{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,2]],"date-time":"2026-05-02T06:52:28Z","timestamp":1777704748149,"version":"3.51.4"},"reference-count":41,"publisher":"SAGE Publications","issue":"1","license":[{"start":{"date-parts":[[2020,5,13]],"date-time":"2020-05-13T00:00:00Z","timestamp":1589328000000},"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":[[2020,7,17]]},"abstract":"<jats:p>In this paper, orders based on uni-nullnorms on bounded lattices are introduced and discussed. By this way, the existing orders in the literature induced by t-norms, t-conorms, uninorms and nullnorms are extended to much more general form. The relationships between the orders induced by uni-nullnorms and the orders induced by their underlying t-norms, t-conorms, uninorms and nullnorms are presented. A necessary and sufficient condition making a bounded lattice again a lattice with respect to the orders based on uni-nullnorms is given. Also, the relationships between the partially ordered sets based on the orders induced by t-norms and induced by their N-dual t-conorms and conjugate t-norms, which are special uni-nullnorms, are investigated.<\/jats:p>","DOI":"10.3233\/jifs-191583","type":"journal-article","created":{"date-parts":[[2020,5,15]],"date-time":"2020-05-15T12:48:39Z","timestamp":1589546919000},"page":"645-663","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":2,"title":["Ordering based on uni-nullnorms"],"prefix":"10.1177","volume":"39","author":[{"given":"M. Nesibe","family":"Kesicio\u011flu","sequence":"first","affiliation":[{"name":"Department of Mathematics, Recep Tayyip Erdogan University, Rize, Turkey"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Esra","family":"\u015eaml\u0131","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Recep Tayyip Erdogan University, Rize, Turkey"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"179","published-online":{"date-parts":[[2020,5,13]]},"reference":[{"key":"e_1_3_1_2_2","first-page":"15","article-title":"Prime filters of hyperlattices","volume":"24","author":"Ameri R.","year":"2016","unstructured":"AmeriR., Amiri-BideshkiM., SaeidA.B. and Ho\u0161kov\u00e1-Mayerov\u00e1\u0160., Prime filters of hyperlattices, An Stiint Univ \u201cOvidius\u201d Constanta Ser Mat 24 (2016), 15\u201326.","journal-title":"An Stiint Univ \u201cOvidius\u201d Constanta Ser Mat"},{"key":"e_1_3_1_3_2","first-page":"25","article-title":"Distributive and Dual Distributive Elements in Hyperlattices","volume":"25","author":"Ameri R.","year":"2017","unstructured":"AmeriR., Amiri-BideshkiM., Ho\u0161kov\u00e1-Mayerov\u00e1\u0160. and SaeidA.B., Distributive and Dual Distributive Elements in Hyperlattices, An Stiint Univ \u201cOvidius\u201d Constanta Ser Mat 25 (2017), 25\u201336.","journal-title":"An Stiint Univ \u201cOvidius\u201d Constanta Ser Mat"},{"key":"e_1_3_1_4_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.fss.2016.12.004"},{"key":"e_1_3_1_5_2","volume-title":"Studies in Fuzziness and Soft Computing","author":"Baczy\u0144ski M.","year":"2008","unstructured":"Baczy\u0144skiM., JayaramB., Fuzzy implications, Studies in Fuzziness and Soft Computing, vol. 231, Springer, Berlin, Heidelberg, 2008."},{"key":"e_1_3_1_6_2","doi-asserted-by":"publisher","DOI":"10.1016\/S0165-0114(98)00259-0"},{"key":"e_1_3_1_7_2","volume-title":"Studies in Fuzziness and Soft Computing","author":"Beliakov G.","year":"2016","unstructured":"BeliakovG., BustinceH., CalvoT., A practical guide to averaging functions, Studies in Fuzziness and Soft Computing, vol. 329, Springer, 2016."},{"key":"e_1_3_1_8_2","unstructured":"BeliakovG. PraderaA. CalvoT. Aggregation Functions: A guide for practitioners Springer-Verlag Berlin Heidelberg 2007."},{"key":"e_1_3_1_9_2","unstructured":"BirkhoffG. Lattice Theory 3rd edition American Mathematical Society Colloquium Publishers Providence 1967."},{"key":"e_1_3_1_10_2","doi-asserted-by":"publisher","DOI":"10.1016\/S0165-0114(99)00125-6"},{"key":"e_1_3_1_11_2","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-7908-1787-4"},{"key":"e_1_3_1_12_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.fss.2014.09.003"},{"key":"e_1_3_1_13_2","doi-asserted-by":"crossref","unstructured":"DuboisD. PradeH. Fundamentals of fuzzy sets Kluwer Acad Publ Boston 2000.","DOI":"10.1007\/978-1-4615-4429-6"},{"key":"e_1_3_1_14_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.ins.2015.10.019"},{"key":"e_1_3_1_15_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.ins.2019.03.077"},{"key":"e_1_3_1_16_2","doi-asserted-by":"publisher","DOI":"10.1142\/S0218488597000312"},{"key":"e_1_3_1_17_2","unstructured":"GrabischM. MarichalJ.