{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T04:14:16Z","timestamp":1760242456976,"version":"build-2065373602"},"reference-count":42,"publisher":"MDPI AG","issue":"8","license":[{"start":{"date-parts":[[2017,8,18]],"date-time":"2017-08-18T00:00:00Z","timestamp":1503014400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>In this work, by Zadeh\u2019s extension principle, we extend representable uninorms and their fuzzy implications (coimplications) to type-2 fuzzy sets. Emphatically, we investigate in which algebras of fuzzy truth values the extended operations are type-2 uninorms and type-2 fuzzy implications (coimplications), respectively.<\/jats:p>","DOI":"10.3390\/sym9080160","type":"journal-article","created":{"date-parts":[[2017,8,21]],"date-time":"2017-08-21T04:12:17Z","timestamp":1503288737000},"page":"160","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["On Extended Representable Uninorms and Their Extended Fuzzy Implications (Coimplications)"],"prefix":"10.3390","volume":"9","author":[{"given":"Aifang","family":"Xie","sequence":"first","affiliation":[{"name":"Department of mathematics, School of Scienece, Nanchang University, Nanchang 330031, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2017,8,18]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"199","DOI":"10.1016\/0020-0255(75)90036-5","article-title":"The concept of a linguistic variable and its applications in approximate reasoning (I)","volume":"8","author":"Zadeh","year":"1975","journal-title":"Inf. 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