{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,21]],"date-time":"2025-11-21T06:30:31Z","timestamp":1763706631578,"version":"build-2065373602"},"reference-count":39,"publisher":"MDPI AG","issue":"8","license":[{"start":{"date-parts":[[2023,8,11]],"date-time":"2023-08-11T00:00:00Z","timestamp":1691712000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Key Project of Natural Science Foundation of Educational Committee of Henan Province","award":["23A110014"],"award-info":[{"award-number":["23A110014"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>A new variance formula is developed using the generalized inverse of an increasing function. Based on the variance formula, a new entropy formula for any uncertain variable is provided. Most of the entropy formulas in the literature are special cases of the new entropy formula. Using the new entropy formula, the maximum entropy distribution for unimodel entropy of uncertain variables is provided without using the Euler\u2013Lagrange equation.<\/jats:p>","DOI":"10.3390\/e25081195","type":"journal-article","created":{"date-parts":[[2023,8,11]],"date-time":"2023-08-11T10:20:16Z","timestamp":1691749216000},"page":"1195","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["On the Entropy and the Maximum Entropy Principle of Uncertain Variables"],"prefix":"10.3390","volume":"25","author":[{"given":"Yujun","family":"Liu","sequence":"first","affiliation":[{"name":"School of Mathematics and Statistics, Anyang Normal University, Anyang 455000, China"}]},{"given":"Guanzhong","family":"Ma","sequence":"additional","affiliation":[{"name":"School of Mathematics and Statistics, Anyang Normal University, Anyang 455000, China"}]}],"member":"1968","published-online":{"date-parts":[[2023,8,11]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"379","DOI":"10.1002\/j.1538-7305.1948.tb01338.x","article-title":"A mathematical theory of communication","volume":"27","author":"Shannon","year":"1948","journal-title":"Bell Syst. 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