-L. MesiarR. PapE. Aggregation Functions Cambridge University Press 2009."},{"key":"e_1_3_1_18_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.fss.2014.05.001"},{"key":"e_1_3_1_19_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.ins.2015.06.052"},{"key":"e_1_3_1_20_2","first-page":"300","article-title":"A T-partial order obtained from t-norms","volume":"47","author":"Kara\u00e7al F.","year":"2011","unstructured":"Kara\u00e7alF. and Kesicio\u011fluM.N., A T-partial order obtained from t-norms, Kybernetika 47 (2011), 300\u2013314.","journal-title":"Kybernetika"},{"key":"e_1_3_1_21_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.ins.2013.12.047"},{"key":"e_1_3_1_22_2","doi-asserted-by":"publisher","DOI":"10.1142\/S0218488518500307"},{"key":"e_1_3_1_23_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.ins.2017.05.020"},{"key":"e_1_3_1_24_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.fss.2018.12.020"},{"key":"e_1_3_1_25_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.fss.2017.08.010"},{"key":"e_1_3_1_26_2","first-page":"877","article-title":"About the equivalence of nullnorms on bounded lattice","volume":"53","author":"Kesicio\u011flu M.N.","year":"2017","unstructured":"Kesicio\u011fluM.N., About the equivalence of nullnorms on bounded lattice, Kybernetika 53 (2017), 877\u2013891.","journal-title":"Kybernetika"},{"key":"e_1_3_1_27_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.fss.2014.10.006"},{"key":"e_1_3_1_28_2","unstructured":"KlementE.P. MesiarR. PapE. Triangular Norms Kluwer Academic Publishers Dordrecht 2000."},{"key":"e_1_3_1_29_2","unstructured":"KlementE.P. MesiarR. (Eds.) Logical Algebraic Analytic and Probabilistic Aspects of Triangular Norms Elsevier Amsterdam 2005."},{"key":"e_1_3_1_30_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.fss.2017.07.013"},{"key":"e_1_3_1_31_2","doi-asserted-by":"publisher","DOI":"10.1016\/0020-0255(91)90007-H"},{"key":"e_1_3_1_32_2","doi-asserted-by":"publisher","DOI":"10.1142\/S0218488599000039"},{"key":"e_1_3_1_33_2","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9939-1986-0840614-0"},{"key":"e_1_3_1_34_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.ijar.2019.01.006"},{"key":"e_1_3_1_35_2","first-page":"75","article-title":"The distributive equations for idempotent uninorms and nullnorms","volume":"202","author":"Qin F.","year":"2012","unstructured":"QinF., ZhaoB., The distributive equations for idempotent uninorms and nullnorms, Fuzzy Sets and Systems 202 (2012), 75\u201388.","journal-title":"Fuzzy Sets and Systems"},{"key":"e_1_3_1_36_2","doi-asserted-by":"publisher","DOI":"10.3233\/JIFS-161495"},{"key":"e_1_3_1_37_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.fss.2017.03.001"},{"key":"e_1_3_1_38_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.fss.2019.01.001"},{"key":"e_1_3_1_39_2","doi-asserted-by":"publisher","DOI":"10.1016\/S0165-0114(00)00027-0"},{"key":"e_1_3_1_40_2","doi-asserted-by":"publisher","DOI":"10.1016\/0165-0114(95)00133-6"},{"key":"e_1_3_1_41_2","doi-asserted-by":"publisher","DOI":"10.3233\/JIFS-171286"},{"key":"e_1_3_1_42_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.fss.2019.09.002"}],"container-title":["Journal of Intelligent &amp; Fuzzy Systems"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.3233\/JIFS-191583","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/journals.sagepub.com\/doi\/full-xml\/10.3233\/JIFS-191583","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.3233\/JIFS-191583","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,29]],"date-time":"2026-04-29T09:41:55Z","timestamp":1777455715000},"score":1,"resource":{"primary":{"URL":"https:\/\/journals.sagepub.com\/doi\/10.3233\/JIFS-191583"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,5,13]]},"references-count":41,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2020,7,17]]}},"alternative-id":["10.3233\/JIFS-191583"],"URL":"https:\/\/doi.org\/10.3233\/jifs-191583","relation":{},"ISSN":["1064-1246","1875-8967"],"issn-type":[{"value":"1064-1246","type":"print"},{"value":"1875-8967","type":"electronic"}],"subject":[],"published":{"date-parts":[[2020,5,13]]}}}