{"id":"https://openalex.org/W4308611984","doi":"https://doi.org/10.1007/s44196-022-00152-y","title":"Pythagorean Fuzzy Bonferroni Mean with Weighted Interaction Operator and Its Application in Fusion of Online Multidimensional Ratings","display_name":"Pythagorean Fuzzy Bonferroni Mean with Weighted Interaction Operator and Its Application in Fusion of Online Multidimensional Ratings","publication_year":2022,"publication_date":"2022-11-09","ids":{"openalex":"https://openalex.org/W4308611984","doi":"https://doi.org/10.1007/s44196-022-00152-y"},"language":"en","primary_location":{"id":"doi:10.1007/s44196-022-00152-y","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s44196-022-00152-y","pdf_url":"https://link.springer.com/content/pdf/10.1007/s44196-022-00152-y.pdf","source":{"id":"https://openalex.org/S190680769","display_name":"International Journal of Computational Intelligence Systems","issn_l":"1875-6883","issn":["1875-6883","1875-6891"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319965","host_organization_name":"Springer Nature","host_organization_lineage":["https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Computational Intelligence Systems","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://link.springer.com/content/pdf/10.1007/s44196-022-00152-y.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5055250816","display_name":"Yi Yang","orcid":"https://orcid.org/0000-0002-7062-9221"},"institutions":[{"id":"https://openalex.org/I49934816","display_name":"Hunan University of Technology","ror":"https://ror.org/04j3vr751","country_code":"CN","type":"education","lineage":["https://openalex.org/I49934816"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Yi Yang","raw_affiliation_strings":["School of Advanced Interdisciplinary Studies, Hunan University of Technology and Business, No. 569, Yuelu Avenue, Changsha, 410205, China","School of Digital Media and Humanities, Hunan University of Technology and Business, No. 569, Yuelu Avenue, Changsha, 410205, China","The Key Research Bases of Philosophy and Social Sciences of General Colleges and Universities in Hunan Province, Center for Big Data Intelligence of Smart Society Research, No. 569, Yuelu Avenue, Changsha, 410205, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Advanced Interdisciplinary Studies, Hunan University of Technology and Business, No. 569, Yuelu Avenue, Changsha, 410205, China","institution_ids":["https://openalex.org/I49934816"]},{"raw_affiliation_string":"School of Digital Media and Humanities, Hunan University of Technology and Business, No. 569, Yuelu Avenue, Changsha, 410205, China","institution_ids":["https://openalex.org/I49934816"]},{"raw_affiliation_string":"The Key Research Bases of Philosophy and Social Sciences of General Colleges and Universities in Hunan Province, Center for Big Data Intelligence of Smart Society Research, No. 569, Yuelu Avenue, Changsha, 410205, China","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5102310615","display_name":"Feifan Yang","orcid":"https://orcid.org/0000-0002-9925-2536"},"institutions":[{"id":"https://openalex.org/I49934816","display_name":"Hunan University of Technology","ror":"https://ror.org/04j3vr751","country_code":"CN","type":"education","lineage":["https://openalex.org/I49934816"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Feifan Yang","raw_affiliation_strings":["School of Advanced Interdisciplinary Studies, Hunan University of Technology and Business, No. 569, Yuelu Avenue, Changsha, 410205, China","The Key Research Bases of Philosophy and Social Sciences of General Colleges and Universities in Hunan Province, Center for Big Data Intelligence of Smart Society Research, No. 569, Yuelu Avenue, Changsha, 410205, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Advanced Interdisciplinary Studies, Hunan University of Technology and Business, No. 569, Yuelu Avenue, Changsha, 410205, China","institution_ids":["https://openalex.org/I49934816"]},{"raw_affiliation_string":"The Key Research Bases of Philosophy and Social Sciences of General Colleges and Universities in Hunan Province, Center for Big Data Intelligence of Smart Society Research, No. 569, Yuelu Avenue, Changsha, 410205, China","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100332951","display_name":"Jie Chen","orcid":"https://orcid.org/0000-0002-6937-8090"},"institutions":[{"id":"https://openalex.org/I49934816","display_name":"Hunan University of