{"id":"https://openalex.org/W2790405367","doi":"https://doi.org/10.1002/int.21973","title":"Interval-valued Pythagorean fuzzy extended Bonferroni mean for dealing with heterogenous relationship among attributes","display_name":"Interval-valued Pythagorean fuzzy extended Bonferroni mean for dealing with heterogenous relationship among attributes","publication_year":2018,"publication_date":"2018-03-23","ids":{"openalex":"https://openalex.org/W2790405367","doi":"https://doi.org/10.1002/int.21973","mag":"2790405367"},"language":"en","primary_location":{"id":"doi:10.1002/int.21973","doi":"https://doi.org/10.1002/int.21973","is_oa":true,"landing_page_url":"https://doi.org/10.1002/int.21973","pdf_url":"https://onlinelibrary.wiley.com/doi/pdfdirect/10.1002/int.21973","source":{"id":"https://openalex.org/S57950554","display_name":"International Journal of Intelligent Systems","issn_l":"0884-8173","issn":["0884-8173","1098-111X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-scientific","ccf-c","cwts-core","dongbi-c","jufo-1","norway-1","poland-100","russia-white-list-1"],"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Intelligent Systems","raw_type":"journal-article"},"volume":null,"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"bronze","oa_url":"https://onlinelibrary.wiley.com/doi/pdfdirect/10.1002/int.21973","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5088064886","display_name":"Decui Liang","orcid":"https://orcid.org/0000-0002-0655-1255","observed_orcids":["https://orcid.org/0000-0002-0655-1255"]},"institutions":[{"id":"https://openalex.org/I150229711","display_name":"University of Electronic Science and Technology of China","ror":"https://ror.org/04qr3zq92","country_code":"CN","type":"education","lineage":["https://openalex.org/I150229711"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Decui Liang","raw_affiliation_strings":["School of Management and Economics; University of Electronic Science and Technology of China; Chengdu 610054 People's Republic of China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Management and Economics; University of Electronic Science and Technology of China; Chengdu 610054 People's Republic of China","institution_ids":["https://openalex.org/I150229711"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5047319327","display_name":"Adjei Peter Darko","orcid":"https://orcid.org/0000-0003-1621-4209","observed_orcids":["https://orcid.org/0000-0003-1621-4209"]},"institutions":[{"id":"https://openalex.org/I150229711","display_name":"University of Electronic Science and Technology of China","ror":"https://ror.org/04qr3zq92","country_code":"CN","type":"education","lineage":["https://openalex.org/I150229711"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Adjei Peter Darko","raw_affiliation_strings":["School of Management and Economics; University of Electronic Science and Technology of China; Chengdu 610054 People's Republic of China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Management and Economics; University of Electronic Science and Technology of China; Chengdu 610054 People's Republic of China","institution_ids":["https://openalex.org/I150229711"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100437308","display_name":"Zeshui Xu","orcid":"https://orcid.org/0000-0003-3547-2908","observed_orcids":["https://orcid.org/0000-0003-3547-2908"]},"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":true,"raw_author_name":"Zeshui Xu","raw_affiliation_strings":["Business School, Sichuan University, Chengdu, Sichuan, 610065 People's Republic of China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Business School, Sichuan University, Chengdu, Sichuan, 610065 People's Republic of China","institution_ids":["https://openalex.org/I24185976"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5100437308"],"corresponding_institution_ids":["https://openalex.org/I24185976"],"apc_list":{"value":2700,"currency":"USD","value_usd":2700},"apc_paid":null,"fwci":5.7704,"has_fulltext":true,"cited_by_count":41,"citation_normalized_percentile":{"value":0.96077415,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":93,"max":99},"biblio":{"volume":"33","issue":"7","first_page":"1381","last_page":"1411"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10050","display_name":"Multi-Criteria Decision Making","score":0.9970999956130981,"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":0.9970999956130981,"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/T11671","display_name":"Fuzzy and Soft Set Theory","score":0.00139999995008111,"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":0.00019999999494757503,"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/interval-valued-pythagorean-fuzzy-sets","display_name":"interval-valued Pythagorean fuzzy sets","score":1.0},{"id":"https://openalex.org/keywords/aggregation-operators","display_name":"aggregation