{"id":"https://openalex.org/W2949866758","doi":"https://doi.org/10.1109/tsmc.2019.2919243","title":"A Generalized Golden Rule Representative Value for Multiple-Criteria Decision Analysis","display_name":"A Generalized Golden Rule Representative Value for Multiple-Criteria Decision Analysis","publication_year":2019,"publication_date":"2019-06-11","ids":{"openalex":"https://openalex.org/W2949866758","doi":"https://doi.org/10.1109/tsmc.2019.2919243","mag":"2949866758"},"language":"en","primary_location":{"id":"doi:10.1109/tsmc.2019.2919243","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tsmc.2019.2919243","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":true,"oa_status":"green","oa_url":"https://figshare.com/articles/journal_contribution/A_generalized_golden_rule_representative_value_for_multiple-criteria_decision_analysis/22979321","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5049730248","display_name":"Zeyi Liu","orcid":"https://orcid.org/0000-0003-2177-8906"},"institutions":[{"id":"https://openalex.org/I142108993","display_name":"Southwest University","ror":"https://ror.org/01kj4z117","country_code":"CN","type":"education","lineage":["https://openalex.org/I142108993"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Zeyi Liu","raw_affiliation_strings":["School of Computer and Information Science, Southwest University, Chongqing, China"],"raw_orcid":"https://orcid.org/0000-0003-2177-8906","affiliations":[{"raw_affiliation_string":"School of Computer and Information Science, Southwest University, Chongqing, China","institution_ids":["https://openalex.org/I142108993"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5075353851","display_name":"Fuyuan Xiao","orcid":"https://orcid.org/0000-0002-6303-895X"},"institutions":[{"id":"https://openalex.org/I142108993","display_name":"Southwest University","ror":"https://ror.org/01kj4z117","country_code":"CN","type":"education","lineage":["https://openalex.org/I142108993"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Fuyuan Xiao","raw_affiliation_strings":["School of Computer and Information Science, Southwest University, Chongqing, China"],"raw_orcid":"https://orcid.org/0000-0002-6303-895X","affiliations":[{"raw_affiliation_string":"School of Computer and Information Science, Southwest University, Chongqing, China","institution_ids":["https://openalex.org/I142108993"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5058936239","display_name":"Chin\u2010Teng Lin","orcid":"https://orcid.org/0000-0001-8371-8197"},"institutions":[{"id":"https://openalex.org/I114017466","display_name":"University of Technology Sydney","ror":"https://ror.org/03f0f6041","country_code":"AU","type":"education","lineage":["https://openalex.org/I114017466"]}],"countries":["AU"],"is_corresponding":false,"raw_author_name":"Chin-Teng Lin","raw_affiliation_strings":["Center for Artificial Intelligence, Faculty of Engineering and IT, University of Technology Sydney, Sydney, NSW, Australia"],"raw_orcid":"https://orcid.org/0000-0001-8371-8197","affiliations":[{"raw_affiliation_string":"Center for Artificial Intelligence, Faculty of Engineering and IT, University of Technology Sydney, Sydney, NSW, Australia","institution_ids":["https://openalex.org/I114017466"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5069403329","display_name":"Byeong Ho Kang","orcid":"https://orcid.org/0000-0003-3476-8838"},"institutions":[{"id":"https://openalex.org/I129801699","display_name":"University of Tasmania","ror":"https://ror.org/01nfmeh72","country_code":"AU","type":"education","lineage":["https://openalex.org/I129801699"]}],"countries":["AU"],"is_corresponding":false,"raw_author_name":"Byeong Ho Kang","raw_affiliation_strings":["Discipline of ICT, School of Technology, Environments and Design, University of Tasmania, Hobart, TAS, Australia"],"raw_orcid":"https://orcid.org/0000-0003-3476-8838","affiliations":[{"raw_affiliation_string":"Discipline of ICT, School of Technology, Environments and Design, University of Tasmania, Hobart, TAS, Australia","institution_ids":["https://openalex.org/I129801699"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5007077356","display_name":"Zehong Cao","orcid":"https://orcid.org/0000-0003-3656-0328"},"institutions":[{"id":"https://openalex.org/I129801699","display_name":"University of Tasmania","ror":"https://ror.org/01nfmeh72","country_code":"AU","type":"education","lineage":["https://openalex.org/I129801699"]}],"countries":["AU"],"is_corresponding":false,"raw_author_name":"Zehong Cao","raw_affiliation_strings":["Discipline of ICT, School of Technology, Environments and Design, University of Tasmania, Hobart, TAS, Australia"],"raw_orcid":"https://orcid.org/0000-0003-3656-0328","affiliations":[{"raw_affiliation_string":"Discipline of ICT, School of Technology, Environments and Design, University of