Technology","ror":"https://ror.org/04j3vr751","country_code":"CN","type":"education","lineage":["https://openalex.org/I49934816"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Jie Chen","raw_affiliation_strings":["School of Advanced Interdisciplinary Studies, Hunan University of Technology and Business, No. 569, Yuelu Avenue, Changsha, 410205, China","The Key Research Bases of Philosophy and Social Sciences of General Colleges and Universities in Hunan Province, Center for Big Data Intelligence of Smart Society Research, No. 569, Yuelu Avenue, Changsha, 410205, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Advanced Interdisciplinary Studies, Hunan University of Technology and Business, No. 569, Yuelu Avenue, Changsha, 410205, China","institution_ids":["https://openalex.org/I49934816"]},{"raw_affiliation_string":"The Key Research Bases of Philosophy and Social Sciences of General Colleges and Universities in Hunan Province, Center for Big Data Intelligence of Smart Society Research, No. 569, Yuelu Avenue, Changsha, 410205, China","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5037235449","display_name":"Yangyan Zeng","orcid":null},"institutions":[{"id":"https://openalex.org/I49934816","display_name":"Hunan University of Technology","ror":"https://ror.org/04j3vr751","country_code":"CN","type":"education","lineage":["https://openalex.org/I49934816"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yangyan Zeng","raw_affiliation_strings":["School of Advanced Interdisciplinary Studies, Hunan University of Technology and Business, No. 569, Yuelu Avenue, Changsha, 410205, China","The Key Research Bases of Philosophy and Social Sciences of General Colleges and Universities in Hunan Province, Center for Big Data Intelligence of Smart Society Research, No. 569, Yuelu Avenue, Changsha, 410205, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Advanced Interdisciplinary Studies, Hunan University of Technology and Business, No. 569, Yuelu Avenue, Changsha, 410205, China","institution_ids":["https://openalex.org/I49934816"]},{"raw_affiliation_string":"The Key Research Bases of Philosophy and Social Sciences of General Colleges and Universities in Hunan Province, Center for Big Data Intelligence of Smart Society Research, No. 569, Yuelu Avenue, Changsha, 410205, China","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100665315","display_name":"Limei Liu","orcid":"https://orcid.org/0009-0008-9973-2100"},"institutions":[{"id":"https://openalex.org/I49934816","display_name":"Hunan University of Technology","ror":"https://ror.org/04j3vr751","country_code":"CN","type":"education","lineage":["https://openalex.org/I49934816"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Limei Liu","raw_affiliation_strings":["School of Advanced Interdisciplinary Studies, Hunan University of Technology and Business, No. 569, Yuelu Avenue, Changsha, 410205, China","The Key Research Bases of Philosophy and Social Sciences of General Colleges and Universities in Hunan Province, Center for Big Data Intelligence of Smart Society Research, No. 569, Yuelu Avenue, Changsha, 410205, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Advanced Interdisciplinary Studies, Hunan University of Technology and Business, No. 569, Yuelu Avenue, Changsha, 410205, China","institution_ids":["https://openalex.org/I49934816"]},{"raw_affiliation_string":"The Key Research Bases of Philosophy and Social Sciences of General Colleges and Universities in Hunan Province, Center for Big Data Intelligence of Smart Society Research, No. 569, Yuelu Avenue, Changsha, 410205, China","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":5,"corresponding_author_ids":["https://openalex.org/A5055250816"],"corresponding_institution_ids":["https://openalex.org/I49934816"],"apc_list":{"value":1390,"currency":"GBP","value_usd":1704},"apc_paid":{"value":1390,"currency":"GBP","value_usd":1704},"fwci":1.3512,"has_fulltext":true,"cited_by_count":8,"citation_normalized_percentile":{"value":0.82499198,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":94,"max":97},"biblio":{"volume":"15","issue":"1","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10050","display_name":"Multi-Criteria Decision Making","score":0.9994000196456909,"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":0.9994000196456909,"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":0.9860000014305115,"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/T13955","display_name":"Evaluation Methods in Various Fields","score":0.9842000007629395,"subfield":{"id":"https://openalex.org/subfields/2302","display_name":"Ecological