operators","score":0.7599999904632568},{"id":"https://openalex.org/keywords/multiple-attribute-decision-making","display_name":"multiple attribute decision making","score":0.925000011920929},{"id":"https://openalex.org/keywords/weighted-aggregation-operators","display_name":"weighted aggregation operators","score":0.621999979019165}],"concepts":[{"id":"https://openalex.org/C100461760","wikidata":"https://www.wikidata.org/wiki/Q11518","display_name":"Pythagorean theorem","level":2,"score":0.8362084627151489},{"id":"https://openalex.org/C2778067643","wikidata":"https://www.wikidata.org/wiki/Q166507","display_name":"Interval (graph theory)","level":2,"score":0.6111811995506287},{"id":"https://openalex.org/C127808970","wikidata":"https://www.wikidata.org/wiki/Q385989","display_name":"Bonferroni correction","level":2,"score":0.5976007580757141},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5625407695770264},{"id":"https://openalex.org/C42011625","wikidata":"https://www.wikidata.org/wiki/Q1055058","display_name":"Fuzzy set","level":3,"score":0.524994969367981},{"id":"https://openalex.org/C58166","wikidata":"https://www.wikidata.org/wiki/Q224821","display_name":"Fuzzy logic","level":2,"score":0.5082711577415466},{"id":"https://openalex.org/C42812","wikidata":"https://www.wikidata.org/wiki/Q1082910","display_name":"Partition (number theory)","level":2,"score":0.49806642532348633},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.46202075481414795},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.39449799060821533},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.3377223014831543},{"id":"https://openalex.org/C124101348","wikidata":"https://www.wikidata.org/wiki/Q172491","display_name":"Data mining","level":1,"score":0.3290509879589081},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.21701830625534058},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.12837105989456177},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"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/C158448853","wikidata":"https://www.wikidata.org/wiki/Q425218","display_name":"Repressor","level":4,"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/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C86339819","wikidata":"https://www.wikidata.org/wiki/Q407384","display_name":"Transcription factor","level":3,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1002/int.21973","doi":"https://doi.org/10.1002/int.21973","is_oa":true,"landing_page_url":"https://doi.org/10.1002/int.21973","pdf_url":"https://onlinelibrary.wiley.com/doi/pdfdirect/10.1002/int.21973","source":{"id":"https://openalex.org/S57950554","display_name":"International Journal of Intelligent Systems","issn_l":"0884-8173","issn":["0884-8173","1098-111X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-scientific","ccf-c","cwts-core","dongbi-c","jufo-1","norway-1","poland-100","russia-white-list-1"],"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Intelligent Systems","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.1002/int.21973","doi":"https://doi.org/10.1002/int.21973","is_oa":true,"landing_page_url":"https://doi.org/10.1002/int.21973","pdf_url":"https://onlinelibrary.wiley.com/doi/pdfdirect/10.1002/int.21973","source":{"id":"https://openalex.org/S57950554","display_name":"International Journal of Intelligent Systems","issn_l":"0884-8173","issn":["0884-8173","1098-111X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-scientific","ccf-c","cwts-core","dongbi-c","jufo-1","norway-1","poland-100","russia-white-list-1"],"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Intelligent Systems","raw_type":"journal-article"},"sustainable_development_goals":[],"sustainable_development_goals_aurora":[],"study_designs":[],"awards":[{"id":"https://openalex.org/G176656473","display_name":"\u57fa\u4e8e\u51b3\u7b56\u7c97\u7cd9\u96c6\u7684\u6a21\u7cca\u591a\u5206\u7c7b\u4e09\u652f\u51b3\u7b56\u65b9\u6cd5\u4e0e\u5e94\u7528\u7814\u7a76","funder_award_id":"71571148","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G1825022960","display_name":null,"funder_award_id":"71432003","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G2726983198","display_name":null,"funder_award_id":"SC15C009","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G3155004010","display_name":null,"funder_award_id":"71432003","funder_id":"https://openalex.org/F4320335787","funder_display_name":"Fundamental Research Funds for the Central Universities"},{"id":"https://openalex.org/G3377703749","display_name":null,"funder_award_id":"71571148","funder_id":"https://openalex.org/F4320335787","funder_display_name":"Fundamental Research Funds for the Central Universities"},{"id":"https://openalex.org/G4268637735","display_name":null,"funder_award_id":"71401026","funder_id":"https://openalex.org/F4320335787","funder_display_name":"Fundamental Research Funds for the Central