{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,2]],"date-time":"2026-07-02T05:41:49Z","timestamp":1782970909267,"version":"3.54.5"},"reference-count":70,"publisher":"Institute of Electrical and Electronics Engineers (IEEE)","issue":"4","license":[{"start":{"date-parts":[[2021,4,1]],"date-time":"2021-04-01T00:00:00Z","timestamp":1617235200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/ieeexplore.ieee.org\/Xplorehelp\/downloads\/license-information\/IEEE.html"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["61473336"],"award-info":[{"award-number":["61473336"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Youth Science and Technology New Star Program of Shaanxi Province","award":["2016KJXX-24"],"award-info":[{"award-number":["2016KJXX-24"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["IEEE Trans. Fuzzy Syst."],"published-print":{"date-parts":[[2021,4]]},"DOI":"10.1109\/tfuzz.2020.2966154","type":"journal-article","created":{"date-parts":[[2020,1,13]],"date-time":"2020-01-13T20:47:01Z","timestamp":1578948421000},"page":"846-860","source":"Crossref","is-referenced-by-count":37,"title":["Two General Construction Ways Toward Unified Framework of Ordinal Sums of Fuzzy Implications"],"prefix":"10.1109","volume":"29","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-8364-7739","authenticated-orcid":false,"given":"Hongjun","family":"Zhou","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"263","reference":[{"key":"ref70","doi-asserted-by":"publisher","DOI":"10.1109\/TFUZZ.2017.2776861"},{"key":"ref39","doi-asserted-by":"publisher","DOI":"10.1016\/j.fss.2003.06.008"},{"key":"ref38","doi-asserted-by":"publisher","DOI":"10.1016\/j.fss.2018.08.007"},{"key":"ref33","doi-asserted-by":"publisher","DOI":"10.1109\/TFUZZ.2016.2551285"},{"key":"ref32","doi-asserted-by":"publisher","DOI":"10.1016\/j.ijar.2017.10.003"},{"key":"ref31","doi-asserted-by":"publisher","DOI":"10.1016\/j.fss.2018.10.015"},{"key":"ref30","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-35677-3_1"},{"key":"ref37","first-page":"351","article-title":"$QL$-implications versus $D$-implications","volume":"42","author":"mas","year":"2006","journal-title":"Kybernetika"},{"key":"ref36","doi-asserted-by":"publisher","DOI":"10.1016\/j.ins.2014.04.021"},{"key":"ref35","doi-asserted-by":"publisher","DOI":"10.1016\/j.ins.2015.09.033"},{"key":"ref34","doi-asserted-by":"publisher","DOI":"10.1109\/TFUZZ.2017.2756832"},{"key":"ref60","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-319-26211-6_4"},{"key":"ref62","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-319-59306-7_20"},{"key":"ref61","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-319-66830-7_58"},{"key":"ref63","doi-asserted-by":"publisher","DOI":"10.1109\/TFUZZ.2015.2486810"},{"key":"ref28","doi-asserted-by":"publisher","DOI":"10.1109\/91.983282"},{"key":"ref64","doi-asserted-by":"publisher","DOI":"10.1016\/j.fss.2019.01.002"},{"key":"ref27","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-662-43505-2_12"},{"key":"ref65","first-page":"82","article-title":"Fuzzy logic and fuzzy reasoning","author":"wang","year":"0","journal-title":"Proc 7th Nat Many-Valued Fuzzy Logic Aca Conf Xi&#x2019;an"},{"key":"ref66","doi-asserted-by":"publisher","DOI":"10.1007\/BF02882835"},{"key":"ref29","first-page":"1","article-title":"Fuzzy implication operator with parameter and its properties","volume":"19","author":"zhang","year":"2006","journal-title":"J Liaocheng Univ (Nat Sci )"},{"key":"ref67","doi-asserted-by":"publisher","DOI":"10.1109\/TFUZZ.2011.2171188"},{"key":"ref68","doi-asserted-by":"publisher","DOI":"10.1109\/TFUZZ.2012.2221719"},{"key":"ref69","doi-asserted-by":"publisher","DOI":"10.1016\/j.fss.2013.07.020"},{"key":"ref2","doi-asserted-by":"publisher","DOI":"10.1109\/TFUZZ.2007.896304"},{"key":"ref1","author":"baczy?ski","year":"2008","journal-title":"Fuzzy Implications"},{"key":"ref20","doi-asserted-by":"publisher","DOI":"10.1016\/j.ins.2019.04.038"},{"key":"ref22","doi-asserted-by":"publisher","DOI":"10.1016\/j.ijar.2018.03.008"},{"key":"ref21","doi-asserted-by":"publisher","DOI":"10.1016\/j.ijar.2016.12.013"},{"key":"ref24","doi-asserted-by":"publisher","DOI":"10.1016\/j.ins.2018.12.021"},{"key":"ref23","doi-asserted-by":"publisher","DOI":"10.1016\/j.fss.2017.07.016"},{"key":"ref26","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-35677-3"},{"key":"ref25","doi-asserted-by":"publisher","DOI":"10.1016\/j.apal.2003.01.001"},{"key":"ref50","doi-asserted-by":"publisher","DOI":"10.1007\/978-94-015-9540-7"},{"key":"ref51","first-page":"52","article-title":"Generalized ordinal sum theorem and its consequence to the construction of triangular