{"id":"https://openalex.org/W2805140319","doi":"https://doi.org/10.1142/s0219622018500359","title":"A Reliable Method for Consistency Improving of Interval Multiplicative Preference Relations Expressed under Uncertainty","display_name":"A Reliable Method for Consistency Improving of Interval Multiplicative Preference Relations Expressed under Uncertainty","publication_year":2018,"publication_date":"2018-05-30","ids":{"openalex":"https://openalex.org/W2805140319","doi":"https://doi.org/10.1142/s0219622018500359","mag":"2805140319"},"language":"en","primary_location":{"id":"doi:10.1142/s0219622018500359","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0219622018500359","pdf_url":null,"source":{"id":"https://openalex.org/S207089700","display_name":"International Journal of Information Technology & Decision Making","issn_l":"0219-6220","issn":["0219-6220","1793-6845"],"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 Information Technology & Decision Making","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/A5111420747","display_name":"Virgilio L\u00f3pez\u2010Moral\u00e8s","orcid":"https://orcid.org/0000-0003-2043-8766"},"institutions":[{"id":"https://openalex.org/I104854061","display_name":"Universidad Aut\u00f3noma del Estado de Hidalgo","ror":"https://ror.org/031f8kt38","country_code":"MX","type":"education","lineage":["https://openalex.org/I104854061"]}],"countries":["MX"],"is_corresponding":true,"raw_author_name":"Virgilio L\u00f3pez-Morales","raw_affiliation_strings":["Centro de Investigaci\u00f3n en Tecnolog\u00edas de Informaci\u00f3n y Sistemas, Universidad Aut\u00f3noma del Estado de Hidalgo, Carretera Pachuca-Tulancingo km. 4.5, Pachuca 42184, M\u00e9xico"],"raw_orcid":"https://orcid.org/0000-0003-2043-8766","affiliations":[{"raw_affiliation_string":"Centro de Investigaci\u00f3n en Tecnolog\u00edas de Informaci\u00f3n y Sistemas, Universidad Aut\u00f3noma del Estado de Hidalgo, Carretera Pachuca-Tulancingo km. 4.5, Pachuca 42184, M\u00e9xico","institution_ids":["https://openalex.org/I104854061"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5111420747"],"corresponding_institution_ids":["https://openalex.org/I104854061"],"apc_list":null,"apc_paid":null,"fwci":0.6619,"has_fulltext":false,"cited_by_count":7,"citation_normalized_percentile":{"value":0.73850679,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"17","issue":"05","first_page":"1561","last_page":"1585"},"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":0.9922999739646912,"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/T11063","display_name":"Rough Sets and Fuzzy Logic","score":0.9865999817848206,"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/consistency","display_name":"Consistency (knowledge bases)","score":0.7944682836532593},{"id":"https://openalex.org/keywords/multiplicative-function","display_name":"Multiplicative function","score":0.7408449053764343},{"id":"https://openalex.org/keywords/preference","display_name":"Preference","score":0.6305311918258667},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.604135274887085},{"id":"https://openalex.org/keywords/interval","display_name":"Interval (graph theory)","score":0.5998894572257996},{"id":"https://openalex.org/keywords/preference-relation","display_name":"Preference relation","score":0.5754002332687378},{"id":"https://openalex.org/keywords/multiple-criteria-decision-analysis","display_name":"Multiple-criteria decision analysis","score":0.5575255751609802},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5233466029167175},{"id":"https://openalex.org/keywords/operator","display_name":"Operator (biology)","score":0.47537198662757874},{"id":"https://openalex.org/keywords/relation","display_name":"Relation (database)","score":0.466551274061203},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.45869961380958557},{"id":"https://openalex.org/keywords/interval-arithmetic","display_name":"Interval arithmetic","score":0.4402191936969757},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.41240257024765015},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.36753493547439575},{"id":"https://openalex.org/keywords/data-mining","display_name":"Data mining","score":0.3294614851474762},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.1999606490135193},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.13931065797805786}],"concepts":[{"id":"https://openalex.org/C2776436953","wikidata":"https://www.wikidata.org/wiki/Q5163215","display_name":"Consistency (knowledge bases)","level":2,"score":0.7944682836532593},{"id":"https://openalex.org/C42747912","wikidata":"https://www.wikidata.org/wiki/Q1048447","display_name":"Multiplicative function","level":2,"score":0.7408449053764343},{"id":"https://openalex.org/C2781249084","wikidata":"https://www.wikidata.org/wiki/Q908656","display_name":"Preference","level":2,"score":0.6305311918258667},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.604135274887085},{"id":"https://openalex.org/C2778067643","wikidata":"https://www.wikidata.org/wiki/Q166507","display_name":"Interval (graph theory)","level":2,"score":0.5998894572257996},{"id":"https://openalex.org/C2777062324","wikidata":"https://www.wikidata.org/wiki/Q25036211","display_name":"Preference relation","level":3,"score":0.5754002332687378},{"id":"https://openalex.org/C11105738","wikidata":"https://www.wikidata.org/wiki/Q1895805","display_name":"Multiple-criteria decision analysis","level":2,"score":0.5575255751609802},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5233466029167175},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.47537198662757874},{"id":"https://openalex.org/C25343380","wikidata":"https://www.wikidata.org/wiki/Q277521","display_name":"Relation (database)","level":2,"score":0.466551274061203},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.45869961380958557},{"id":"https://openalex.org/C191252586","wikidata":"https://www.wikidata.org/wiki/Q1671453","display_name":"Interval