{"id":"https://openalex.org/W3160251459","doi":"https://doi.org/10.1109/tfuzz.2021.3078817","title":"Analysis of Ranking Consistency in Linguistic Multiple Attribute Decision Making: The Roles of Granularity and Decision Rules","display_name":"Analysis of Ranking Consistency in Linguistic Multiple Attribute Decision Making: The Roles of Granularity and Decision Rules","publication_year":2021,"publication_date":"2021-05-11","ids":{"openalex":"https://openalex.org/W3160251459","doi":"https://doi.org/10.1109/tfuzz.2021.3078817","mag":"3160251459"},"language":"en","primary_location":{"id":"doi:10.1109/tfuzz.2021.3078817","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tfuzz.2021.3078817","pdf_url":null,"source":{"id":"https://openalex.org/S134177497","display_name":"IEEE Transactions on Fuzzy Systems","issn_l":"1063-6706","issn":["1063-6706","1941-0034"],"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 Fuzzy 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/A5101885559","display_name":"Sihai Zhao","orcid":"https://orcid.org/0000-0002-7681-0937"},"institutions":[{"id":"https://openalex.org/I24185976","display_name":"Sichuan University","ror":"https://ror.org/011ashp19","country_code":"CN","type":"education","lineage":["https://openalex.org/I24185976"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Sihai Zhao","raw_affiliation_strings":["Center for Network Big Data and Decision-Making, Business School, Sichuan University, Chengdu, China"],"raw_orcid":"https://orcid.org/0000-0002-7681-0937","affiliations":[{"raw_affiliation_string":"Center for Network Big Data and Decision-Making, Business School, Sichuan University, Chengdu, China","institution_ids":["https://openalex.org/I24185976"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5050358854","display_name":"Yucheng Dong","orcid":"https://orcid.org/0000-0002-0028-6796"},"institutions":[{"id":"https://openalex.org/I158809036","display_name":"Shenzhen Institute of Information Technology","ror":"https://ror.org/03wrf9427","country_code":"CN","type":"education","lineage":["https://openalex.org/I158809036"]},{"id":"https://openalex.org/I24185976","display_name":"Sichuan University","ror":"https://ror.org/011ashp19","country_code":"CN","type":"education","lineage":["https://openalex.org/I24185976"]},{"id":"https://openalex.org/I4210099437","display_name":"Hubei University Of Economics","ror":"https://ror.org/012a84b59","country_code":"CN","type":"education","lineage":["https://openalex.org/I4210099437"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yucheng Dong","raw_affiliation_strings":["Center for Network Big Data and Decision-Making, Business School, Sichuan University, Chengdu, China","School of Information Management and Statistics, Hubei University of Economics, Wuhan, China","School of Management, Shenzhen Institute of Information Technology, Shenzhen, China"],"raw_orcid":"https://orcid.org/0000-0002-0028-6796","affiliations":[{"raw_affiliation_string":"Center for Network Big Data and Decision-Making, Business School, Sichuan University, Chengdu, China","institution_ids":["https://openalex.org/I24185976"]},{"raw_affiliation_string":"School of Information Management and Statistics, Hubei University of Economics, Wuhan, China","institution_ids":["https://openalex.org/I4210099437"]},{"raw_affiliation_string":"School of Management, Shenzhen Institute of Information Technology, Shenzhen, China","institution_ids":["https://openalex.org/I158809036"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5112638293","display_name":"Luis Martine","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Luis Martine","raw_affiliation_strings":["Department of Computer Science, University of Jaén, Jaén, Spain"],"raw_orcid":"https://orcid.org/0000-0003-4245-8813","affiliations":[{"raw_affiliation_string":"Department of Computer Science, University of Jaén, Jaén, Spain","institution_ids":[]}]},{"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 and Computer Engineering, University of