{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,27]],"date-time":"2025-12-27T15:08:58Z","timestamp":1766848138937,"version":"build-2065373602"},"reference-count":13,"publisher":"MDPI AG","issue":"12","license":[{"start":{"date-parts":[[2021,12,15]],"date-time":"2021-12-15T00:00:00Z","timestamp":1639526400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["61873329"],"award-info":[{"award-number":["61873329"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"the High Level Talent Project of Hainan Natural Science Foundation","award":["2019RC168"],"award-info":[{"award-number":["2019RC168"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>As a mathematical tool to rationally handle degrees of belief in human beings, uncertainty theory has been widely applied in the research and development of various domains, including science and engineering. As a fundamental part of uncertainty theory, uncertainty distribution is the key approach in the characterization of an uncertain variable. This paper shows a new formula to calculate the uncertainty distribution of strictly monotone function of uncertain variables, which breaks the habitual thinking that only the former formula can be used. In particular, the new formula is symmetrical to the former formula, which shows that when it is too intricate to deal with a problem using the former formula, the problem can be observed from another perspective by using the new formula. New ideas may be obtained from the combination of uncertainty theory and symmetry.<\/jats:p>","DOI":"10.3390\/sym13122429","type":"journal-article","created":{"date-parts":[[2021,12,15]],"date-time":"2021-12-15T21:47:36Z","timestamp":1639604856000},"page":"2429","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["A New Formula for Calculating Uncertainty Distribution of Function of Uncertain Variables"],"prefix":"10.3390","volume":"13","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-0298-5996","authenticated-orcid":false,"given":"Yuxing","family":"Jia","sequence":"first","affiliation":[{"name":"Department of Mathematical Sciences, Tsinghua University, Beijing 100084, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yuer","family":"Lv","sequence":"additional","affiliation":[{"name":"School of Science, Hainan University, Haikou 570228, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Zhigang","family":"Wang","sequence":"additional","affiliation":[{"name":"School of Science, Hainan University, Haikou 570228, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2021,12,15]]},"reference":[{"key":"ref_1","first-page":"3","article-title":"Why is there a need for uncertainty theory","volume":"6","author":"Liu","year":"2012","journal-title":"J. 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Math."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"4845","DOI":"10.3233\/JIFS-191535","article-title":"A revision of sufficient and necessary condition of uncertainty distribution","volume":"38","author":"Liu","year":"2020","journal-title":"J. Intell. Fuzzy Syst."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"549","DOI":"10.1007\/s00500-012-0930-5","article-title":"Extreme value theorems of uncertain process with application to insurance risk model","volume":"17","author":"Liu","year":"2013","journal-title":"Soft Comput."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"2856","DOI":"10.1109\/TFUZZ.2019.2945246","article-title":"Shortage index and shortage time of uncertain production risk process","volume":"28","author":"Lio","year":"2020","journal-title":"IEEE Trans. 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Uncertain Syst."}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/13\/12\/2429\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T07:48:41Z","timestamp":1760168921000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/13\/12\/2429"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,12,15]]},"references-count":13,"journal-issue":{"issue":"12","published-online":{"date-parts":[[2021,12]]}},"alternative-id":["sym13122429"],"URL":"https:\/\/doi.org\/10.3390\/sym13122429","relation":{},"ISSN":["2073-8994"],"issn-type":[{"type":"electronic","value":"2073-8994"}],"subject":[],"published":{"date-parts":[[2021,12,15]]}}}