{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,3]],"date-time":"2026-07-03T14:48:50Z","timestamp":1783090130815,"version":"3.54.6"},"reference-count":66,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2018,2,16]],"date-time":"2018-02-16T00:00:00Z","timestamp":1518739200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>In the paper we propose, using the logical entropy function, a new kind of entropy in product MV-algebras, namely the logical entropy and its conditional version. Fundamental characteristics of these quantities have been shown and subsequently, the results regarding the logical entropy have been used to define the logical mutual information of experiments in the studied case. In addition, we define the logical cross entropy and logical divergence for the examined situation and prove basic properties of the suggested quantities. To illustrate the results, we provide several numerical examples.<\/jats:p>","DOI":"10.3390\/e20020129","type":"journal-article","created":{"date-parts":[[2018,2,20]],"date-time":"2018-02-20T03:54:22Z","timestamp":1519098862000},"page":"129","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":11,"title":["Logical Divergence, Logical Entropy, and Logical Mutual Information in Product MV-Algebras"],"prefix":"10.3390","volume":"20","author":[{"given":"Dagmar","family":"Markechov\u00e1","sequence":"first","affiliation":[{"name":"Department of Mathematics, Faculty of Natural Sciences, Constantine the Philosopher University in Nitra, A. Hlinku 1, SK-949 01 Nitra, Slovakia"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Batool","family":"Mosapour","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Farhangian University, 7616914111 Kerman, Iran"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Abolfazl","family":"Ebrahimzadeh","sequence":"additional","affiliation":[{"name":"Young Researchers and Elite Club, Zahedan Branch, Islamic Azad University, 9816883673 Zahedan, Iran"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2018,2,16]]},"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. Tech. J."},{"key":"ref_2","unstructured":"Gray, R.M. (2009). 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