{"id":"https://openalex.org/W2888892697","doi":"https://doi.org/10.3233/jifs-18927","title":"The arithmetic of multidimensional Z-number","display_name":"The arithmetic of multidimensional Z-number","publication_year":2018,"publication_date":"2018-08-29","ids":{"openalex":"https://openalex.org/W2888892697","doi":"https://doi.org/10.3233/jifs-18927","mag":"2888892697"},"language":"en","primary_location":{"id":"doi:10.3233/jifs-18927","is_oa":false,"landing_page_url":"https://doi.org/10.3233/jifs-18927","pdf_url":null,"source":{"id":"https://openalex.org/S179157397","display_name":"Journal of Intelligent & Fuzzy Systems","issn_l":"1064-1246","issn":["1064-1246","1875-8967"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310318577","host_organization_name":"IOS Press","host_organization_lineage":["https://openalex.org/P4310318577"],"host_organization_lineage_names":["IOS Press"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Intelligent &amp; 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/A5001917021","display_name":"Kai-wen Shen","orcid":"https://orcid.org/0000-0002-1767-1391"},"institutions":[{"id":"https://openalex.org/I139660479","display_name":"Central South University","ror":"https://ror.org/00f1zfq44","country_code":"CN","type":"education","lineage":["https://openalex.org/I139660479"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Kai-Wen Shen","raw_affiliation_strings":["School of Business, Central South University, Changsha, China"],"affiliations":[{"raw_affiliation_string":"School of Business, Central South University, Changsha, China","institution_ids":["https://openalex.org/I139660479"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100436355","display_name":"Jian\u2010qiang Wang","orcid":"https://orcid.org/0000-0001-7668-4881"},"institutions":[{"id":"https://openalex.org/I139660479","display_name":"Central South University","ror":"https://ror.org/00f1zfq44","country_code":"CN","type":"education","lineage":["https://openalex.org/I139660479"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Jian-Qiang Wang","raw_affiliation_strings":["School of Business, Central South University, Changsha, China"],"affiliations":[{"raw_affiliation_string":"School of Business, Central South University, Changsha, China","institution_ids":["https://openalex.org/I139660479"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5032246216","display_name":"Tieli Wang","orcid":null},"institutions":[{"id":"https://openalex.org/I91935597","display_name":"University of South China","ror":"https://ror.org/03mqfn238","country_code":"CN","type":"education","lineage":["https://openalex.org/I91935597"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Tie-Li Wang","raw_affiliation_strings":["Management School, University of South China, Hengyang, PR China","E-mail:","Fax: +86 7318710006"],"affiliations":[{"raw_affiliation_string":"Management School, University of South China, Hengyang, PR China","institution_ids":["https://openalex.org/I91935597"]},{"raw_affiliation_string":"E-mail:","institution_ids":[]},{"raw_affiliation_string":"Fax: +86 7318710006","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5100436355"],"corresponding_institution_ids":["https://openalex.org/I139660479"],"apc_list":null,"apc_paid":null,"fwci":1.9057,"has_fulltext":false,"cited_by_count":24,"citation_normalized_percentile":{"value":0.87083773,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"36","issue":"2","first_page":"1647","last_page":"1661"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10050","display_name":"Multi-Criteria Decision Making","score":0.998199999332428,"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":0.998199999332428,"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/T11357","display_name":"Risk and Safety Analysis","score":0.9940999746322632,"subfield":{"id":"https://openalex.org/subfields/1804","display_name":"Statistics, Probability and Uncertainty"},"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/T10928","display_name":"Probabilistic and Robust Engineering Design","score":0.9771000146865845,"subfield":{"id":"https://openalex.org/subfields/1804","display_name":"Statistics, Probability and Uncertainty"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/reliability","display_name":"Reliability (semiconductor)","score":0.6557660102844238},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.6525164842605591},{"id":"https://openalex.org/keywords/representation","display_name":"Representation (politics)","score":0.6047892570495605},{"id":"https://openalex.org/keywords/measure","display_name":"Measure (data warehouse)","score":0.5768448710441589},{"id":"https://openalex.org/keywords/series","display_name":"Series (stratigraphy)","score":0.5294054746627808},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.4958055913448334},{"id":"https://openalex.org/keywords/multidimensional-analysis","display_name":"Multidimensional analysis","score":0.45292770862579346},{"id":"https://openalex.org/keywords/multidimensional-data","display_name":"Multidimensional data","score":0.4312096834182739},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3905153274536133},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.37763166427612305},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3477633595466614},{"id":"https://openalex.org/keywords/data-mining","display_name":"Data mining","score":0.3181449770927429},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.14325934648513794}],"concepts":[{"id":"https://openalex.org/C43214815","wikidata":"https://www.wikidata.org/wiki/Q7310987","display_name":"Reliability (semiconductor)","level":3,"score":0.6557660102844238},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6525164842605591},{"id":"https://openalex.org/C2776359362","wikidata":"https://www.wikidata.org/wiki/Q2145286","display_name":"Representation (politics)","level":3,"score":0.6047892570495605},{"id":"https://openalex.org/C2780009758","wikidata":"https://www.wikidata.org/wiki/Q6804172","display_name":"Measure (data warehouse)","level":2,"score":0.5768448710441589},{"id":"https://openalex.org/C143724316","wikidata":"https://www.wikidata.org/wiki/Q312468","display_name":"Series (stratigraphy)","level":2,"score":0.5294054746627808},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.4958055913448334},{"id":"https://openalex.org/C169191187","wikidata":"https://www.wikidata.org/wiki/Q1418353","display_name":"Multidimensional analysis","level":2,"score":0.45292770862579346},{"id":"https://openalex.org/C3019022308","wikidata":"https://www.wikidata.org/wiki/Q1418353","display_name":"Multidimensional data","level":2,"score":0.4312096834182739},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3905153274536133},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.37763166427612305},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3477633595466614},{"id":"https://openalex.org/C124101348","wikidata":"https://www.wikidata.org/wiki/Q172491","display_name":"Data mining","level":1,"score":0.3181449770927429},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.14325934648513794},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","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/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C163258240","wikidata":"https://www.wikidata.org/wiki/Q25342","display_name":"Power (physics)","level":2,"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/C151730666","wikidata":"https://www.wikidata.org/wiki/Q7205","display_name":"Paleontology","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/C94625758","wikidata":"https://www.wikidata.org/wiki/Q7163","display_name":"Politics","level":2,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.3233/jifs-18927","is_oa":false,"landing_page_url":"https://doi.org/10.3233/jifs-18927","pdf_url":null,"source":{"id":"https://openalex.org/S179157397","display_name":"Journal of Intelligent & Fuzzy Systems","issn_l":"1064-1246","issn":["1064-1246","1875-8967"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310318577","host_organization_name":"IOS Press","host_organization_lineage":["https://openalex.org/P4310318577"],"host_organization_lineage_names":["IOS Press"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Intelligent &amp; Fuzzy Systems","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":46,"referenced_works":["https://openalex.org/W1505344996","https://openalex.org/W1552255123","https://openalex.org/W1915503570","https://openalex.org/W1969482876","https://openalex.org/W1980564456","https://openalex.org/W1997952930","https://openalex.org/W2026832772","https://openalex.org/W2038190934","https://openalex.org/W2042774699","https://openalex.org/W2049102614","https://openalex.org/W2080561531","https://openalex.org/W2080986991","https://openalex.org/W2085154346","https://openalex.org/W2116365436","https://openalex.org/W2122361993","https://openalex.org/W2153972126","https://openalex.org/W2198113157","https://openalex.org/W2282407434","https://openalex.org/W2317916567","https://openalex.org/W2340270372","https://openalex.org/W2476464628","https://openalex.org/W2485144656","https://openalex.org/W2509038672","https://openalex.org/W2521399310","https://openalex.org/W2525252824","https://openalex.org/W2534926100","https://openalex.org/W2537989414","https://openalex.org/W2576544140","https://openalex.org/W2586751834","https://openalex.org/W2587051469","https://openalex.org/W2594053547","https://openalex.org/W2625829080","https://openalex.org/W2744102091","https://openalex.org/W2747719191","https://openalex.org/W2752921537","https://openalex.org/W2755209665","https://openalex.org/W2756214476","https://openalex.org/W2766466462","https://openalex.org/W2774553171","https://openalex.org/W2790775326","https://openalex.org/W2794273717","https://openalex.org/W2803062135","https://openalex.org/W2902274251","https://openalex.org/W4211007335","https://openalex.org/W4292158025","https://openalex.org/W6699821906"],"related_works":["https://openalex.org/W1585485335","https://openalex.org/W1544010218","https://openalex.org/W2106202144","https://openalex.org/W2367886317","https://openalex.org/W1641902366","https://openalex.org/W4299279426","https://openalex.org/W1852954565","https://openalex.org/W2997472482","https://openalex.org/W2383972685","https://openalex.org/W2354452279"],"abstract_inverted_index":{"The":[0,107],"Z-number":[1,25],"has":[2],"become":[3],"a":[4,103,116],"new":[5],"representation":[6],"of":[7,11,54,70,96,109,118],"evaluation":[8],"information":[9,55],"because":[10,42],"its":[12],"superiority":[13],"in":[14],"describing":[15],"reliability":[16],"measure.":[17],"Current":[18],"studies":[19],"focuses":[20],"mainly":[21],"on":[22,34],"the":[23,68,71,93,97,110],"unidimensional":[24],"like":[26],"Z":[27],"=":[28],"(about":[29],"25":[30,80],"min,":[31],"usually).":[32],"Studies":[33],"multidimensional":[35,72,98],"cases":[36],"have":[37],"not":[38],"been":[39],"reported.":[40],"However,":[41],"people":[43],"often":[44],"describe":[45,57],"things":[46],"from":[47],"various":[48],"aspects,":[49],"using":[50],"only":[51],"one":[52],"aspect":[53],"to":[56,83],"uncertain":[58],"events":[59],"fully":[60],"is":[61,113],"difficult.":[62],"In":[63],"this":[64,88],"paper,":[65],"we":[66,90],"propose":[67,102],"concept":[69],"Z-number,":[73],"such":[74],"as":[75],"((about":[76],"20":[77],"miles,":[78],"about":[79],"min),":[81],"usually)":[82],"handle":[84],"complex":[85],"information.":[86],"For":[87],"purpose,":[89],"first":[91],"define":[92],"basic":[94],"operations":[95],"Z-number.":[99],"We":[100],"then":[101],"feasible":[104],"comparison":[105],"method.":[106],"effectiveness":[108],"proposed":[111],"method":[112],"demonstrated":[114],"by":[115],"series":[117],"numerical":[119],"examples.":[120]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":4},{"year":2023,"cited_by_count":5},{"year":2022,"cited_by_count":4},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":4},{"year":2019,"cited_by_count":4}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
