{"id":"https://openalex.org/W2921655505","doi":"https://doi.org/10.1142/s0218488519500156","title":"The Distributivity Equations of Semi-Uninorms","display_name":"The Distributivity Equations of Semi-Uninorms","publication_year":2019,"publication_date":"2019-03-07","ids":{"openalex":"https://openalex.org/W2921655505","doi":"https://doi.org/10.1142/s0218488519500156","mag":"2921655505"},"language":"en","primary_location":{"id":"doi:10.1142/s0218488519500156","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218488519500156","pdf_url":null,"source":{"id":"https://openalex.org/S69518169","display_name":"International Journal of Uncertainty Fuzziness and Knowledge-Based Systems","issn_l":"0218-4885","issn":["0218-4885","1793-6411"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5066907969","display_name":"Yong Su","orcid":"https://orcid.org/0000-0001-5746-9908"},"institutions":[{"id":"https://openalex.org/I111599522","display_name":"Jiangnan University","ror":"https://ror.org/04mkzax54","country_code":"CN","type":"education","lineage":["https://openalex.org/I111599522"]},{"id":"https://openalex.org/I87445476","display_name":"Xi'an Jiaotong University","ror":"https://ror.org/017zhmm22","country_code":"CN","type":"education","lineage":["https://openalex.org/I87445476"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Yong Su","raw_affiliation_strings":["School of Mathematics and Statistics, Xi\u2019an Jiaotong University, Xi\u2019an 710049, China","School of Sciences, Jiangnan University, Wuxi, Jiangsu 21422, China","School of Mathematics and Statistics, Xi'an Jiaotong University, Xi'an 710049, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics, Xi\u2019an Jiaotong University, Xi\u2019an 710049, China","institution_ids":["https://openalex.org/I87445476"]},{"raw_affiliation_string":"School of Sciences, Jiangnan University, Wuxi, Jiangsu 21422, China","institution_ids":["https://openalex.org/I111599522"]},{"raw_affiliation_string":"School of Mathematics and Statistics, Xi'an Jiaotong University, Xi'an 710049, China","institution_ids":["https://openalex.org/I87445476"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5102923717","display_name":"Huawen Liu","orcid":"https://orcid.org/0000-0003-0535-4652"},"institutions":[{"id":"https://openalex.org/I154099455","display_name":"Shandong University","ror":"https://ror.org/0207yh398","country_code":"CN","type":"education","lineage":["https://openalex.org/I154099455"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Hua-Wen Liu","raw_affiliation_strings":["School of Mathematics, Shandong University, Jinan, Shandong 250100, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics, Shandong University, Jinan, Shandong 250100, China","institution_ids":["https://openalex.org/I154099455"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5003799782","display_name":"Witold Pedrycz","orcid":"https://orcid.org/0000-0002-9335-9930"},"institutions":[{"id":"https://openalex.org/I154425047","display_name":"University of Alberta","ror":"https://ror.org/0160cpw27","country_code":"CA","type":"education","lineage":["https://openalex.org/I154425047"]},{"id":"https://openalex.org/I185163786","display_name":"King Abdulaziz University","ror":"https://ror.org/02ma4wv74","country_code":"SA","type":"education","lineage":["https://openalex.org/I185163786"]},{"id":"https://openalex.org/I66083562","display_name":"Systems Research Institute","ror":"https://ror.org/0111cp837","country_code":"PL","type":"facility","lineage":["https://openalex.org/I66083562","https://openalex.org/I99542240"]},{"id":"https://openalex.org/I99542240","display_name":"Polish Academy of Sciences","ror":"https://ror.org/01dr6c206","country_code":"PL","type":"government","lineage":["https://openalex.org/I99542240"]}],"countries":["CA","PL","SA"],"is_corresponding":false,"raw_author_name":"Witold Pedrycz","raw_affiliation_strings":["Department of Electrical & Computer Engineering, University of Alberta, Edmonton T6R 2V4 AB, Canada","Department of Electrical and Computer Engineering, Faculty of Engineering, King Abdulaziz University, Jeddah, 21589, Saudi Arabia","Systems Research Institute, Polish Academy of Sciences, Warsaw, Poland"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Electrical & Computer Engineering, University of Alberta, Edmonton T6R 2V4 AB, Canada","institution_ids":["https://openalex.org/I154425047"]},{"raw_affiliation_string":"Department of Electrical and Computer Engineering, Faculty of Engineering, King Abdulaziz University, Jeddah, 21589, Saudi Arabia","institution_ids":["https://openalex.org/I185163786"]},{"raw_affiliation_string":"Systems Research Institute, Polish Academy of Sciences, Warsaw, Poland","institution_ids":["https://openalex.org/I66083562","https://openalex.org/I99542240"]}]}],"institutions":[],"countries_distinct_count":4,"institutions_distinct_count":7,"corresponding_author_ids":["https://openalex.org/A5066907969"],"corresponding_institution_ids":["https://openalex.org/I111599522","https://openalex.org/I87445476"],"apc_list":null,"apc_paid":null,"fwci":0.5932,"has_fulltext":false,"cited_by_count":9,"citation_normalized_percentile":{"value":0.70923582,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"27","issue":"02","first_page":"329","last_page":"349"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10050","display_name":"Multi-Criteria Decision Making","score":0.9995999932289124,"subfield":{"id":"https://openalex.org/subfields/1803","display_name":"Management Science and Operations Research"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},"topics":[{"id":"https://openalex.org/T10050","display_name":"Multi-Criteria Decision Making","score":0.9995999932289124,"subfield":{"id":"https://openalex.org/subfields/1803","display_name":"Management Science and Operations Research"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T11727","display_name":"Advanced Algebra and