Modeling"},"field":{"id":"https://openalex.org/fields/23","display_name":"Environmental Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/operator","display_name":"Operator (biology)","score":0.7787092924118042},{"id":"https://openalex.org/keywords/pythagorean-theorem","display_name":"Pythagorean theorem","score":0.7103691697120667},{"id":"https://openalex.org/keywords/ranking","display_name":"Ranking (information retrieval)","score":0.6020083427429199},{"id":"https://openalex.org/keywords/fuzzy-logic","display_name":"Fuzzy logic","score":0.5720159411430359},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5360548496246338},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.48798173666000366},{"id":"https://openalex.org/keywords/data-mining","display_name":"Data mining","score":0.4716833233833313},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4246904253959656},{"id":"https://openalex.org/keywords/machine-learning","display_name":"Machine learning","score":0.3700437545776367}],"concepts":[{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.7787092924118042},{"id":"https://openalex.org/C100461760","wikidata":"https://www.wikidata.org/wiki/Q11518","display_name":"Pythagorean theorem","level":2,"score":0.7103691697120667},{"id":"https://openalex.org/C189430467","wikidata":"https://www.wikidata.org/wiki/Q7293293","display_name":"Ranking (information retrieval)","level":2,"score":0.6020083427429199},{"id":"https://openalex.org/C58166","wikidata":"https://www.wikidata.org/wiki/Q224821","display_name":"Fuzzy logic","level":2,"score":0.5720159411430359},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5360548496246338},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.48798173666000366},{"id":"https://openalex.org/C124101348","wikidata":"https://www.wikidata.org/wiki/Q172491","display_name":"Data mining","level":1,"score":0.4716833233833313},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4246904253959656},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.3700437545776367},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","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/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/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1007/s44196-022-00152-y","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s44196-022-00152-y","pdf_url":"https://link.springer.com/content/pdf/10.1007/s44196-022-00152-y.pdf","source":{"id":"https://openalex.org/S190680769","display_name":"International Journal of Computational Intelligence Systems","issn_l":"1875-6883","issn":["1875-6883","1875-6891"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319965","host_organization_name":"Springer Nature","host_organization_lineage":["https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Computational Intelligence Systems","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:39fd38a9f8824add8d63fc181dbab6ed","is_oa":true,"landing_page_url":"https://doaj.org/article/39fd38a9f8824add8d63fc181dbab6ed","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"International Journal of Computational Intelligence Systems, Vol 15, Iss 1, Pp 1-15 (2022)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.1007/s44196-022-00152-y","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s44196-022-00152-y","pdf_url":"https://link.springer.com/content/pdf/10.1007/s44196-022-00152-y.pdf","source":{"id":"https://openalex.org/S190680769","display_name":"International Journal of Computational Intelligence Systems","issn_l":"1875-6883","issn":["1875-6883","1875-6891"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319965","host_organization_name":"Springer Nature","host_organization_lineage":["https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Computational Intelligence Systems","raw_type":"journal-article"},"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/16","score":0.8100000023841858,"display_name":"Peace, Justice and strong institutions"}],"awards":[{"id":"https://openalex.org/G3339004819","display_name":null,"funder_award_id":"72201097","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G6483441127","display_name":null,"funder_award_id":"20YJCZH210","funder_id":"https://openalex.org/F4320336573","funder_display_name":"Humanities and Social Sciences Youth Foundation, Ministry of Education of the People's Republic of China"},{"id":"https://openalex.org/G7111357464","display_name":null,"funder_award_id":"2020JJ5112","funder_id":"https://openalex.org/F4320322843","funder_display_name":"Natural