{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,2]],"date-time":"2026-05-02T06:58:48Z","timestamp":1777705128273,"version":"3.51.4"},"reference-count":19,"publisher":"SAGE Publications","issue":"1","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["IFS"],"published-print":{"date-parts":[[2024,1,10]]},"abstract":"<jats:p>Saminger-Platz, Klement, and Mesiar (2008) extended t-norms from a complete sublattice to its respective lattice using the conventional definition of sublattice. In contrast, Palmeira and Bedregal (2012) introduced a more inclusive sublattice definition, via retractions. They expanded various important mathematical operators, including t-norms, t-conorms, fuzzy negations, and automorphisms. They also introduced De Morgan triples (semi-triples) for these operators and provided their extensions in their groundbreaking work. In this paper, we propose a method of extending quasi-overlap functions and quasi-grouping functions defined on bounded sublattices (in a broad sense) to a bounded superlattice. To achieve that, we use the technique proposed by Palmeira and Bedregal. We also define: quasi-overlap (resp. quasi-grouping) functions generated from quasi-grouping (resp. quasi-overlap) functions and frontier fuzzy negations, De Morgan (semi)triples for the classes of quasi-overlap functions, quasi-grouping functions and fuzzy negations, as well as its respective extensions. Finally we study properties of all extensions defined.<\/jats:p>","DOI":"10.3233\/jifs-232805","type":"journal-article","created":{"date-parts":[[2023,11,17]],"date-time":"2023-11-17T11:28:28Z","timestamp":1700220508000},"page":"863-877","source":"Crossref","is-referenced-by-count":0,"title":["On retractions and extension of quasi-overlap and quasi-grouping functions defined on bounded lattices"],"prefix":"10.1177","volume":"46","author":[{"given":"Ana Shirley","family":"Monteiro","sequence":"first","affiliation":[{"name":"Instituto Federal de Educa\u00e7\u00e3o, Ci\u00eancia e Tecnologia do Cear\u00e1, Maracana\u00fa, Cear\u00e1, Brazil"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Regivan","family":"Santiago","sequence":"additional","affiliation":[{"name":"Departamento de Inform\u00e1tica e Matem\u00e1tica Aplicada, Universidade Federal do Rio Grande do Norte, Natal, Brazil"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Benjam\u00edn","family":"Bedregal","sequence":"additional","affiliation":[{"name":"Departamento de Inform\u00e1tica e Matem\u00e1tica Aplicada, Universidade Federal do Rio Grande do Norte, Natal, Brazil"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Eduardo","family":"Palmeira","sequence":"additional","affiliation":[{"name":"Departamento de Ci\u00eancias Exatas e Tecnol\u00f3gicas, Universidade Estadual de Santa Cruz, Ilh\u00e9us, Brazil"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Juscelino","family":"Ara\u00fajo","sequence":"additional","affiliation":[{"name":"Departamento de Inform\u00e1tica e Matem\u00e1tica Aplicada, Universidade Federal do Rio Grande do Norte, Natal, 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