norms","volume":"80","author":"jenei","year":"1999","journal-title":"Busefal"},{"key":"ref59","article-title":"On some constructions of ordinal sums of fuzzy implications","author":"dryga?","year":"0","journal-title":"Proc Joint 17th World Congr Int Fuzzy Syst Assoc 9th Int Conf Soft Comput Intell Syst"},{"key":"ref58","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-319-65545-1_10"},{"key":"ref57","doi-asserted-by":"crossref","first-page":"189","DOI":"10.5486\/PMD.1965.12.1-4.19","article-title":"Representation of associative functions","volume":"12","author":"ling","year":"1965","journal-title":"Publ Math Debrecen"},{"key":"ref56","doi-asserted-by":"publisher","DOI":"10.3233\/JIFS-171057"},{"key":"ref55","doi-asserted-by":"publisher","DOI":"10.1016\/j.fss.2014.04.008"},{"key":"ref54","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-7908-1796-6_11"},{"key":"ref53","doi-asserted-by":"publisher","DOI":"10.1016\/j.ijar.2016.04.007"},{"key":"ref52","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-319-25135-6_6"},{"key":"ref10","author":"wang","year":"1997","journal-title":"A Course in Fuzzy Systems and Control"},{"key":"ref11","doi-asserted-by":"publisher","DOI":"10.1109\/91.660804"},{"key":"ref40","doi-asserted-by":"publisher","DOI":"10.1007\/s005000050057"},{"key":"ref12","doi-asserted-by":"publisher","DOI":"10.1109\/TFUZZ.2004.825075"},{"key":"ref13","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4615-0633-1"},{"key":"ref14","doi-asserted-by":"publisher","DOI":"10.1007\/978-94-017-1650-5"},{"key":"ref15","first-page":"307","article-title":"From computing with numbers to computing with words from manipulation of measures to manipulation of perceptions","volume":"12","author":"zadeh","year":"2002","journal-title":"Int J Appl Math Comput Sci"},{"key":"ref16","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-7908-1873-4","author":"zadeh","year":"1999","journal-title":"Computing with Words in Information\/Intelligent Systems Foundations"},{"key":"ref17","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4615-5473-8_4"},{"key":"ref18","first-page":"215","article-title":"Fuzzy morphology based on uninorms","author":"de baets","year":"0","journal-title":"Proc 7th Int Fuzzy Syst Assoc World Congr"},{"key":"ref19","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-7908-1847-5"},{"key":"ref4","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-662-43505-2"},{"key":"ref3","doi-asserted-by":"publisher","DOI":"10.1093\/oso\/9780190200015.001.0001"},{"key":"ref6","author":"gottwald","year":"2001","journal-title":"A Treatise on Many-Valued Logics"},{"key":"ref5","volume":"1?2","author":"cintula","year":"2011","journal-title":"Handbook of Mathematical Fuzzy Logic"},{"key":"ref8","author":"galatos","year":"2007","journal-title":"Residuated Lattices An Algebraic Glimpse at Substructural Logics"},{"key":"ref7","author":"zhou","year":"2015","journal-title":"Probabilistially Quantitative Logic and Its Applications"},{"key":"ref49","doi-asserted-by":"publisher","DOI":"10.2307\/2372706"},{"key":"ref9","author":"cox","year":"1998","journal-title":"The Fuzzy Systems Handbook A Practitioner's Guide to Building Using and Maintaining Fuzzy Systems"},{"key":"ref46","doi-asserted-by":"publisher","DOI":"10.1515\/tmmp-2016-0018"},{"key":"ref45","doi-asserted-by":"publisher","DOI":"10.1016\/j.ins.2014.09.021"},{"key":"ref48","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-319-40596-4_34"},{"key":"ref47","article-title":"New types of ordinal sum of fuzzy implications","author":"baczy?ski","year":"0","journal-title":"Proc IEEE Int Conf Fuzzy Syst"},{"key":"ref42","doi-asserted-by":"publisher","DOI":"10.1016\/j.ins.2003.04.001"},{"key":"ref41","doi-asserted-by":"publisher","DOI":"10.1016\/j.ins.2015.03.049"},{"key":"ref44","doi-asserted-by":"publisher","DOI":"10.1109\/TFUZZ.2012.2222892"},{"key":"ref43","doi-asserted-by":"publisher","DOI":"10.1016\/j.ins.2011.01.030"}],"container-title":["IEEE Transactions on Fuzzy Systems"],"original-title":[],"link":[{"URL":"http:\/\/xplorestaging.ieee.org\/ielx7\/91\/9391743\/08957461.pdf?arnumber=8957461","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,9,25]],"date-time":"2023-09-25T01:47:30Z","timestamp":1695606450000},"score":1,"resource":{"primary":{"URL":"https:\/\/ieeexplore.ieee.org\/document\/8957461\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,4]]},"references-count":70,"journal-issue":{"issue":"4"},"URL":"https:\/\/doi.org\/10.1109\/tfuzz.2020.2966154","relation":{},"ISSN":["1063-6706","1941-0034"],"issn-type":[{"value":"1063-6706","type":"print"},{"value":"1941-0034","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,4]]}}}