{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,23]],"date-time":"2026-01-23T10:04:41Z","timestamp":1769162681446,"version":"3.49.0"},"reference-count":24,"publisher":"MDPI AG","issue":"11","license":[{"start":{"date-parts":[[2021,10,26]],"date-time":"2021-10-26T00:00:00Z","timestamp":1635206400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>Entropy is usually used to measure the uncertainty of uncertain random variables. It has been defined by logarithmic entropy with chance theory. However, this logarithmic entropy sometimes fails to measure the uncertainty of some uncertain random variables. In order to solve this problem, this paper proposes two types of entropy for uncertain random variables: sine entropy and partial sine entropy, and studies some of their properties. Some important properties of sine entropy and partial sine entropy, such as translation invariance and positive linearity, are obtained. In addition, the calculation formulas of sine entropy and partial sine entropy of uncertain random variables are given.<\/jats:p>","DOI":"10.3390\/sym13112023","type":"journal-article","created":{"date-parts":[[2021,10,26]],"date-time":"2021-10-26T23:55:23Z","timestamp":1635292523000},"page":"2023","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["Sine Entropy of Uncertain Random Variables"],"prefix":"10.3390","volume":"13","author":[{"given":"Gang","family":"Shi","sequence":"first","affiliation":[{"name":"College of Information Science and Engineering, Xinjiang University, Urumqi 830046, China"}]},{"given":"Rujun","family":"Zhuang","sequence":"additional","affiliation":[{"name":"College of Information Science and Engineering, Xinjiang University, Urumqi 830046, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7268-8519","authenticated-orcid":false,"given":"Yuhong","family":"Sheng","sequence":"additional","affiliation":[{"name":"College of Mathematical and System Sciences, Xinjiang University, Urumqi 830046, China"}]}],"member":"1968","published-online":{"date-parts":[[2021,10,26]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"373","DOI":"10.1002\/j.1538-7305.1948.tb01338.x","article-title":"The mathematical theory of communication","volume":"27","author":"Shannon","year":"1948","journal-title":"Bell Syst. 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