Tasmania, Hobart, TAS, Australia","institution_ids":["https://openalex.org/I129801699"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":2.7681,"has_fulltext":false,"cited_by_count":22,"citation_normalized_percentile":{"value":0.90475176,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":93,"max":98},"biblio":{"volume":"51","issue":"5","first_page":"3193","last_page":"3204"},"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/T12135","display_name":"Fuzzy Systems and Optimization","score":0.9865000247955322,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10820","display_name":"Fuzzy Logic and Control Systems","score":0.9768000245094299,"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/sigmoid-function","display_name":"Sigmoid function","score":0.6388933658599854},{"id":"https://openalex.org/keywords/interval","display_name":"Interval (graph theory)","score":0.6118760108947754},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5125172138214111},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.502568244934082},{"id":"https://openalex.org/keywords/scalar","display_name":"Scalar (mathematics)","score":0.4914497137069702},{"id":"https://openalex.org/keywords/backpropagation","display_name":"Backpropagation","score":0.475841760635376},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.47314155101776123},{"id":"https://openalex.org/keywords/decision-rule","display_name":"Decision rule","score":0.42779165506362915},{"id":"https://openalex.org/keywords/interval-arithmetic","display_name":"Interval arithmetic","score":0.4185100793838501},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3538269102573395},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.3248935639858246}],"concepts":[{"id":"https://openalex.org/C81388566","wikidata":"https://www.wikidata.org/wiki/Q526668","display_name":"Sigmoid function","level":3,"score":0.6388933658599854},{"id":"https://openalex.org/C2778067643","wikidata":"https://www.wikidata.org/wiki/Q166507","display_name":"Interval (graph theory)","level":2,"score":0.6118760108947754},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5125172138214111},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.502568244934082},{"id":"https://openalex.org/C57691317","wikidata":"https://www.wikidata.org/wiki/Q1289248","display_name":"Scalar (mathematics)","level":2,"score":0.4914497137069702},{"id":"https://openalex.org/C155032097","wikidata":"https://www.wikidata.org/wiki/Q798503","display_name":"Backpropagation","level":3,"score":0.475841760635376},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.47314155101776123},{"id":"https://openalex.org/C84839998","wikidata":"https://www.wikidata.org/wiki/Q5249245","display_name":"Decision rule","level":2,"score":0.42779165506362915},{"id":"https://openalex.org/C191252586","wikidata":"https://www.wikidata.org/wiki/Q1671453","display_name":"Interval arithmetic","level":3,"score":0.4185100793838501},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3538269102573395},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.3248935639858246},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1109/tsmc.2019.2919243","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tsmc.2019.2919243","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"},{"id":"pmh:oai:eprints.utas.edu.au:31126","is_oa":false,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S4306400075","display_name":"Open Access Repository (University of Tasmania)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I129801699","host_organization_name":"University of Tasmania","host_organization_lineage":["https://openalex.org/I129801699"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":"","raw_type":"Article"},{"id":"pmh:oai:figshare.com:article/22979321","is_oa":true,"landing_page_url":"https://figshare.com/articles/journal_contribution/A_generalized_golden_rule_representative_value_for_multiple-criteria_decision_analysis/22979321","pdf_url":null,"source":{"id":"https://openalex.org/S4306402621","display_name":"INDIGO (University of Illinois at Chicago)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I39422238","host_organization_name":"University of Illinois Chicago","host_organization_lineage":["https://openalex.org/I39422238"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Text"},{"id":"pmh:oai:opus.lib.uts.edu.au:10453/147235","is_oa":false,"landing_page_url":"http://hdl.handle.net/10453/147235","pdf_url":null,"source":{"id":"https://openalex.org/S4306401357","display_name":"UTS ePRESS (University of Technology Sydney)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I114017466","host_organization_name":"University of Technology Sydney","host_organization_lineage":["https://openalex.org/I114017466"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Journal Article"}],"best_oa_location":{"id":"pmh:oai:figshare.com:article/22979321","is_oa":true,"landing_page_url":"https://figshare.com/articles/journal_contribution/A_generalized_golden_rule_representative_value_for_multiple-criteria_decision_analysis/22979321","pdf_url":null,"source":{"id":"https://openalex.org/S4306402621","display_name":"INDIGO (University of Illinois at