{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,6]],"date-time":"2026-06-06T00:53:17Z","timestamp":1780707197003,"version":"3.54.1"},"reference-count":51,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2020,4,20]],"date-time":"2020-04-20T00:00:00Z","timestamp":1587340800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"European Social Fund- ESF","award":["MIS-5033021"],"award-info":[{"award-number":["MIS-5033021"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>A modification of the classic logistic map is proposed, using fuzzy triangular numbers. The resulting map is analysed through its Lyapunov exponent (LE) and bifurcation diagrams. It shows higher complexity compared to the classic logistic map and showcases phenomena, like antimonotonicity and crisis. The map is then applied to the problem of pseudo random bit generation, using a simple rule to generate the bit sequence. The resulting random bit generator (RBG) successfully passes the National Institute of Standards and Technology (NIST) statistical tests, and it is then successfully applied to the problem of image encryption.<\/jats:p>","DOI":"10.3390\/e22040474","type":"journal-article","created":{"date-parts":[[2020,4,21]],"date-time":"2020-04-21T03:23:06Z","timestamp":1587439386000},"page":"474","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":51,"title":["Modification of the Logistic Map Using Fuzzy Numbers with Application to Pseudorandom Number Generation and Image Encryption"],"prefix":"10.3390","volume":"22","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-5652-2532","authenticated-orcid":false,"given":"Lazaros","family":"Moysis","sequence":"first","affiliation":[{"name":"Laboratory of Nonlinear Systems\u2014Circuits &amp; Complexity (LaNSCom), Physics Department, Aristotle University of Thessaloniki, 54124 Thessaloniki, Greece"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8763-7255","authenticated-orcid":false,"given":"Christos","family":"Volos","sequence":"additional","affiliation":[{"name":"Laboratory of Nonlinear Systems\u2014Circuits &amp; Complexity (LaNSCom), Physics Department, Aristotle University of Thessaloniki, 54124 Thessaloniki, Greece"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Sajad","family":"Jafari","sequence":"additional","affiliation":[{"name":"Nonlinear Systems and Applications, Faculty of Electrical and Electronics Engineering, Ton Duc Thang University, Ho Chi Minh City 758307, Vietnam"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9106-6982","authenticated-orcid":false,"given":"Jesus M.","family":"Munoz-Pacheco","sequence":"additional","affiliation":[{"name":"Faculty of Electronics Sciences, Autonomous University of Puebla, Puebla 72000, Mexico"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1165-1808","authenticated-orcid":false,"given":"Jacques","family":"Kengne","sequence":"additional","affiliation":[{"name":"Department of Electrical Engineering, University of Dschang, Dschang P.O. 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