{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T04:17:45Z","timestamp":1760242665161,"version":"build-2065373602"},"reference-count":50,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2016,1,18]],"date-time":"2016-01-18T00:00:00Z","timestamp":1453075200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>In the paper we define three kinds of entropy of a fuzzy dynamical system using different entropies of fuzzy partitions. It is shown that different definitions of the entropy of fuzzy partitions lead to different notions of entropies of fuzzy dynamical systems. The relationships between these entropies are studied and connections with the classical case are mentioned as well. Finally, an analogy of the Kolmogorov\u2013Sinai Theorem on generators is proved for fuzzy dynamical systems.<\/jats:p>","DOI":"10.3390\/e18010019","type":"journal-article","created":{"date-parts":[[2016,1,18]],"date-time":"2016-01-18T10:58:33Z","timestamp":1453114713000},"page":"19","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":28,"title":["Entropy of Fuzzy Partitions and Entropy of Fuzzy Dynamical Systems"],"prefix":"10.3390","volume":"18","author":[{"given":"Dagmar","family":"Markechov\u00e1","sequence":"first","affiliation":[{"name":"Department of Mathematics, Faculty of Natural Sciences, Constantine the Philosopher University in Nitra, Trieda A. 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