Chicago)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I39422238","host_organization_name":"University of Illinois Chicago","host_organization_lineage":["https://openalex.org/I39422238"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Text"},"sustainable_development_goals":[{"score":0.800000011920929,"display_name":"Peace, Justice and strong institutions","id":"https://metadata.un.org/sdg/16"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":73,"referenced_works":["https://openalex.org/W84097466","https://openalex.org/W199892901","https://openalex.org/W1485268022","https://openalex.org/W1622676895","https://openalex.org/W1627967085","https://openalex.org/W1965261707","https://openalex.org/W1969373295","https://openalex.org/W1981144549","https://openalex.org/W1988053196","https://openalex.org/W1995654381","https://openalex.org/W2001002255","https://openalex.org/W2032100896","https://openalex.org/W2038266964","https://openalex.org/W2065534279","https://openalex.org/W2079325629","https://openalex.org/W2083862791","https://openalex.org/W2088157920","https://openalex.org/W2116936493","https://openalex.org/W2126942772","https://openalex.org/W2180415311","https://openalex.org/W2198049824","https://openalex.org/W2295533269","https://openalex.org/W2434930227","https://openalex.org/W2461533535","https://openalex.org/W2467903478","https://openalex.org/W2469016422","https://openalex.org/W2485267629","https://openalex.org/W2512389528","https://openalex.org/W2517813057","https://openalex.org/W2522299305","https://openalex.org/W2549472391","https://openalex.org/W2559544114","https://openalex.org/W2592790085","https://openalex.org/W2593472350","https://openalex.org/W2600418635","https://openalex.org/W2606270526","https://openalex.org/W2610473867","https://openalex.org/W2615452289","https://openalex.org/W2618591006","https://openalex.org/W2737747757","https://openalex.org/W2739428828","https://openalex.org/W2742486456","https://openalex.org/W2759156905","https://openalex.org/W2768698326","https://openalex.org/W2772166100","https://openalex.org/W2773125201","https://openalex.org/W2777482433","https://openalex.org/W2779735534","https://openalex.org/W2781830580","https://openalex.org/W2790388419","https://openalex.org/W2792592918","https://openalex.org/W2792740237","https://openalex.org/W2797554143","https://openalex.org/W2809699333","https://openalex.org/W2884226004","https://openalex.org/W2889405224","https://openalex.org/W2889899570","https://openalex.org/W2893182166","https://openalex.org/W2893661446","https://openalex.org/W2900537829","https://openalex.org/W2900934918","https://openalex.org/W2902886279","https://openalex.org/W2907372845","https://openalex.org/W2911458131","https://openalex.org/W2920894740","https://openalex.org/W2921842513","https://openalex.org/W2934195809","https://openalex.org/W4247564555","https://openalex.org/W6715728965","https://openalex.org/W6736092033","https://openalex.org/W6738278612","https://openalex.org/W6754378863","https://openalex.org/W6757616599"],"related_works":["https://openalex.org/W4385957115","https://openalex.org/W2061372042","https://openalex.org/W3047779762","https://openalex.org/W1520030019","https://openalex.org/W2071654592","https://openalex.org/W3104477175","https://openalex.org/W3001577138","https://openalex.org/W2240896738","https://openalex.org/W2993645418","https://openalex.org/W2790814253"],"abstract_inverted_index":{"Multicriteria":[0],"decision":[1,8,26,111],"analysis":[2],"evaluates":[3],"multiple":[4],"conflicting":[5,11],"criteria":[6,12,115],"in":[7,15,24],"making,":[9],"but":[10],"are":[13],"typical":[14],"evaluating":[16],"options.":[17],"As":[18],"the":[19,63,76,82,97,100],"existing":[20],"ordering":[21],"operations":[22],"involved":[23],"multicriteria":[25,110],"making":[27,112],"cannot":[28],"easily":[29],"be":[30],"implemented":[31],"with":[32,40,49,113],"intervals,":[33],"we":[34,52,95,104],"assume":[35],"that":[36],"scalar":[37,88],"representative":[38,58,89],"values":[39],"intervals":[41],"can":[42],"effectively":[43],"avoid":[44],"this":[45],"issue.":[46],"To":[47],"deal":[48],"interval-valued":[50],"criteria,":[51],"propose":[53],"a":[54,106],"generalized":[55],"golden":[56],"rule":[57],"value":[59],"approach,":[60,102],"which":[61],"involves":[62],"sigmoid":[64],"function":[65],"of":[66,81,99],"backpropagation":[67],"neural":[68],"networks":[69],"to":[70,85],"tune":[71],"parameters.":[72],"Our":[73],"approach":[74],"considers":[75],"uncertainties":[77],"and":[78,103],"side":[79],"effects":[80],"interval":[83,114],"variables":[84],"improve":[86],"individual":[87],"values.":[90],"Based":[91],"on":[92],"numerical":[93],"examples,":[94],"address":[96],"effectiveness":[98],"proposed":[101],"provide":[105],"specific":[107],"application":[108],"concerning":[109],"satisfaction.":[116]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":6},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":4}],"updated_date":"2026-03-27T05:58:40.876381","created_date":"2025-10-10T00:00:00"}