{"id":"https://openalex.org/W2469016422","doi":"https://doi.org/10.1109/tsmc.2016.2573919","title":"Using New Version of Extended $t$ -Norms and $s$ -Norms for Aggregating Interval Linguistic Labels","display_name":"Using New Version of Extended $t$ -Norms and $s$ -Norms for Aggregating Interval Linguistic Labels","publication_year":2016,"publication_date":"2016-06-23","ids":{"openalex":"https://openalex.org/W2469016422","doi":"https://doi.org/10.1109/tsmc.2016.2573919","mag":"2469016422"},"language":"en","primary_location":{"id":"doi:10.1109/tsmc.2016.2573919","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tsmc.2016.2573919","pdf_url":null,"source":{"id":"https://openalex.org/S4210209078","display_name":"IEEE Transactions on Systems Man and Cybernetics Systems","issn_l":"2168-2216","issn":["2168-2216","2168-2232"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Systems, Man, and Cybernetics: 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/A5101919286","display_name":"Zhifu Tao","orcid":"https://orcid.org/0000-0003-4039-9178"},"institutions":[{"id":"https://openalex.org/I143868143","display_name":"Anhui University","ror":"https://ror.org/05th6yx34","country_code":"CN","type":"education","lineage":["https://openalex.org/I143868143"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Zhifu Tao","raw_affiliation_strings":["School of Economics, Anhui University, Hefei, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Economics, Anhui University, Hefei, China","institution_ids":["https://openalex.org/I143868143"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100450785","display_name":"Xi Liu","orcid":"https://orcid.org/0000-0002-1110-2382"},"institutions":[{"id":"https://openalex.org/I143868143","display_name":"Anhui University","ror":"https://ror.org/05th6yx34","country_code":"CN","type":"education","lineage":["https://openalex.org/I143868143"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Xi Liu","raw_affiliation_strings":["School of Mathematical Sciences, Anhui University, Hefei, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematical Sciences, Anhui University, Hefei, China","institution_ids":["https://openalex.org/I143868143"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5004641057","display_name":"Huayou Chen","orcid":"https://orcid.org/0000-0002-7312-0367"},"institutions":[{"id":"https://openalex.org/I143868143","display_name":"Anhui University","ror":"https://ror.org/05th6yx34","country_code":"CN","type":"education","lineage":["https://openalex.org/I143868143"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Huayou Chen","raw_affiliation_strings":["School of Mathematical Sciences, Anhui University, Hefei, China"],"raw_orcid":"https://orcid.org/0000-0002-7312-0367","affiliations":[{"raw_affiliation_string":"School of Mathematical Sciences, Anhui University, Hefei, China","institution_ids":["https://openalex.org/I143868143"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5005456443","display_name":"Ligang Zhou","orcid":"https://orcid.org/0000-0002-8512-6125"},"institutions":[{"id":"https://openalex.org/I143868143","display_name":"Anhui University","ror":"https://ror.org/05th6yx34","country_code":"CN","type":"education","lineage":["https://openalex.org/I143868143"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Ligang Zhou","raw_affiliation_strings":["School of Mathematical Sciences, Anhui University, Hefei, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematical Sciences, Anhui University, Hefei, China","institution_ids":["https://openalex.org/I143868143"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I143868143"],"apc_list":null,"apc_paid":null,"fwci":3.6153,"has_fulltext":false,"cited_by_count":26,"citation_normalized_percentile":{"value":0.93111105,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"47","issue":"12","first_page":"3284","last_page":"3298"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10050","display_name":"Multi-Criteria Decision Making","score":0.9998000264167786,"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":0.9998000264167786,"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/T11063","display_name":"Rough Sets and Fuzzy Logic","score":0.9983000159263611,"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/T11727","display_name":"Advanced Algebra and Logic","score":0.993399977684021,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/commutative-property","display_name":"Commutative property","score":0.6413365602493286},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6033059358596802},{"id":"https://openalex.org/keywords/interval","display_name":"Interval (graph theory)","score":0.5979190468788147},{"id":"https://openalex.org/keywords/entropy","display_name":"Entropy (arrow of time)","score":0.533841073513031},{"id":"https://openalex.org/keywords/algebraic-number","display_name":"Algebraic number","score":0.5228381752967834},{"id":"https://openalex.org/keywords/einstein","display_name":"Einstein","score":0.4721548557281494},{"id":"https://openalex.org/keywords/associative-property","display_name":"Associative property","score":0.44477906823158264},{"id":"https://openalex.org/keywords/linguistics","display_name":"Linguistics","score":0.3853371739387512},{"id":"https://openalex.org/keywords/mathematical-economics","display_name":"Mathematical economics","score":0.35835394263267517},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.3379066586494446},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.30884677171707153},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.17901039123535156},{"id":"https://openalex.org/keywords/philosophy","display_name":"Philosophy","score":0.09506890177726746},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.09016364812850952}],"concepts":[{"id":"https://openalex.org/C183778304","wikidata":"https://www.wikidata.org/wiki/Q165474","display_name":"Commutative property","level":2,"score":0.6413365602493286},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6033059358596802},{"id":"https://openalex.org/C2778067643","wikidata":"https://www.wikidata.org/wiki/Q166507","display_name":"Interval (graph theory)","level":2,"score":0.5979190468788147},{"id":"https://openalex.org/C106301342","wikidata":"https://www.wikidata.org/wiki/Q4117933","display_name":"Entropy (arrow of time)","level":2,"score":0.533841073513031},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.5228381752967834},{"id":"https://openalex.org/C146846114","wikidata":"https://www.wikidata.org/wiki/Q901448","display_name":"Einstein","level":2,"score":0.4721548557281494},{"id":"https://openalex.org/C159423971","wikidata":"https://www.wikidata.org/wiki/Q177251","display_name":"Associative property","level":2,"score":0.44477906823158264},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"score":0.3853371739387512},{"id":"https://openalex.org/C144237770","wikidata":"https://www.wikidata.org/wiki/Q747534","display_name":"Mathematical economics","level":1,"score":0.35835394263267517},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.3379066586494446},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.30884677171707153},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.17901039123535156},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.09506890177726746},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.09016364812850952},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tsmc.2016.2573919","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tsmc.2016.2573919","pdf_url":null,"source":{"id":"https://openalex.org/S4210209078","display_name":"IEEE Transactions on Systems Man and Cybernetics Systems","issn_l":"2168-2216","issn":["2168-2216","2168-2232"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Systems, Man, and Cybernetics: Systems","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/16","display_name":"Peace, Justice and strong institutions","score":0.800000011920929}],"awards":[{"id":"https://openalex.org/G2791717321","display_name":"\u57fa\u4e8e\u591a\u6a21\u6001\u4fe1\u606f\u96c6\u6210\u7684\u7ec4\u5408\u9884\u6d4b\u6a21\u578b\u53ca\u5176\u5e94\u7528\u7814\u7a76","funder_award_id":"71501002","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G3669475936","display_name":null,"funder_award_id":"71301001","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G8628183500","display_name":"\u6a21\u7cca\u4fe1\u606f\u73af\u5883\u4e0b\u7684\u7ec4\u5408\u9884\u6d4b\u65b9\u6cd5\u7684\u6709\u6548\u6027\u7406\u8bba\u548c\u5e94\u7528\u7814\u7a76","funder_award_id":"71371011","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":88,"referenced_works":["https://openalex.org/W60482913","https://openalex.org/W600759171","https://openalex.org/W1593125407","https://openalex.org/W1901124019","https://openalex.org/W1973922920","https://openalex.org/W1973931438","https://openalex.org/W1976073056","https://openalex.org/W1976567794","https://openalex.org/W1978062397","https://openalex.org/W1980451630","https://openalex.org/W1980564456","https://openalex.org/W1982562085","https://openalex.org/W1983919696","https://openalex.org/W1985904611","https://openalex.org/W1986686276","https://openalex.org/W1988242538","https://openalex.org/W1989685894","https://openalex.org/W1990844459","https://openalex.org/W1999186087","https://openalex.org/W2000205198","https://openalex.org/W2002604161","https://openalex.org/W2014845900","https://openalex.org/W2019752030","https://openalex.org/W2021332053","https://openalex.org/W2025124974","https://openalex.org/W2027314496","https://openalex.org/W2027349513","https://openalex.org/W2031228760","https://openalex.org/W2032558547","https://openalex.org/W2035090090","https://openalex.org/W2036378460","https://openalex.org/W2038051080","https://openalex.org/W2040765468","https://openalex.org/W2043400189","https://openalex.org/W2045371359","https://openalex.org/W2051527699","https://openalex.org/W2053105283","https://openalex.org/W2057636328","https://openalex.org/W2065893491","https://openalex.org/W2066298895","https://openalex.org/W2067273185","https://openalex.org/W2075963543","https://openalex.org/W2078364725","https://openalex.org/W2083962350","https://openalex.org/W2084186462","https://openalex.org/W2084926750","https://openalex.org/W2087959922","https://openalex.org/W2091275864","https://openalex.org/W2092989683","https://openalex.org/W2094298620","https://openalex.org/W2094772510","https://openalex.org/W2097742402","https://openalex.org/W2105915632","https://openalex.org/W2108856508","https://openalex.org/W2110182592","https://openalex.org/W2111211679","https://openalex.org/W2113181660","https://openalex.org/W2117827905","https://openalex.org/W2125843991","https://openalex.org/W2129314570","https://openalex.org/W2133555750","https://openalex.org/W2138592508","https://openalex.org/W2139564753","https://openalex.org/W2143687879","https://openalex.org/W2144232912","https://openalex.org/W2144798659","https://openalex.org/W2146950091","https://openalex.org/W2148384532","https://openalex.org/W2157041604","https://openalex.org/W2157687268","https://openalex.org/W2159834454","https://openalex.org/W2174826014","https://openalex.org/W2233147346","https://openalex.org/W2309813571","https://openalex.org/W2313407367","https://openalex.org/W2517813057","https://openalex.org/W2912565176","https://openalex.org/W4205117801","https://openalex.org/W4211007335","https://openalex.org/W4214576030","https://openalex.org/W4239974414","https://openalex.org/W4245152641","https://openalex.org/W4252028749","https://openalex.org/W4253058124","https://openalex.org/W4312837445","https://openalex.org/W6618214701","https://openalex.org/W6655719342","https://openalex.org/W6680697056"],"related_works":["https://openalex.org/W1576049389","https://openalex.org/W4288570797","https://openalex.org/W1974287725","https://openalex.org/W4295253537","https://openalex.org/W1723526129","https://openalex.org/W2795912694","https://openalex.org/W2063752695","https://openalex.org/W2059672880","https://openalex.org/W2146163384","https://openalex.org/W1579054707"],"abstract_inverted_index":{"The":[0,101],"aim":[1],"of":[2,27,42,73,97,103,115,133,143],"this":[3],"paper":[4],"is":[5,107,128],"to":[6,65,111,119,139],"develop":[7],"some":[8,79,94],"closed":[9],"algebra":[10],"operational":[11,29,68,75],"laws":[12],"for":[13],"interval":[14,85,104,125],"linguistic":[15,86,105,126],"labels":[16],"based":[17,84],"on":[18],"extended":[19,43,50,52,54,57,80],"t-norms":[20,44,59,81],"and":[21,37,45,56,60,82,109],"s-norms.":[22],"We":[23,91],"discuss":[24],"the":[25,49,113,141,144],"properties":[26,96],"these":[28],"laws,":[30,76],"such":[31,47,74,98],"as":[32,48],"commutative":[33],"law,":[34,36],"associative":[35],"distribution":[38],"law.":[39],"Different":[40],"kinds":[41],"s-norms,":[46,61],"algebraic,":[51],"Einstein,":[53],"Hamacher,":[55],"Frank":[58],"have":[62],"been":[63],"investigated":[64],"produce":[66],"different":[67],"laws.":[69],"As":[70],"an":[71],"application":[72,142],"we":[77],"propose":[78],"s-norms":[83],"weighted":[87],"power":[88],"average":[89],"operators.":[90],"also":[92],"study":[93],"basic":[95],"aggregation":[99],"functions.":[100],"cross-entropy":[102],"information":[106,127],"proposed":[108,145],"applied":[110],"obtain":[112],"weights":[114],"attributes.":[116],"An":[117],"approach":[118],"multiple":[120],"attributes":[121],"decision":[122,135],"making":[123],"with":[124],"proposed.":[129],"Finally,":[130],"two":[131],"cases":[132],"practical":[134],"issues":[136],"are":[137],"illustrated":[138],"show":[140],"method.":[146]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":4},{"year":2020,"cited_by_count":5},{"year":2019,"cited_by_count":5},{"year":2018,"cited_by_count":4},{"year":2017,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
