{"id":"https://openalex.org/W2110447423","doi":"https://doi.org/10.1142/s0219622011004701","title":"SOME ISSUES ON MULTIPLICATIVE CONSISTENCY OF INTERVAL RECIPROCAL RELATIONS","display_name":"SOME ISSUES ON MULTIPLICATIVE CONSISTENCY OF INTERVAL RECIPROCAL RELATIONS","publication_year":2011,"publication_date":"2011-11-01","ids":{"openalex":"https://openalex.org/W2110447423","doi":"https://doi.org/10.1142/s0219622011004701","mag":"2110447423"},"language":"en","primary_location":{"id":"doi:10.1142/s0219622011004701","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0219622011004701","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 &amp; 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/A5065704094","display_name":"Meimei Xia","orcid":"https://orcid.org/0000-0002-8342-9317"},"institutions":[{"id":"https://openalex.org/I76569877","display_name":"Southeast University","ror":"https://ror.org/04ct4d772","country_code":"CN","type":"education","lineage":["https://openalex.org/I76569877"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"MEIMEI XIA","raw_affiliation_strings":["School of Economics and Management, Southeast University, Nanjing, Jiangsu 211189, P. R. China"],"affiliations":[{"raw_affiliation_string":"School of Economics and Management, Southeast University, Nanjing, Jiangsu 211189, P. R. China","institution_ids":["https://openalex.org/I76569877"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100437308","display_name":"Zeshui Xu","orcid":"https://orcid.org/0000-0003-3547-2908"},"institutions":[{"id":"https://openalex.org/I76569877","display_name":"Southeast University","ror":"https://ror.org/04ct4d772","country_code":"CN","type":"education","lineage":["https://openalex.org/I76569877"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"ZESHUI XU","raw_affiliation_strings":["School of Economics and Management, Southeast University, Nanjing, Jiangsu 211189, P. R. China"],"affiliations":[{"raw_affiliation_string":"School of Economics and Management, Southeast University, Nanjing, Jiangsu 211189, P. R. China","institution_ids":["https://openalex.org/I76569877"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5065704094"],"corresponding_institution_ids":["https://openalex.org/I76569877"],"apc_list":null,"apc_paid":null,"fwci":4.9167,"has_fulltext":false,"cited_by_count":29,"citation_normalized_percentile":{"value":0.951155,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"10","issue":"06","first_page":"1043","last_page":"1065"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10050","display_name":"Multi-Criteria Decision Making","score":0.9987999796867371,"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":0.9987999796867371,"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":0.9944999814033508,"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/T13832","display_name":"Advanced Decision-Making Techniques","score":0.9865999817848206,"subfield":{"id":"https://openalex.org/subfields/1710","display_name":"Information Systems"},"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/reciprocal","display_name":"Reciprocal","score":0.9249060750007629},{"id":"https://openalex.org/keywords/multiplicative-function","display_name":"Multiplicative function","score":0.8213788866996765},{"id":"https://openalex.org/keywords/relation","display_name":"Relation (database)","score":0.7309593558311462},{"id":"https://openalex.org/keywords/interval","display_name":"Interval (graph theory)","score":0.7266550064086914},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6943425536155701},{"id":"https://openalex.org/keywords/preference-relation","display_name":"Preference relation","score":0.6385605931282043},{"id":"https://openalex.org/keywords/consistency","display_name":"Consistency (knowledge bases)","score":0.5873494148254395},{"id":"https://openalex.org/keywords/multiplicative-inverse","display_name":"Multiplicative inverse","score":0.5266295075416565},{"id":"https://openalex.org/keywords/preference","display_name":"Preference","score":0.46465104818344116},{"id":"https://openalex.org/keywords/mathematical-economics","display_name":"Mathematical economics","score":0.3242506980895996},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.30156993865966797},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.2222796082496643},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.19688591361045837},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.1708901822566986},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.10193207859992981},{"id":"https://openalex.org/keywords/inverse","display_name":"Inverse","score":0.07971504330635071},{"id":"https://openalex.org/keywords/data-mining","display_name":"Data mining","score":0.07022556662559509}],"concepts":[{"id":"https://openalex.org/C2777742833","wikidata":"https://www.wikidata.org/wiki/Q1964083","display_name":"Reciprocal","level":2,"score":0.9249060750007629},{"id":"https://openalex.org/C42747912","wikidata":"https://www.wikidata.org/wiki/Q1048447","display_name":"Multiplicative function","level":2,"score":0.8213788866996765},{"id":"https://openalex.org/C25343380","wikidata":"https://www.wikidata.org/wiki/Q277521","display_name":"Relation (database)","level":2,"score":0.7309593558311462},{"id":"https://openalex.org/C2778067643","wikidata":"https://www.wikidata.org/wiki/Q166507","display_name":"Interval (graph theory)","level":2,"score":0.7266550064086914},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6943425536155701},{"id":"https://openalex.org/C2777062324","wikidata":"https://www.wikidata.org/wiki/Q25036211","display_name":"Preference relation","level":3,"score":0.6385605931282043},{"id":"https://openalex.org/C2776436953","wikidata":"https://www.wikidata.org/wiki/Q5163215","display_name":"Consistency (knowledge bases)","level":2,"score":0.5873494148254395},{"id":"https://openalex.org/C157351203","wikidata":"https://www.wikidata.org/wiki/Q216906","display_name":"Multiplicative