{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,3]],"date-time":"2026-06-03T19:04:52Z","timestamp":1780513492918,"version":"3.54.1"},"reference-count":47,"publisher":"MDPI AG","issue":"11","license":[{"start":{"date-parts":[[2022,10,26]],"date-time":"2022-10-26T00:00:00Z","timestamp":1666742400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["12271319"],"award-info":[{"award-number":["12271319"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["PID2019-108392GB-I00 (AEI\/10.13039\/501100011033)"],"award-info":[{"award-number":["PID2019-108392GB-I00 (AEI\/10.13039\/501100011033)"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["20&ZD047"],"award-info":[{"award-number":["20&ZD047"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100012456","name":"Major Program of the National Social Science Foundation of China","doi-asserted-by":"publisher","award":["12271319"],"award-info":[{"award-number":["12271319"]}],"id":[{"id":"10.13039\/501100012456","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100012456","name":"Major Program of the National Social Science Foundation of China","doi-asserted-by":"publisher","award":["PID2019-108392GB-I00 (AEI\/10.13039\/501100011033)"],"award-info":[{"award-number":["PID2019-108392GB-I00 (AEI\/10.13039\/501100011033)"]}],"id":[{"id":"10.13039\/501100012456","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100012456","name":"Major Program of the National Social Science Foundation of China","doi-asserted-by":"publisher","award":["20&ZD047"],"award-info":[{"award-number":["20&ZD047"]}],"id":[{"id":"10.13039\/501100012456","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>Overlap and grouping functions are important aggregation operators, especially in information fusion, classification and decision-making problems. However, when we do more in-depth application research (for example, non-commutative fuzzy reasoning, complex multi-attribute decision making and image processing), we find overlap functions as well as grouping functions are required to be commutative (or symmetric), which limit their wide applications. For the above reasons, this paper expands the original notions of overlap functions and grouping functions, and the new concepts of pseudo overlap functions and pseudo grouping functions are proposed on the basis of removing the commutativity of the original functions. Some examples and construction methods of pseudo overlap functions and pseudo grouping functions are presented, and the residuated implication (co-implication) operators derived from them are investigated. Not only that, some applications of pseudo overlap (grouping) functions in multi-attribute (group) decision-making, fuzzy mathematical morphology and image processing are discussed. Experimental results show that, in many application fields, pseudo overlap functions and pseudo grouping functions have greater flexibility and practicability.<\/jats:p>","DOI":"10.3390\/axioms11110593","type":"journal-article","created":{"date-parts":[[2022,10,26]],"date-time":"2022-10-26T09:59:37Z","timestamp":1666778377000},"page":"593","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":36,"title":["Pseudo Overlap Functions, Fuzzy Implications and Pseudo Grouping Functions with Applications"],"prefix":"10.3390","volume":"11","author":[{"given":"Xiaohong","family":"Zhang","sequence":"first","affiliation":[{"name":"Department of Mathematics, Shaanxi University of Science & Technology, Xi\u2019an 710021, China"},{"name":"Shaanxi Joint Laboratory of Artificial Intelligence, Shaanxi University of Science & Technology, Xi\u2019an 710021, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9336-437X","authenticated-orcid":false,"given":"Rong","family":"Liang","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Shaanxi University of Science & Technology, Xi\u2019an 710021, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Humberto","family":"Bustince","sequence":"additional","affiliation":[{"name":"Departamento de Estadistica, Matematicas e Informatica, Universidad Publica de Navarra, Campus Arrosadia s\/n, 31006 Pamplona, Spain"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6757-7934","authenticated-orcid":false,"given":"Benjamin","family":"Bedregal","sequence":"additional","affiliation":[{"name":"Departamento de Informatica e Matematica Aplicada, Universidade Federal do Rio Grande do Norte, Natal 59078-970, Brazil"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Javier","family":"Fernandez","sequence":"additional","affiliation":[{"name":"Departamento de Estadistica, Matematicas e Informatica, Universidad Publica de Navarra, Campus Arrosadia s\/n, 31006 Pamplona, Spain"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Mengyuan","family":"Li","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Shaanxi University of Science & Technology, Xi\u2019an 710021, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Qiqi","family":"Ou","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Shaanxi University of Science & Technology, Xi\u2019an 710021, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2022,10,26]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Grabisch, M., Marichal, J.-L., Mesiar, R., and Pap, E. 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