{"id":"https://openalex.org/W2144515526","doi":"https://doi.org/10.1109/tsmcb.2009.2039477","title":"An Approach to Solve Group-Decision-Making Problems With Ordinal Interval Numbers","display_name":"An Approach to Solve Group-Decision-Making Problems With Ordinal Interval Numbers","publication_year":2010,"publication_date":"2010-02-17","ids":{"openalex":"https://openalex.org/W2144515526","doi":"https://doi.org/10.1109/tsmcb.2009.2039477","mag":"2144515526","pmid":"https://pubmed.ncbi.nlm.nih.gov/20172834"},"language":"en","primary_location":{"id":"doi:10.1109/tsmcb.2009.2039477","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tsmcb.2009.2039477","pdf_url":null,"source":{"id":"https://openalex.org/S4210170378","display_name":"IEEE Transactions on Systems Man and Cybernetics Part B (Cybernetics)","issn_l":"1083-4419","issn":["1083-4419","1941-0492"],"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, Part B (Cybernetics)","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","pubmed"],"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/A5089603342","display_name":"Zhi\u2010Ping Fan","orcid":"https://orcid.org/0000-0001-6778-4637"},"institutions":[{"id":"https://openalex.org/I9224756","display_name":"Northeastern University","ror":"https://ror.org/03awzbc87","country_code":"CN","type":"education","lineage":["https://openalex.org/I9224756"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Zhi-Ping Fan","raw_affiliation_strings":["Department of Management Science and Engineering, School of Business Administration, Northeastern University, Shenyang 110004, China. zpfan@mail.neu.edu.cn","Dept. of Manage. Sci. & Eng., Northeastern Univ., Shenyang, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Management Science and Engineering, School of Business Administration, Northeastern University, Shenyang 110004, China. zpfan@mail.neu.edu.cn","institution_ids":["https://openalex.org/I9224756"]},{"raw_affiliation_string":"Dept. of Manage. Sci. & Eng., Northeastern Univ., Shenyang, China","institution_ids":["https://openalex.org/I9224756"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100613640","display_name":"Yang Liu","orcid":"https://orcid.org/0000-0001-8006-3236"},"institutions":[{"id":"https://openalex.org/I9224756","display_name":"Northeastern University","ror":"https://ror.org/03awzbc87","country_code":"CN","type":"education","lineage":["https://openalex.org/I9224756"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yang Liu","raw_affiliation_strings":["Department of Management Science and Engineering School of Business Administration, Northeastern University, Shenyang, China","Dept. of Manage. Sci. & Eng., Northeastern Univ., Shenyang, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Management Science and Engineering School of Business Administration, Northeastern University, Shenyang, China","institution_ids":["https://openalex.org/I9224756"]},{"raw_affiliation_string":"Dept. of Manage. Sci. & Eng., Northeastern Univ., Shenyang, China","institution_ids":["https://openalex.org/I9224756"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I9224756"],"apc_list":null,"apc_paid":null,"fwci":8.8365,"has_fulltext":false,"cited_by_count":73,"citation_normalized_percentile":{"value":0.97728855,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"40","issue":"5","first_page":"1413","last_page":"1423"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10050","display_name":"Multi-Criteria Decision Making","score":0.9998999834060669,"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":0.9998999834060669,"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":0.9779999852180481,"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/T12709","display_name":"Optimization and Mathematical Programming","score":0.9746999740600586,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/pairwise-comparison","display_name":"Pairwise comparison","score":0.7833307385444641},{"id":"https://openalex.org/keywords/ordinal-data","display_name":"Ordinal data","score":0.764374315738678},{"id":"https://openalex.org/keywords/ranking","display_name":"Ranking (information retrieval)","score":0.7354092001914978},{"id":"https://openalex.org/keywords/interval","display_name":"Interval (graph theory)","score":0.7352096438407898},{"id":"https://openalex.org/keywords/ordinal-optimization","display_name":"Ordinal optimization","score":0.7195523977279663},{"id":"https://openalex.org/keywords/ordinal-regression","display_name":"Ordinal regression","score":0.7188101410865784},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6648740172386169},{"id":"https://openalex.org/keywords/rank","display_name":"Rank (graph theory)","score":0.6636210680007935},{"id":"https://openalex.org/keywords/preference","display_name":"Preference","score":0.5881727337837219},{"id":"https://openalex.org/keywords/group-decision-making","display_name":"Group decision-making","score":0.5376558899879456},{"id":"https://openalex.org/keywords/ordinal-scale","display_name":"Ordinal Scale","score":0.5054090023040771},{"id":"https://openalex.org/keywords/degree","display_name":"Degree (music)","score":0.4326578974723816},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.40093374252319336},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.21638599038124084},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.2154562771320343},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.18899181485176086},{"id":"https://openalex.org/keywords/social-psychology","display_name":"Social