{"title":"The entropy of hyperfuzzy sets","authors":"Z. Nazari, B. Mosapour","doi":"10.1080/1726037X.2018.1436270","DOIUrl":null,"url":null,"abstract":"Abstract This paper deals with studying the entropy of dynamical systems on hyperfuzzy sets. At first we define the entropy of hyperfuzzy partitions and conditional entropy. Then, some basic properties of these notions are established. Furthermore, we introduce the notion of a dynamical systems on hyperfuzzy sets and the entropy of it. Finally, we define a generator of this dynamical system and prove Kolmogorov-Sinai’s Theorem is also true for our mentioned generator.","PeriodicalId":42788,"journal":{"name":"Journal of Dynamical Systems and Geometric Theories","volume":"16 1","pages":"173 - 185"},"PeriodicalIF":0.2000,"publicationDate":"2018-07-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/1726037X.2018.1436270","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Dynamical Systems and Geometric Theories","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1080/1726037X.2018.1436270","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
Abstract This paper deals with studying the entropy of dynamical systems on hyperfuzzy sets. At first we define the entropy of hyperfuzzy partitions and conditional entropy. Then, some basic properties of these notions are established. Furthermore, we introduce the notion of a dynamical systems on hyperfuzzy sets and the entropy of it. Finally, we define a generator of this dynamical system and prove Kolmogorov-Sinai’s Theorem is also true for our mentioned generator.
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