Science Foundation of\u00a0Hunan Province"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320322843","display_name":"Natural Science Foundation of\u00a0Hunan Province","ror":null},{"id":"https://openalex.org/F4320336573","display_name":"Humanities and Social Sciences Youth Foundation, Ministry of Education of the People's Republic of China","ror":null}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4308611984.pdf","grobid_xml":"https://content.openalex.org/works/W4308611984.grobid-xml"},"referenced_works_count":37,"referenced_works":["https://openalex.org/W1829951598","https://openalex.org/W2013908206","https://openalex.org/W2050868309","https://openalex.org/W2321837546","https://openalex.org/W2344746133","https://openalex.org/W2783992566","https://openalex.org/W2806626872","https://openalex.org/W2885661319","https://openalex.org/W2893477467","https://openalex.org/W2895980456","https://openalex.org/W2900337413","https://openalex.org/W2913509214","https://openalex.org/W2920996254","https://openalex.org/W2934716425","https://openalex.org/W2939464956","https://openalex.org/W2947577298","https://openalex.org/W2965957848","https://openalex.org/W2982485006","https://openalex.org/W2988347501","https://openalex.org/W2990472840","https://openalex.org/W3042518792","https://openalex.org/W3092336417","https://openalex.org/W3109432046","https://openalex.org/W3109761444","https://openalex.org/W3121968591","https://openalex.org/W3134959257","https://openalex.org/W3167169082","https://openalex.org/W3185532111","https://openalex.org/W3195704927","https://openalex.org/W3196501469","https://openalex.org/W3204921395","https://openalex.org/W3210167446","https://openalex.org/W4206228606","https://openalex.org/W4220931981","https://openalex.org/W4283067317","https://openalex.org/W4285061422","https://openalex.org/W6758652401"],"related_works":["https://openalex.org/W2995447873","https://openalex.org/W1802380781","https://openalex.org/W4210969441","https://openalex.org/W3035601835","https://openalex.org/W2997325129","https://openalex.org/W2747160131","https://openalex.org/W2930412558","https://openalex.org/W3204527492","https://openalex.org/W2889230580","https://openalex.org/W2884025808"],"abstract_inverted_index":{"Abstract":[0],"Aiming":[1],"at":[2],"the":[3,29,36,47,59,77,84,91,105,119,122,134,138,163,176,179,186,189,195,201],"aggregation":[4,152],"problem":[5],"of":[6,31,39,49,100,121,124,178,188,197],"online":[7,149],"multi-attribute":[8],"interactive":[9,54],"ratings,":[10,147],"a":[11,97,169],"decision-making":[12,34,153,202],"method":[13,99,123,165],"based":[14,132],"on":[15,43,126,133,200],"Pythagorean":[16,40,85,142],"Fuzzy":[17],"Bonferroni":[18,61],"mean":[19,62],"with":[20,63],"weighted":[21,64],"interaction":[22,65,101],"(PFWIBM)":[23],"operator":[24,69,93,107,136,191,198],"is":[25,94,108,160,166,204],"developed":[26],"by":[27,110],"mining":[28],"advantages":[30,38,187],"ratings":[32,116],"driven":[33],"and":[35,58,66,80,89,114,137,145,181,194],"quantitative":[37],"fuzzy":[41,86,143],"sets":[42,144],"linguistic":[44,146],"ratings.":[45],"First,":[46],"shortcomings":[48],"existing":[50],"operators":[51],"in":[52,104],"criterion":[53],"representation":[55],"are":[56,70,73,192],"analyzed,":[57],"improved":[60],"its":[67],"dual":[68],"defined,":[71],"which":[72],"used":[74],"to":[75,117,168,174],"aggregate":[76],"membership":[78],"information":[79,82],"non-membership":[81],"under":[83],"environment,":[87],"respectively,":[88],"then":[90],"PFWIBM":[92,106],"constructed.":[95],"Second,":[96],"generation":[98],"coefficients":[102],"embedded":[103],"designed":[109],"combining":[111],"expert":[112],"knowledge":[113],"user":[115],"overcome":[118],"limitations":[120],"relying":[125],"subjective":[127],"setting":[128],"parameter":[129],"values.":[130],"Third,":[131],"proposed":[135,164,190],"transformation":[139],"relationship":[140],"between":[141],"an":[148],"multi-dimensional":[150],"rating":[151],"approach":[154],"for":[155],"solving":[156],"product":[157],"raking":[158],"problems":[159],"developed.":[161],"Finally,":[162],"applied":[167],"passenger":[170],"car":[171],"ranking":[172],"example":[173],"show":[175],"feasibility":[177],"method,":[180],"through":[182],"some":[183],"comparative":[184],"analysis,":[185],"clarified,":[193],"influence":[196],"parameters":[199],"results":[203],"analyzed.":[205]},"counts_by_year":[{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":3}],"updated_date":"2026-05-06T08:25:59.206177","created_date":"2025-10-10T00:00:00"}