psychology","score":0.06992295384407043}],"concepts":[{"id":"https://openalex.org/C184898388","wikidata":"https://www.wikidata.org/wiki/Q1435712","display_name":"Pairwise comparison","level":2,"score":0.7833307385444641},{"id":"https://openalex.org/C85461838","wikidata":"https://www.wikidata.org/wiki/Q7100785","display_name":"Ordinal data","level":2,"score":0.764374315738678},{"id":"https://openalex.org/C189430467","wikidata":"https://www.wikidata.org/wiki/Q7293293","display_name":"Ranking (information retrieval)","level":2,"score":0.7354092001914978},{"id":"https://openalex.org/C2778067643","wikidata":"https://www.wikidata.org/wiki/Q166507","display_name":"Interval (graph theory)","level":2,"score":0.7352096438407898},{"id":"https://openalex.org/C81386100","wikidata":"https://www.wikidata.org/wiki/Q7100792","display_name":"Ordinal optimization","level":3,"score":0.7195523977279663},{"id":"https://openalex.org/C110313322","wikidata":"https://www.wikidata.org/wiki/Q7100793","display_name":"Ordinal regression","level":2,"score":0.7188101410865784},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6648740172386169},{"id":"https://openalex.org/C164226766","wikidata":"https://www.wikidata.org/wiki/Q7293202","display_name":"Rank (graph theory)","level":2,"score":0.6636210680007935},{"id":"https://openalex.org/C2781249084","wikidata":"https://www.wikidata.org/wiki/Q908656","display_name":"Preference","level":2,"score":0.5881727337837219},{"id":"https://openalex.org/C20701700","wikidata":"https://www.wikidata.org/wiki/Q388791","display_name":"Group decision-making","level":2,"score":0.5376558899879456},{"id":"https://openalex.org/C2909711754","wikidata":"https://www.wikidata.org/wiki/Q7100785","display_name":"Ordinal Scale","level":2,"score":0.5054090023040771},{"id":"https://openalex.org/C2775997480","wikidata":"https://www.wikidata.org/wiki/Q586277","display_name":"Degree (music)","level":2,"score":0.4326578974723816},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.40093374252319336},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.21638599038124084},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2154562771320343},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.18899181485176086},{"id":"https://openalex.org/C77805123","wikidata":"https://www.wikidata.org/wiki/Q161272","display_name":"Social psychology","level":1,"score":0.06992295384407043},{"id":"https://openalex.org/C15744967","wikidata":"https://www.wikidata.org/wiki/Q9418","display_name":"Psychology","level":0,"score":0.0},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","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":[{"descriptor_ui":"D000465","descriptor_name":"Algorithms","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D000465","descriptor_name":"Algorithms","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D000465","descriptor_name":"Algorithms","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D001185","descriptor_name":"Artificial Intelligence","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D001185","descriptor_name":"Artificial Intelligence","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D001185","descriptor_name":"Artificial Intelligence","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D003198","descriptor_name":"Computer Simulation","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D003198","descriptor_name":"Computer Simulation","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D003198","descriptor_name":"Computer Simulation","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D003661","descriptor_name":"Decision Support Techniques","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D003661","descriptor_name":"Decision Support Techniques","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D003661","descriptor_name":"Decision Support Techniques","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D006126","descriptor_name":"Group Processes","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D006126","descriptor_name":"Group Processes","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D006126","descriptor_name":"Group Processes","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D008433","descriptor_name":"Mathematics","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D008433","descriptor_name":"Mathematics","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D008433","descriptor_name":"Mathematics","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D008962","descriptor_name":"Models, Theoretical","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D008962","descriptor_name":"Models, Theoretical","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D008962","descriptor_name":"Models, Theoretical","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D010363","descriptor_name":"Pattern Recognition, Automated","qualifier_ui":"Q000379","qualifier_name":"methods","is_major_topic":false},{"descriptor_ui":"D010363","descriptor_name":"Pattern Recognition, Automated","qualifier_ui":"Q000379","qualifier_name":"methods","is_major_topic":false},{"descriptor_ui":"D010363","descriptor_name":"Pattern