inverse","level":3,"score":0.5266295075416565},{"id":"https://openalex.org/C2781249084","wikidata":"https://www.wikidata.org/wiki/Q908656","display_name":"Preference","level":2,"score":0.46465104818344116},{"id":"https://openalex.org/C144237770","wikidata":"https://www.wikidata.org/wiki/Q747534","display_name":"Mathematical economics","level":1,"score":0.3242506980895996},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.30156993865966797},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2222796082496643},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.19688591361045837},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.1708901822566986},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.10193207859992981},{"id":"https://openalex.org/C207467116","wikidata":"https://www.wikidata.org/wiki/Q4385666","display_name":"Inverse","level":2,"score":0.07971504330635071},{"id":"https://openalex.org/C124101348","wikidata":"https://www.wikidata.org/wiki/Q172491","display_name":"Data mining","level":1,"score":0.07022556662559509},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"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/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1142/s0219622011004701","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0219622011004701","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 &amp; Decision Making","raw_type":"journal-article"},{"id":"pmh:oai:RePEc:wsi:ijitdm:v:10:y:2011:i:06:n:s0219622011004701","is_oa":false,"landing_page_url":"http://www.worldscientific.com/doi/abs/10.1142/S0219622011004701","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":[{"score":0.7699999809265137,"display_name":"Peace, Justice and strong institutions","id":"https://metadata.un.org/sdg/16"}],"awards":[],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320335769","display_name":"Graduate Research and Innovation Projects of Jiangsu Province","ror":null},{"id":"https://openalex.org/F4320336125","display_name":"National Science Fund for Distinguished Young Scholars","ror":null}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":57,"referenced_works":["https://openalex.org/W128876804","https://openalex.org/W138055454","https://openalex.org/W166751945","https://openalex.org/W194786220","https://openalex.org/W1541230581","https://openalex.org/W1546067212","https://openalex.org/W1564285798","https://openalex.org/W1606108510","https://openalex.org/W1967350113","https://openalex.org/W1967631404","https://openalex.org/W1968642553","https://openalex.org/W1969786369","https://openalex.org/W1979733078","https://openalex.org/W1993277820","https://openalex.org/W1993472498","https://openalex.org/W1995038982","https://openalex.org/W1995906594","https://openalex.org/W1997713472","https://openalex.org/W1998661617","https://openalex.org/W2003579441","https://openalex.org/W2003684370","https://openalex.org/W2004421467","https://openalex.org/W2019484595","https://openalex.org/W2022373133","https://openalex.org/W2024224018","https://openalex.org/W2025447782","https://openalex.org/W2028881626","https://openalex.org/W2033447266","https://openalex.org/W2044568429","https://openalex.org/W2050203067","https://openalex.org/W2052087572","https://openalex.org/W2057791961","https://openalex.org/W2084612136","https://openalex.org/W2087713365","https://openalex.org/W2089336319","https://openalex.org/W2091943101","https://openalex.org/W2094559091","https://openalex.org/W2107698705","https://openalex.org/W2113532413","https://openalex.org/W2115951219","https://openalex.org/W2116080612","https://openalex.org/W2118078791","https://openalex.org/W2118763747","https://openalex.org/W2134690501","https://openalex.org/W2137624040","https://openalex.org/W2145906330","https://openalex.org/W2150546380","https://openalex.org/W2163481099","https://openalex.org/W2168936936","https://openalex.org/W2923916621","https://openalex.org/W3142850553","https://openalex.org/W4210259099","https://openalex.org/W4239177862","https://openalex.org/W4242486132","https://openalex.org/W4248841288","https://openalex.org/W4252626958","https://openalex.org/W4285719527"],"related_works":["https://openalex.org/W2023689789","https://openalex.org/W2904696227","https://openalex.org/W1595663582","https://openalex.org/W2055647634","https://openalex.org/W2554624503","https://openalex.org/W1995862218","https://openalex.org/W256110547","https://openalex.org/W2110447423","https://openalex.org/W2360538742","https://openalex.org/W2156665634"],"abstract_inverted_index":{"Consistency":[0],"plays":[1],"an":[2,79],"important":[3],"part":[4],"in":[5],"decision":[6],"making":[7],"with":[8,109],"interval":[9,14,29,53,66,81,96],"reciprocal":[10,30,47,54,67,82,97],"relation":[11,31,68],"also":[12,102],"called":[13],"fuzzy":[15],"preference":[16],"relation.":[17,55,83],"In":[18],"this":[19],"paper,":[20],"we":[21,57],"give":[22],"the":[23,62,70,75,106,110],"definition":[24],"of":[25,44],"perfect":[26,51,63,93],"multiplicative":[27,45,64,94],"consistent":[28,46,52,65,95],"and":[32,73],"discuss":[33],"its":[34],"properties.":[35],"A":[36],"method":[37,88],"is":[38,89],"proposed":[39,90,107],"to":[40,60,104],"construct":[41],"a":[42,50,85],"set":[43],"relations":[48],"from":[49,69,78],"Then":[56],"develop":[58],"methods":[59,108],"get":[61],"inconsistent":[71],"one":[72],"estimate":[74],"missing":[76],"values":[77],"incomplete":[80],"Finally,":[84],"group":[86],"decision-making":[87],"based":[91],"on":[92],"relations.":[98],"Some":[99],"examples":[100],"are":[101],"given":[103],"compare":[105],"existing":[111],"ones.":[112]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":3},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":2},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":5},{"year":2013,"cited_by_count":5},{"year":2012,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
