{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,2]],"date-time":"2026-05-02T06:28:27Z","timestamp":1777703307816,"version":"3.51.4"},"reference-count":27,"publisher":"SAGE Publications","issue":"2","license":[{"start":{"date-parts":[[2015,10,5]],"date-time":"2015-10-05T00:00:00Z","timestamp":1444003200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/journals.sagepub.com\/page\/policies\/text-and-data-mining-license"}],"content-domain":{"domain":["journals.sagepub.com"],"crossmark-restriction":true},"short-container-title":["Journal of Intelligent &amp; Fuzzy Systems"],"published-print":{"date-parts":[[2015,10,5]]},"abstract":"<jats:title>Abstract<\/jats:title>\n                  <jats:p>\n                    In this paper, we further study implications, coimplications and left (right) semi-uninorms on a complete lattice. We firstly show that the\n                    <jats:italic>N<\/jats:italic>\n                    -dual operation of the right (left) residual implication, which is generated by a left (right)-conjunctive right (left) infinitely \u2228-distributive left (right) semi-uninorm, is the right (left) residual coimplication generated by its\n                    <jats:italic>N<\/jats:italic>\n                    -dual operation. As a dual result, the\n                    <jats:italic>N<\/jats:italic>\n                    -dual operation of the right (left) residual coimplication, which is generated by a left (right)-disjunctive right (left) infinitely \u2227-distributive left (right) semi-uninorm, is the right (left) residual implication generated by its\n                    <jats:italic>N<\/jats:italic>\n                    -dual operation. Then, we demonstrate that the\n                    <jats:italic>N<\/jats:italic>\n                    -dual operations of the left (right) semi-uninorms induced by an implication and a coimplication, which satisfy the neutrality principle, are the left (right) semi-uninorms. Finally, we reveal the relationships between conjunctive right (left) infinitely \u2228-distributive left (right) semi-uninorms induced by implications and disjunctive right (left) infinitely \u2227-distributive left (right) semi-uninorms induced by coimplications, where both implications and coimplications satisfy the neutrality principle.\n                  <\/jats:p>","DOI":"10.3233\/ifs-151622","type":"journal-article","created":{"date-parts":[[2015,10,6]],"date-time":"2015-10-06T12:06:19Z","timestamp":1444133179000},"page":"927-938","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":1,"title":["Relations among implications, coimplications and left (right) semi-uninorms"],"prefix":"10.1177","volume":"29","author":[{"given":"Meixia","family":"Niu","sequence":"first","affiliation":[{"name":"School of Mathematical Sciences, Yancheng Teachers University, Jiangsu, People\u2019s Republic of China"},{"name":"Department of Mathematics, Qinghai Normal University, Xining, People\u2019s Republic of China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xiaoying","family":"Hao","sequence":"additional","affiliation":[{"name":"School of Mathematical Sciences, Yancheng Teachers University, Jiangsu, People\u2019s Republic of China"},{"name":"Department of Mathematics, Qinghai Normal University, Xining, People\u2019s Republic of China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Zhudeng","family":"Wang","sequence":"additional","affiliation":[{"name":"School of Mathematical Sciences, Yancheng Teachers University, Jiangsu, People\u2019s Republic of China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"179","published-online":{"date-parts":[[2015,10,5]]},"reference":[{"key":"e_1_3_1_2_2","article-title":"Studies in Fuzziness and Soft Computing","volume":"231","author":"Baczy\u0144ski M","year":"2008","unstructured":"Baczy\u0144skiMJayaramB2008Studies in Fuzziness 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