Universities"},{"id":"https://openalex.org/G5139483164","display_name":null,"funder_award_id":"ZYGX2014J100","funder_id":"https://openalex.org/F4320335787","funder_display_name":"Fundamental Research Funds for the Central Universities"},{"id":"https://openalex.org/G6750187272","display_name":"\u7fa4\u51b3\u7b56\u4e0b\u6a21\u7cca\u51b3\u7b56\u7c97\u7cd9\u96c6\u7684\u51b2\u7a81\u5206\u6790\u53ca\u5176\u5e94\u7528\u65b9\u6cd5\u7814\u7a76","funder_award_id":"71401026","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G861659355","display_name":null,"funder_award_id":"ZYGX2014J100","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320329878","display_name":"Central University Basic Research Fund of China","ror":null},{"id":"https://openalex.org/F4320335787","display_name":"Fundamental Research Funds for the Central Universities","ror":null}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2790405367.pdf","grobid_xml":"https://content.openalex.org/works/W2790405367.grobid-xml"},"referenced_works_count":41,"referenced_works":["https://openalex.org/W1427155388","https://openalex.org/W1536418809","https://openalex.org/W1668569279","https://openalex.org/W1765570948","https://openalex.org/W1829951598","https://openalex.org/W1929809731","https://openalex.org/W1967753042","https://openalex.org/W1969352744","https://openalex.org/W1970781361","https://openalex.org/W1980564456","https://openalex.org/W1989995659","https://openalex.org/W1998274657","https://openalex.org/W2006285333","https://openalex.org/W2007538282","https://openalex.org/W2013908206","https://openalex.org/W2013932252","https://openalex.org/W2040765468","https://openalex.org/W2040832520","https://openalex.org/W2050868309","https://openalex.org/W2058024711","https://openalex.org/W2065752753","https://openalex.org/W2074605814","https://openalex.org/W2079457935","https://openalex.org/W2093497681","https://openalex.org/W2104077967","https://openalex.org/W2153047559","https://openalex.org/W2289047752","https://openalex.org/W2292359941","https://openalex.org/W2311142332","https://openalex.org/W2343846868","https://openalex.org/W2344746133","https://openalex.org/W2345848912","https://openalex.org/W2412590235","https://openalex.org/W2418398260","https://openalex.org/W2462459838","https://openalex.org/W2528059267","https://openalex.org/W2530680027","https://openalex.org/W2593418740","https://openalex.org/W2604920622","https://openalex.org/W2806626872","https://openalex.org/W4211007335"],"related_works":["https://openalex.org/W2806626872","https://openalex.org/W2773604414","https://openalex.org/W2739534728","https://openalex.org/W2988347501","https://openalex.org/W2593183563","https://openalex.org/W2800049629","https://openalex.org/W4385150387","https://openalex.org/W2899516004","https://openalex.org/W2773133168","https://openalex.org/W2913509214"],"abstract_inverted_index":{"Owing":[0],"to":[1,12,44,56],"the":[2,25,29,53,58,63,71,77,81,84,127,146,160],"information":[3],"insufficiency,":[4],"it":[5],"might":[6],"be":[7],"difficult":[8],"for":[9,41,134],"decision":[10,42,137],"makers":[11,43],"precisely":[13],"evaluate":[14,45],"their":[15,46,115],"assessments":[16,47],"in":[17],"real":[18],"decision-making.":[19],"As":[20],"a":[21,142],"new":[22,92],"extension":[23],"of":[24,74,114,145,162],"Pythagorean":[26,31,86,97,105],"fuzzy":[27,32,87,98,106],"sets,":[28],"interval-valued":[30,85,96,104],"sets":[33],"(IVPFSs)":[34],"can":[35],"availably":[36],"provide":[37],"enough":[38],"input":[39],"space":[40],"with":[48,139],"interval":[49],"numbers.":[50],"By":[51],"extending":[52],"Bonferroni":[54,65,100,108],"mean":[55,66,101,109],"model":[57],"heterogeneous":[59],"interrelationship":[60],"among":[61,76],"attributes,":[62,78],"extended":[64,99,107],"(EBM)":[67],"was":[68],"examined.":[69],"Considering":[70],"partition":[72],"structure":[73],"relationship":[75],"we":[79,130],"introduce":[80],"EBM":[82],"into":[83],"environment":[88],"and":[89,102,118],"develop":[90],"two":[91],"aggregation":[93],"operators,":[94],"namely,":[95],"weighted":[103],"(WIVPFEBM)":[110],"operators.":[111],"Meanwhile,":[112],"some":[113],"special":[116],"cases":[117],"properties":[119],"are":[120],"also":[121],"deeply":[122],"discussed.":[123],"Subsequently,":[124],"by":[125,153],"employing":[126],"WIVPFEBM":[128],"operator,":[129],"propose":[131],"an":[132],"approach":[133],"multiple":[135],"attribute":[136],"making":[138],"IVPFSs.":[140],"Finally,":[141],"practical":[143],"illustration":[144],"E-commerce":[147],"project":[148],"selection":[149],"problem":[150],"is":[151],"investigated":[152],"our":[154,163],"proposed":[155],"method,":[156],"which":[157],"successfully":[158],"demonstrates":[159],"applicability":[161],"results.":[164]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":6},{"year":2021,"cited_by_count":5},{"year":2020,"cited_by_count":4},{"year":2019,"cited_by_count":13},{"year":2018,"cited_by_count":7}],"updated_date":"2026-10-30T12:39:25.321706","created_date":"2018-03-29T00:00:00"}