Logic","score":0.9955999851226807,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10820","display_name":"Fuzzy Logic and Control Systems","score":0.9937000274658203,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/distributivity","display_name":"Distributivity","score":0.9626622796058655},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7612801790237427},{"id":"https://openalex.org/keywords/associative-property","display_name":"Associative property","score":0.7176915407180786},{"id":"https://openalex.org/keywords/commutative-property","display_name":"Commutative property","score":0.7110246419906616},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.5614029169082642},{"id":"https://openalex.org/keywords/property","display_name":"Property (philosophy)","score":0.5425418615341187},{"id":"https://openalex.org/keywords/fuzzy-logic","display_name":"Fuzzy logic","score":0.5272746682167053},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.3652450740337372},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3611948788166046},{"id":"https://openalex.org/keywords/epistemology","display_name":"Epistemology","score":0.15742909908294678},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.14862647652626038},{"id":"https://openalex.org/keywords/distributive-property","display_name":"Distributive property","score":0.11547493934631348},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.11214759945869446}],"concepts":[{"id":"https://openalex.org/C138390121","wikidata":"https://www.wikidata.org/wiki/Q5283219","display_name":"Distributivity","level":3,"score":0.9626622796058655},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7612801790237427},{"id":"https://openalex.org/C159423971","wikidata":"https://www.wikidata.org/wiki/Q177251","display_name":"Associative property","level":2,"score":0.7176915407180786},{"id":"https://openalex.org/C183778304","wikidata":"https://www.wikidata.org/wiki/Q165474","display_name":"Commutative property","level":2,"score":0.7110246419906616},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.5614029169082642},{"id":"https://openalex.org/C189950617","wikidata":"https://www.wikidata.org/wiki/Q937228","display_name":"Property (philosophy)","level":2,"score":0.5425418615341187},{"id":"https://openalex.org/C58166","wikidata":"https://www.wikidata.org/wiki/Q224821","display_name":"Fuzzy logic","level":2,"score":0.5272746682167053},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.3652450740337372},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3611948788166046},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.15742909908294678},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.14862647652626038},{"id":"https://openalex.org/C11821877","wikidata":"https://www.wikidata.org/wiki/Q187959","display_name":"Distributive property","level":2,"score":0.11547493934631348},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.11214759945869446},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1142/s0218488519500156","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218488519500156","pdf_url":null,"source":{"id":"https://openalex.org/S69518169","display_name":"International Journal of Uncertainty Fuzziness and Knowledge-Based Systems","issn_l":"0218-4885","issn":["0218-4885","1793-6411"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":8,"referenced_works":["https://openalex.org/W331624705","https://openalex.org/W2019333527","https://openalex.org/W2050352691","https://openalex.org/W2114065574","https://openalex.org/W2397557663","https://openalex.org/W2728755087","https://openalex.org/W4255392953","https://openalex.org/W4301436440"],"related_works":["https://openalex.org/W2095709139","https://openalex.org/W1576049389","https://openalex.org/W1723526129","https://openalex.org/W4288570797","https://openalex.org/W1974287725","https://openalex.org/W4295253537","https://openalex.org/W2018362963","https://openalex.org/W2795912694","https://openalex.org/W2059672880","https://openalex.org/W880814422"],"abstract_inverted_index":{"Distributivity":[0],"between":[1,48,62,137],"two":[2,49,63,138,149,166],"operations":[3],"is":[4,13,110,115,128],"a":[5],"property":[6],"posed":[7],"many":[8],"years":[9],"ago":[10],"\u2014":[11],"that":[12,55],"especially":[14],"interesting":[15],"in":[16,40,75,93,156],"the":[17,43,46,76,90,95,101,132,135,146,157,164],"framework":[18],"of":[19,23,45,52,83,87,107,161],"logical":[20],"connectives":[21],"because":[22],"its":[24],"applications":[25],"to":[26,116,120,129],"fuzzy":[27],"logic":[28],"and":[29,68,103],"approximate":[30],"reasoning":[31],"as":[32],"their":[33],"applications.":[34],"Since":[35],"semi-uninorms":[36,50,80,150],"have":[37],"been":[38,72],"used":[39],"these":[41],"topics,":[42],"study":[44],"distributivity":[47,61,96,121,136,147],"becomes":[51],"particular":[53],"interest":[54],"calls":[56],"for":[57,123,142],"thorough":[58],"studies.":[59],"The":[60,105,112,125],"semi-uninorms,":[64,162],"which":[65],"are":[66,81,140],"non-commutative":[67],"non-associative":[69],"uninorms,":[70],"has":[71],"developed":[73],"only":[74,152],"cases":[77],"when":[78,151],"both":[79],"examples":[82],"very":[84],"special":[85],"classes":[86,160],"semi-uninorms.":[88,124,143],"On":[89],"other":[91],"hand,":[92],"general,":[94],"does":[97],"not":[98],"rely":[99],"on":[100],"commutativity":[102],"associativity.":[104],"objective":[106],"this":[108],"work":[109],"twofold.":[111],"first":[113],"one":[114,127,153],"show":[117],"new":[118],"solutions":[119],"equations":[122],"second":[126],"check":[130],"whether":[131],"results":[133],"concerning":[134],"uninorms":[139],"valid":[141],"We":[144],"investigate":[145],"involving":[148],"semi-uninrom":[154],"lies":[155],"most":[158],"studied":[159],"achieving":[163],"above":[165],"objectives":[167],"simultaneously.":[168]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":1},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":1}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}