{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,2]],"date-time":"2026-05-02T06:37:40Z","timestamp":1777703860948,"version":"3.51.4"},"reference-count":19,"publisher":"SAGE Publications","issue":"1","license":[{"start":{"date-parts":[[2018,6,28]],"date-time":"2018-06-28T00:00:00Z","timestamp":1530144000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/journals.sagepub.com\/page\/policies\/text-and-data-mining-license"}],"content-domain":{"domain":["journals.sagepub.com"],"crossmark-restriction":true},"short-container-title":["Journal of Intelligent &amp; Fuzzy Systems"],"published-print":{"date-parts":[[2018,7,27]]},"abstract":"<jats:p>In the papers by Riecan et al. (Fuzzy Sets Syst. 96, 1998) and Ebrahimzadeh et al. (Mathematics, 5, 2017) some fuzzy modifications of Shannon and logical entropy have been studied and the general scheme involving the presented models has been introduced. The present paper deals with providing analogies of these results for the case of Tsallis entropy. In particular, chain rules and concavity property for Tsallis entropy of partitions on the appropriate algebraic structure are established. Using the concept of Tsallis entropy of partitions, we define Tsallis entropy of dynamical systems and prove concavity property of Tsallis entropy of dynamical systems. Finally, we prove the version of Kolmogorov-Sinai Theorem for Tsallis entropy.<\/jats:p>","DOI":"10.3233\/jifs-17901","type":"journal-article","created":{"date-parts":[[2018,6,29]],"date-time":"2018-06-29T16:41:35Z","timestamp":1530290495000},"page":"1119-1126","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":1,"title":["Tsallis entropy of dynamical systems \u2013 a general scheme"],"prefix":"10.1177","volume":"35","author":[{"given":"Abolfazl","family":"Ebrahimzadeh","sequence":"first","affiliation":[{"name":"Department of Mathematics, Zahedan Branch, Islamic Azad University, Zahedan, Iran"}]},{"given":"Zahra","family":"Eslami Giski","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Sirjan Branch, Islamic Azad University, Sirjan, Iran"}]}],"member":"179","published-online":{"date-parts":[[2018,6,28]]},"reference":[{"key":"e_1_3_2_2_2","doi-asserted-by":"publisher","DOI":"10.1016\/S0375-9601(00)00337-6"},{"key":"e_1_3_2_3_2","doi-asserted-by":"publisher","DOI":"10.1016\/S0019-9958(70)80040-7"},{"key":"e_1_3_2_4_2","first-page":"879","article-title":"Quantum conditional logical entropy of dynamical systems","volume":"36","author":"Ebrahimzadeh A.","year":"2016","unstructured":"EbrahimzadehA., Quantum conditional logical entropy of dynamical systems, Italian Journal of Pure and Applied Mathematics 36 (2016), 879\u2013886.","journal-title":"Italian Journal of Pure and Applied Mathematics"},{"key":"e_1_3_2_5_2","doi-asserted-by":"publisher","DOI":"10.1515\/phys-2015-0058"},{"key":"e_1_3_2_6_2","first-page":"107","article-title":"The entropy of countable dynamical systems","volume":"76","author":"Ebrahimzadeh A.","year":"2014","unstructured":"EbrahimzadehA. and EbrahimiM., The entropy of countable dynamical systems, UPB Sci Bull, Series A 76 (2014), 107\u2013114.","journal-title":"UPB Sci Bull, Series A"},{"key":"e_1_3_2_7_2","doi-asserted-by":"publisher","DOI":"10.3390\/math5010004"},{"key":"e_1_3_2_8_2","doi-asserted-by":"publisher","DOI":"10.3233\/JIFS-162303"},{"key":"e_1_3_2_9_2","doi-asserted-by":"publisher","DOI":"10.1063\/1.2165744"},{"key":"e_1_3_2_10_2","doi-asserted-by":"publisher","DOI":"10.1109\/TIT.2005.855606"},{"key":"e_1_3_2_11_2","unstructured":"GrayR.-M. 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