Alberta, Edmonton, AB, Canada","Systems Research Institute, Polish Academy of Sciences, Warsaw, Poland","Faculty of Engineering, King Abdulaziz University, Jeddah, Saudi Arabia"],"raw_orcid":"https://orcid.org/0000-0002-9335-9930","affiliations":[{"raw_affiliation_string":"Department of Electrical and Computer Engineering, University of Alberta, Edmonton, AB, Canada","institution_ids":["https://openalex.org/I154425047"]},{"raw_affiliation_string":"Systems Research Institute, Polish Academy of Sciences, Warsaw, Poland","institution_ids":["https://openalex.org/I66083562","https://openalex.org/I99542240"]},{"raw_affiliation_string":"Faculty of Engineering, King Abdulaziz University, Jeddah, Saudi Arabia","institution_ids":["https://openalex.org/I185163786"]}]}],"institutions":[],"countries_distinct_count":4,"institutions_distinct_count":7,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.7337,"has_fulltext":false,"cited_by_count":12,"citation_normalized_percentile":{"value":0.84495906,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"30","issue":"7","first_page":"2266","last_page":"2278"},"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/T11063","display_name":"Rough Sets and Fuzzy Logic","score":0.9675999879837036,"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/T12945","display_name":"Quality Function Deployment in Product Design","score":0.9580000042915344,"subfield":{"id":"https://openalex.org/subfields/1405","display_name":"Management of Technology and Innovation"},"field":{"id":"https://openalex.org/fields/14","display_name":"Business, Management and Accounting"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/consistency","display_name":"Consistency (knowledge bases)","score":0.7685420513153076},{"id":"https://openalex.org/keywords/ranking","display_name":"Ranking (information retrieval)","score":0.7580794095993042},{"id":"https://openalex.org/keywords/tuple","display_name":"Tuple","score":0.5662708282470703},{"id":"https://openalex.org/keywords/granularity","display_name":"Granularity","score":0.5246127843856812},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.49597224593162537},{"id":"https://openalex.org/keywords/preference","display_name":"Preference","score":0.4805193841457367},{"id":"https://openalex.org/keywords/representation","display_name":"Representation (politics)","score":0.4788377583026886},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4746045470237732},{"id":"https://openalex.org/keywords/natural-language-processing","display_name":"Natural language processing","score":0.450473427772522},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.4327644109725952},{"id":"https://openalex.org/keywords/rank","display_name":"Rank (graph theory)","score":0.43247342109680176},{"id":"https://openalex.org/keywords/linguistics","display_name":"Linguistics","score":0.42459022998809814},{"id":"https://openalex.org/keywords/similarity","display_name":"Similarity (geometry)","score":0.4224676489830017},{"id":"https://openalex.org/keywords/scale","display_name":"Scale (ratio)","score":0.4169754087924957},{"id":"https://openalex.org/keywords/data-mining","display_name":"Data mining","score":0.3478652536869049},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.20877709984779358},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.09507825970649719}],"concepts":[{"id":"https://openalex.org/C2776436953","wikidata":"https://www.wikidata.org/wiki/Q5163215","display_name":"Consistency (knowledge bases)","level":2,"score":0.7685420513153076},{"id":"https://openalex.org/C189430467","wikidata":"https://www.wikidata.org/wiki/Q7293293","display_name":"Ranking (information retrieval)","level":2,"score":0.7580794095993042},{"id":"https://openalex.org/C118930307","wikidata":"https://www.wikidata.org/wiki/Q600590","display_name":"Tuple","level":2,"score":0.5662708282470703},{"id":"https://openalex.org/C177774035","wikidata":"https://www.wikidata.org/wiki/Q1246948","display_name":"Granularity","level":2,"score":0.5246127843856812},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.49597224593162537},{"id":"https://openalex.org/C2781249084","wikidata":"https://www.wikidata.org/wiki/Q908656","display_name":"Preference","level":2,"score":0.4805193841457367},{"id":"https://openalex.org/C2776359362","wikidata":"https://www.wikidata.org/wiki/Q2145286","display_name":"Representation (politics)","level":3,"score":0.4788377583026886},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4746045470237732},{"id":"https://openalex.org/C204321447","wikidata":"https://www.wikidata.org/wiki/Q30642","display_name":"Natural language processing","level":1,"score":0.450473427772522},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.4327644109725952},{"id":"https://openalex.org/C164226766","wikidata":"https://www.wikidata.org/wiki/Q7293202","display_name":"Rank (graph theory)","level":2,"score":0.43247342109680176},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"score":0.42459022998809814},{"id":"https://openalex.org/C103278499","wikidata":"https://www.wikidata.org/wiki/Q254465","display_name":"Similarity (geometry)","level":3,"score":0.4224676489830017},{"id":"https://openalex.org/C2778755073","wikidata":"https://www.wikidata.org/wiki/Q10858537","display_name":"Scale (ratio)","level":2,"score":0.4169754087924957},{"id":"https://openalex.org/C124101348","wikidata":"https://www.wikidata.org/wiki/Q172491","display_name":"Data mining","level":1,"score":0.3478652536869049},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.20877709984779358},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.09507825970649719},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.0},{"id":"https://openalex.org/C94625758","wikidata":"https://www.wikidata.org/wiki/Q7163","display_name":"Politics","level":2,"score":0.0},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0},{"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/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.0},{"id":"https://openalex.org/C115961682","wikidata":"https://www.wikidata.org/wiki/Q860623","display_name":"Image (mathematics)","level":2,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"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:10.1109/tfuzz.2021.3078817","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tfuzz.2021.3078817","pdf_url":null,"source":{"id":"https://openalex.org/S134177497","display_name":"IEEE Transactions on Fuzzy Systems","issn_l":"1063-6706","issn":["1063-6706","1941-0034"],"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 Fuzzy 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/G3491031325","display_name":"\u7fa4\u4f53\u51b3\u7b56\u4e2d\u504f\u597d\u6f14\u5316\u4e0e\u5173\u7cfb\u64cd\u7eb5\u6a21\u578b\u53ca\u5e94\u7528\u7814\u7a76","funder_award_id":"71871149","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G6239703929","display_name":null,"funder_award_id":"sksyl201705","funder_id":"https://openalex.org/F4320322990","funder_display_name":"Sichuan University"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320322990","display_name":"Sichuan University","ror":"https://ror.org/011ashp19"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":56,"referenced_works":["https://openalex.org/W1965473535","https://openalex.org/W1972591816","https://openalex.org/W1979474742","https://openalex.org/W1986813400","https://openalex.org/W2012908264","https://openalex.org/W2016959119","https://openalex.org/W2025124974","https://openalex.org/W2028206456","https://openalex.org/W2037767697","https://openalex.org/W2038166912","https://openalex.org/W2045995140","https://openalex.org/W2047702632","https://openalex.org/W2049947502","https://openalex.org/W2060907774","https://openalex.org/W2075288746","https://openalex.org/W2076584270","https://openalex.org/W2094298620","https://openalex.org/W2108856508","https://openalex.org/W2113181660","https://openalex.org/W2117827905","https://openalex.org/W2125843991","https://openalex.org/W2138907258","https://openalex.org/W2144798659","https://openalex.org/W2146