arithmetic","level":3,"score":0.4402191936969757},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.41240257024765015},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.36753493547439575},{"id":"https://openalex.org/C124101348","wikidata":"https://www.wikidata.org/wiki/Q172491","display_name":"Data mining","level":1,"score":0.3294614851474762},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.1999606490135193},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.13931065797805786},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"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/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"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/C86339819","wikidata":"https://www.wikidata.org/wiki/Q407384","display_name":"Transcription factor","level":3,"score":0.0},{"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/C158448853","wikidata":"https://www.wikidata.org/wiki/Q425218","display_name":"Repressor","level":4,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1142/s0219622018500359","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0219622018500359","pdf_url":null,"source":{"id":"https://openalex.org/S207089700","display_name":"International Journal of Information Technology & Decision Making","issn_l":"0219-6220","issn":["0219-6220","1793-6845"],"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 Information Technology & Decision Making","raw_type":"journal-article"},{"id":"pmh:oai:RePEc:wsi:ijitdm:v:17:y:2018:i:05:n:s0219622018500359","is_oa":false,"landing_page_url":"http://www.worldscientific.com/doi/abs/10.1142/S0219622018500359","pdf_url":null,"source":{"id":"https://openalex.org/S4306401271","display_name":"RePEc: Research Papers in Economics","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I77793887","host_organization_name":"Federal Reserve Bank of St. Louis","host_organization_lineage":["https://openalex.org/I77793887"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":null,"sustainable_development_goals":[{"display_name":"Peace, Justice and strong institutions","score":0.7900000214576721,"id":"https://metadata.un.org/sdg/16"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":45,"referenced_works":["https://openalex.org/W1830792952","https://openalex.org/W1963675712","https://openalex.org/W1964346230","https://openalex.org/W1967631404","https://openalex.org/W1968642553","https://openalex.org/W1977551697","https://openalex.org/W1983619252","https://openalex.org/W1985316359","https://openalex.org/W1997713472","https://openalex.org/W2004030638","https://openalex.org/W2012491224","https://openalex.org/W2018164936","https://openalex.org/W2021388613","https://openalex.org/W2024428474","https://openalex.org/W2025447782","https://openalex.org/W2026923435","https://openalex.org/W2029278175","https://openalex.org/W2031299513","https://openalex.org/W2032270076","https://openalex.org/W2033375693","https://openalex.org/W2034409469","https://openalex.org/W2051440091","https://openalex.org/W2053047891","https://openalex.org/W2055892602","https://openalex.org/W2056059065","https://openalex.org/W2065209593","https://openalex.org/W2065984263","https://openalex.org/W2067896914","https://openalex.org/W2068385836","https://openalex.org/W2069403107","https://openalex.org/W2079912001","https://openalex.org/W2100873074","https://openalex.org/W2109756042","https://openalex.org/W2118763747","https://openalex.org/W2153233136","https://openalex.org/W2155747427","https://openalex.org/W2160685811","https://openalex.org/W2162848031","https://openalex.org/W2275427856","https://openalex.org/W2518272248","https://openalex.org/W2537861727","https://openalex.org/W2591222206","https://openalex.org/W2773008388","https://openalex.org/W4245699803","https://openalex.org/W4246182238"],"related_works":["https://openalex.org/W1525093886","https://openalex.org/W2520934858","https://openalex.org/W2990487117","https://openalex.org/W2012882356","https://openalex.org/W2098412892","https://openalex.org/W109635080","https://openalex.org/W4213384165","https://openalex.org/W2377262226","https://openalex.org/W2531534085","https://openalex.org/W4285295794"],"abstract_inverted_index":{"When":[0],"a":[1,13,36,117,137],"diverse":[2],"group":[3],"of":[4,52,74,116],"experts":[5],"share":[6],"their":[7,94],"knowledge":[8],"to":[9,126],"ascertain":[10],"and":[11,49,58,65,110,119,130,142],"solve":[12],"particular":[14],"multiple":[15],"criteria":[16],"decision-making":[17],"(MCDM)":[18],"problem,":[19],"uncertainty":[20,95],"arises":[21],"from":[22],"several":[23],"sources.":[24],"In":[25,85,124],"those":[26],"cases,":[27],"the":[28,47,50,81,106,114],"interval":[29],"multiplicative":[30],"preference":[31],"relation":[32],"(IMPR)":[33],"approach":[34,102],"is":[35,103,122],"useful":[37],"technique":[38],"when":[39],"verifying":[40],"consistency.":[41,99],"As":[42],"illustrated":[43],"in":[44,72],"this":[45,86],"paper,":[46],"validation":[48],"improvement":[51],"consistency":[53],"require":[54],"robust":[55],"analysis":[56],"tools":[57],"algorithms.":[59],"The":[60,100],"proposed":[61],"methodology":[62],"provides":[63],"reliable":[64,118],"consistent":[66,120],"IMPR,":[67],"which":[68],"can":[69],"be":[70],"quantified":[71],"terms":[73],"row":[75],"geometric":[76],"mean":[77],"method":[78,83],"(RGMM)":[79],"or":[80],"eigenvalue":[82],"(EM).":[84],"manner,":[87],"decision":[88],"makers\u2019":[89],"choices":[90],"are":[91,140],"implicitly":[92],"including":[93],"while":[96],"maintaining":[97],"acceptable":[98],"present":[101],"based":[104],"on":[105],"Hadamard\u2019s":[107],"dissimilarity":[108],"operator":[109],"through":[111],"an":[112],"algorithm,":[113],"derivation":[115],"IMPR":[121],"synthesized.":[123],"order":[125],"illustrate":[127],"our":[128],"results":[129],"compare":[131],"them":[132],"appropriately":[133],"with":[134],"other":[135],"methodologies,":[136],"few":[138],"examples":[139],"addressed":[141],"solved.":[143]},"counts_by_year":[{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}