{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,6]],"date-time":"2026-01-06T13:21:53Z","timestamp":1767705713665},"reference-count":23,"publisher":"World Scientific Pub Co Pte Lt","issue":"02","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Unc. Fuzz. Knowl. Based Syst."],"published-print":{"date-parts":[[2015,4]]},"abstract":"<jats:p> Uninorms are important generalizations of triangular norms and conorms, with a neutral element lying anywhere in the unit interval, and left (right) semi-uninorms are non-commutative and non-associative extensions of uninorms. In this paper, we study the relations between implications and left (right) semi-uninorms on a complete lattice. We firstly investigate the left (right) semi-uninorms induced by implications, give some conditions such that the operations induced by implications constitute left or right semi-uninorms, and demonstrate that the operations induced by a right infinitely \u2227-distributive implication, which satisfies the order property, are left (right) infinitely \u2228-distributive left (right) semi-uninorms. Then, we discuss the residual operations of left (right) semi-uninorms and show that left (right) residual operators of strict left (right)-conjunctive left (right) infinitely \u2228-distributive left (right) semi-uninorms are right infinitely \u2227-distributive implications that satisfy the order property. Finally, we reveal the relationships between strict left (right)-conjunctive left (right) infinitely \u2228-distributive left (right) semi-uninorms and right infinitely \u2227-distributive implications which satisfy the order property. <\/jats:p>","DOI":"10.1142\/s0218488515500105","type":"journal-article","created":{"date-parts":[[2015,4,29]],"date-time":"2015-04-29T08:43:42Z","timestamp":1430297022000},"page":"245-261","source":"Crossref","is-referenced-by-count":3,"title":["The Relations between Implications and Left (Right) Semi-Uninorms on a Complete Lattice"],"prefix":"10.1142","volume":"23","author":[{"given":"Xiaoying","family":"Hao","sequence":"first","affiliation":[{"name":"School of Mathematical Sciences, Yancheng Teachers University, Jiangsu 224002, P. R. China"},{"name":"Department of Mathematics, Qinghai Normal University, Xining 810000, P. R. China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Meixia","family":"Niu","sequence":"additional","affiliation":[{"name":"School of Mathematical Sciences, Yancheng Teachers University, Jiangsu 224002, P. R. China"},{"name":"Department of Mathematics, Qinghai Normal University, Xining 810000, P. R. China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Zhudeng","family":"Wang","sequence":"additional","affiliation":[{"name":"School of Mathematical Sciences, Yancheng Teachers University, Jiangsu 224002, P. R. 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