570554","https://openalex.org/W2157423656","https://openalex.org/W2162848031","https://openalex.org/W2170493368","https://openalex.org/W2170729459","https://openalex.org/W2211293561","https://openalex.org/W2288292841","https://openalex.org/W2346604114","https://openalex.org/W2414078667","https://openalex.org/W2506768821","https://openalex.org/W2530583575","https://openalex.org/W2554417110","https://openalex.org/W2579555219","https://openalex.org/W2595118259","https://openalex.org/W2604952463","https://openalex.org/W2610473867","https://openalex.org/W2773632529","https://openalex.org/W2792056137","https://openalex.org/W2793902308","https://openalex.org/W2905653691","https://openalex.org/W2920236394","https://openalex.org/W2940082359","https://openalex.org/W2984747650","https://openalex.org/W2990367142","https://openalex.org/W2999233237","https://openalex.org/W3091722739","https://openalex.org/W3106288544","https://openalex.org/W3150478326","https://openalex.org/W4233072629","https://openalex.org/W4240596782","https://openalex.org/W4245152641","https://openalex.org/W4246352385","https://openalex.org/W6683094445"],"related_works":["https://openalex.org/W2896465866","https://openalex.org/W1977387692","https://openalex.org/W3168190260","https://openalex.org/W2921897409","https://openalex.org/W2079626118","https://openalex.org/W2390724719","https://openalex.org/W4248709109","https://openalex.org/W1569703977","https://openalex.org/W2772240868","https://openalex.org/W2291894432"],"abstract_inverted_index":{"Linguistic":[0],"multiple":[1],"attribute":[2],"decision":[3,12,113,173,198,216],"making":[4],"(LMADM)":[5],"has":[6,53],"been":[7],"widely":[8],"used":[9,112],"in":[10,30,35,50,105,161,202,218,224],"different":[11],"contexts":[13],"to":[14,140,175],"achieve":[15],"a":[16,54,59],"final":[17],"solution,":[18,143],"e.g.,":[19],"obtaining":[20],"the":[21,67,73,79,91,99,153,156,171,177,185,195,203,207,211,214,221],"ranking":[22,74,102,128,159,180,222],"of":[23,75,155,197,213],"alternatives.":[24],"Evaluation":[25],"information":[26],"using":[27],"linguistic":[28,38,48,60,68,81,92,100,157,178],"scales":[29],"LMADM":[31,51,106],"is":[32],"usually":[33],"expressed":[34],"simple":[36,47,80],"discrete":[37],"terms.":[39],"In":[40],"this":[41,96],"article,":[42],"we":[43,183],"consider":[44],"that":[45,88],"each":[46],"term":[49],"actually":[52],"continuous":[55],"representation":[56],"(denoted":[57],"as":[58],"two":[61,93],"tuples)":[62],"whose":[63],"rounding":[64],"operation":[65],"matches":[66],"term.":[69],"Under":[70],"such":[71],"conditions,":[72,205],"alternatives":[76],"based":[77,89],"on":[78,90],"terms":[82],"may":[83],"not":[84],"be":[85],"consistent":[86],"with":[87],"tuples.":[94],"Thus,":[95],"article":[97],"studies":[98],"scale":[101,158,179],"consistency":[103,160,165,204],"issue":[104],"under":[107],"seven":[108],"classical":[109],"and":[110,144,188,200,206],"commonly":[111],"rules:":[114],"weighted":[115,118,120,124],"averaging,":[116,119,122,126],"ordered":[117,123],"geometric":[121,125],"preference":[127,137],"organization":[129],"method":[130],"for":[131,135,170],"enrichment":[132],"evaluation,":[133],"technique":[134],"order":[136],"by":[138],"similarity":[139],"an":[141],"ideal":[142],"elimination":[145],"et":[146],"choice":[147],"translating":[148],"reality.":[149],"We":[150],"first":[151],"define":[152],"concept":[154],"LMADM.":[162,225],"Afterward,":[163],"several":[164],"conditions":[166],"are":[167],"presented":[168],"analytically":[169],"selected":[172,215],"rules":[174,199,217],"guarantee":[176],"consistency.":[181],"Finally,":[182],"present":[184],"detailed":[186],"theoretical":[187,192],"simulation-based":[189,208],"comparisons.":[190],"The":[191],"comparisons":[193,209],"show":[194],"roles":[196],"granularity":[201],"demonstrate":[210],"performance":[212],"defending":[219],"against":[220],"inconsistency":[223]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":7},{"year":2022,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}