{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,11]],"date-time":"2026-04-11T18:42:16Z","timestamp":1775932936916,"version":"3.50.1"},"reference-count":31,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2025,3,21]],"date-time":"2025-03-21T00:00:00Z","timestamp":1742515200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"European Union-Next Generation EU through the National Recovery and Resilience Plan of the Republic of Bulgaria","award":["DUECOS BG-RRP-2.004-0001-C01"],"award-info":[{"award-number":["DUECOS BG-RRP-2.004-0001-C01"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>This article presents a new approach to solving fuzzy advection\u2013diffusion equations using double fuzzy transforms, called the double fuzzy Yang\u2013General transform. This unique double fuzzy transformation is a combination of single fuzzy Yang and General transforms. Some of the basic properties of this new transform include existence and linearity and how they relate to partial derivatives. A solution framework for the linear fuzzy advection\u2013diffusion equation is developed to show the application of the double fuzzy Yang\u2013General transform. To illustrate the proposed method for solving these equations, we have included a solution to a numerical problem.<\/jats:p>","DOI":"10.3390\/axioms14040240","type":"journal-article","created":{"date-parts":[[2025,3,24]],"date-time":"2025-03-24T06:21:38Z","timestamp":1742797298000},"page":"240","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["A New Double Fuzzy Integral Transform for Solving an Advection\u2013Diffusion Equation"],"prefix":"10.3390","volume":"14","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-7377-9121","authenticated-orcid":false,"given":"Atanaska","family":"Georgieva","sequence":"first","affiliation":[{"name":"Faculty of Mathematics and Informatics, University of Plovdiv, 4000 Plovdiv, Bulgaria"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6315-6238","authenticated-orcid":false,"given":"Slav I.","family":"Cholakov","sequence":"additional","affiliation":[{"name":"Faculty of Mathematics and Informatics, University of Plovdiv, 4000 Plovdiv, Bulgaria"}]},{"given":"Mira","family":"Spasova","sequence":"additional","affiliation":[{"name":"Faculty of Mathematics and Informatics, University of Plovdiv, 4000 Plovdiv, Bulgaria"}]}],"member":"1968","published-online":{"date-parts":[[2025,3,21]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Di Martino, F., Perfilieva, I., and Sessa, S. 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