl 0818.28008

Instead of a measure space a fuzzy measure space is considered together with a measure-preserving transformation \(T\). The entropy \(H(P, T)\) of this system with respect to a fuzzy partition \(P\) is defined and its properties are examined. The author announces to introduce in a next paper the entropy \(h(T)\) of a fuzzy dynamical system. However, it has been realized in a paper by P. Maličký, the reviewer and M. Liptovsky [Teubner-Texte Math. 94, 135-138 (1987; Zbl 0643.58008)]. The construction has the following defect (considered in the above- mentioned paper): if the given fuzzy \(\sigma\)-algebra contains constant functions, then \(h(T)= \infty\). This defect has been repaired by T. Hudetz [see the reviewer, Atti. Semin. Mat. Fis. Univ. Modena 42, No. 2, 485-494 (1994)].

MSC:

28E10 Fuzzy measure theory
28D20 Entropy and other invariants

Citations:

Zbl 0643.58008
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References:

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