Recognition, Automated","qualifier_ui":"Q000379","qualifier_name":"methods","is_major_topic":false},{"descriptor_ui":"D011340","descriptor_name":"Problem Solving","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D011340","descriptor_name":"Problem Solving","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D011340","descriptor_name":"Problem Solving","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true}],"locations_count":2,"locations":[{"id":"doi:10.1109/tsmcb.2009.2039477","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tsmcb.2009.2039477","pdf_url":null,"source":{"id":"https://openalex.org/S4210170378","display_name":"IEEE Transactions on Systems Man and Cybernetics Part B (Cybernetics)","issn_l":"1083-4419","issn":["1083-4419","1941-0492"],"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, Part B (Cybernetics)","raw_type":"journal-article"},{"id":"pmid:20172834","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/20172834","pdf_url":null,"source":{"id":"https://openalex.org/S4306525036","display_name":"PubMed","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE transactions on systems, man, and cybernetics. Part B, Cybernetics : a publication of the IEEE Systems, Man, and Cybernetics Society","raw_type":null}],"best_oa_location":null,"sustainable_development_goals":[{"display_name":"Peace, Justice and strong institutions","id":"https://metadata.un.org/sdg/16","score":0.800000011920929}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":34,"referenced_works":["https://openalex.org/W35369483","https://openalex.org/W1546303393","https://openalex.org/W1967631404","https://openalex.org/W1972529917","https://openalex.org/W1976567794","https://openalex.org/W1982240267","https://openalex.org/W1995006674","https://openalex.org/W1999581778","https://openalex.org/W2000016084","https://openalex.org/W2004505784","https://openalex.org/W2004513102","https://openalex.org/W2012908264","https://openalex.org/W2013934519","https://openalex.org/W2016075546","https://openalex.org/W2022373133","https://openalex.org/W2030238309","https://openalex.org/W2041280856","https://openalex.org/W2042102899","https://openalex.org/W2063427286","https://openalex.org/W2073405920","https://openalex.org/W2075108881","https://openalex.org/W2082319470","https://openalex.org/W2087055909","https://openalex.org/W2089336319","https://openalex.org/W2091328381","https://openalex.org/W2111617065","https://openalex.org/W2138962584","https://openalex.org/W2139816113","https://openalex.org/W2145906330","https://openalex.org/W2163481099","https://openalex.org/W2164711537","https://openalex.org/W2168435616","https://openalex.org/W2168867141","https://openalex.org/W2619793045"],"related_works":["https://openalex.org/W3021328243","https://openalex.org/W2051517726","https://openalex.org/W66181126","https://openalex.org/W2093964375","https://openalex.org/W2166716405","https://openalex.org/W2023060082","https://openalex.org/W2506242593","https://openalex.org/W2173081572","https://openalex.org/W4236508908","https://openalex.org/W27744225"],"abstract_inverted_index":{"The":[0],"ordinal":[1,41,53,75,81,84,109,124],"interval":[2,42,54,76,85,110,125],"number":[3,86],"is":[4,18,34,69,87,138,148,153],"a":[5,49,127],"form":[6],"of":[7,32,40,52,60,103,136,172],"uncertain":[8],"preference":[9,38],"information":[10,39],"in":[11,21,44,82,95],"group":[12],"decision":[13],"making":[14],"(GDM),":[15],"while":[16],"it":[17],"seldom":[19],"discussed":[20],"the":[22,29,56,61,101,113,161,170,173],"existing":[23],"research.":[24],"This":[25],"paper":[26],"investigates":[27],"how":[28],"ranking":[30,48,62,80],"order":[31],"alternatives":[33,73,137,158],"determined":[35],"based":[36,144],"on":[37,106,133,145],"numbers":[43,77,111],"GDM":[45],"problems.":[46],"When":[47],"large":[50],"quantity":[51],"numbers,":[55,126],"efficiency":[57],"and":[58,92,112,140],"accuracy":[59],"process":[63],"are":[64,166],"critical.":[65],"A":[66],"new":[67],"approach":[68],"proposed":[70,174],"to":[71,89,118,156,168],"rank":[72,119,157],"using":[74],"when":[78],"every":[79],"an":[83,141,151],"thought":[88],"be":[90],"uniformly":[91],"independently":[93],"distributed":[94],"its":[96],"interval.":[97],"First,":[98],"we":[99],"give":[100],"definition":[102],"possibility":[104,130],"degree":[105,131],"comparing":[107,122],"two":[108,164],"related":[114],"theory":[115],"analysis.":[116],"Then,":[117],"alternatives,":[120],"by":[121,159],"multiple":[123],"collective":[128],"expectation":[129],"matrix":[132,147],"pairwise":[134],"comparisons":[135],"built,":[139],"optimization":[142],"model":[143],"this":[146],"constructed.":[149],"Furthermore,":[150],"algorithm":[152],"also":[154],"presented":[155],"solving":[160],"model.":[162],"Finally,":[163],"examples":[165],"used":[167],"illustrate":[169],"use":[171],"approach.":[175]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":4},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":3},{"year":2020,"cited_by_count":4},{"year":2019,"cited_by_count":5},{"year":2018,"cited_by_count":5},{"year":2017,"cited_by_count":6},{"year":2016,"cited_by_count":6},{"year":2015,"cited_by_count":6},{"year":2014,"cited_by_count":6},{"year":2013,"cited_by_count":10},{"year":2012,"cited_by_count":8}],"updated_date":"2026-06-26T08:34:08.712188","created_date":"2025-10-10T00:00:00"}