{"id":"https://openalex.org/W2011005393","doi":"https://doi.org/10.1016/j.fss.2013.12.013","title":"A novel cluster validity index for fuzzy clustering based on bipartite modularity","display_name":"A novel cluster validity index for fuzzy clustering based on bipartite modularity","publication_year":2014,"publication_date":"2014-01-04","ids":{"openalex":"https://openalex.org/W2011005393","doi":"https://doi.org/10.1016/j.fss.2013.12.013","mag":"2011005393"},"language":"en","primary_location":{"id":"doi:10.1016/j.fss.2013.12.013","is_oa":false,"landing_page_url":"https://doi.org/10.1016/j.fss.2013.12.013","pdf_url":null,"source":{"id":"https://openalex.org/S169411308","display_name":"Fuzzy Sets and Systems","issn_l":"0165-0114","issn":["0165-0114","1872-6801"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Fuzzy Sets and 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/A5100379745","display_name":"Dawei Zhang","orcid":"https://orcid.org/0000-0002-0952-421X"},"institutions":[{"id":"https://openalex.org/I153374732","display_name":"Liaoning Normal University","ror":"https://ror.org/04c3cgg32","country_code":"CN","type":"education","lineage":["https://openalex.org/I153374732"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Dawei Zhang","raw_affiliation_strings":["School of Computer Science and Technology, Liaoning Normal University, Liaoning, Dalian 116081, PR China"],"affiliations":[{"raw_affiliation_string":"School of Computer Science and Technology, Liaoning Normal University, Liaoning, Dalian 116081, PR China","institution_ids":["https://openalex.org/I153374732"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5018528913","display_name":"Min Ji","orcid":"https://orcid.org/0000-0001-7739-3744"},"institutions":[{"id":"https://openalex.org/I153374732","display_name":"Liaoning Normal University","ror":"https://ror.org/04c3cgg32","country_code":"CN","type":"education","lineage":["https://openalex.org/I153374732"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Min Ji","raw_affiliation_strings":["School of Computer Science and Technology, Liaoning Normal University, Liaoning, Dalian 116081, PR China"],"affiliations":[{"raw_affiliation_string":"School of Computer Science and Technology, Liaoning Normal University, Liaoning, Dalian 116081, PR China","institution_ids":["https://openalex.org/I153374732"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5064324343","display_name":"Jun Yang","orcid":"https://orcid.org/0000-0001-6740-4358"},"institutions":[{"id":"https://openalex.org/I153374732","display_name":"Liaoning Normal University","ror":"https://ror.org/04c3cgg32","country_code":"CN","type":"education","lineage":["https://openalex.org/I153374732"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Jun Yang","raw_affiliation_strings":["School of Urban and Environmental Science, Liaoning Normal University, Liaoning, Dalian 116029, PR China"],"affiliations":[{"raw_affiliation_string":"School of Urban and Environmental Science, Liaoning Normal University, Liaoning, Dalian 116029, PR China","institution_ids":["https://openalex.org/I153374732"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100419716","display_name":"Yong Zhang","orcid":"https://orcid.org/0000-0001-6577-5235"},"institutions":[{"id":"https://openalex.org/I153374732","display_name":"Liaoning Normal University","ror":"https://ror.org/04c3cgg32","country_code":"CN","type":"education","lineage":["https://openalex.org/I153374732"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yong Zhang","raw_affiliation_strings":["School of Computer Science and Technology, Liaoning Normal University, Liaoning, Dalian 116081, PR China"],"affiliations":[{"raw_affiliation_string":"School of Computer Science and Technology, Liaoning Normal University, Liaoning, Dalian 116081, PR China","institution_ids":["https://openalex.org/I153374732"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5010329426","display_name":"Fuding Xie","orcid":"https://orcid.org/0000-0003-1392-2699"},"institutions":[{"id":"https://openalex.org/I153374732","display_name":"Liaoning Normal University","ror":"https://ror.org/04c3cgg32","country_code":"CN","type":"education","lineage":["https://openalex.org/I153374732"]},{"id":"https://openalex.org/I4210120485","display_name":"Academy of Mathematics and Systems Science","ror":"https://ror.org/02jkmyk67","country_code":"CN","type":"facility","lineage":["https://openalex.org/I19820366","https://openalex.org/I4210120485"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Fuding Xie","raw_affiliation_strings":["Academy of Mathematics and System Sciences, Chinese Academy of Science, Beijing 100080, PR China","School of Urban and Environmental Science, Liaoning Normal University, Liaoning, Dalian 116029, PR China"],"affiliations":[{"raw_affiliation_string":"Academy of Mathematics and System Sciences, Chinese Academy of Science, Beijing 100080, PR China","institution_ids":["https://openalex.org/I4210120485"]},{"raw_affiliation_string":"School of Urban and Environmental Science, Liaoning Normal University, Liaoning, Dalian 116029, PR China","institution_ids":["https://openalex.org/I153374732"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":5,"corresponding_author_ids":["https://openalex.org/A5010329426"],"corresponding_institution_ids":["https://openalex.org/I153374732","https://openalex.org/I4210120485"],"apc_list":{"value":2600,"currency":"USD","value_usd":2600},"apc_paid":null,"fwci":7.2073,"has_fulltext":false,"cited_by_count":46,"citation_normalized_percentile":{"value":0.96980366,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"253","issue":null,"first_page":"122","last_page":"137"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10637","display_name":"Advanced Clustering Algorithms Research","score":0.9986000061035156,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10637","display_name":"Advanced Clustering Algorithms Research","score":0.9986000061035156,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"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/T10064","display_name":"Complex Network Analysis Techniques","score":0.9872999787330627,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10057","display_name":"Face and Expression Recognition","score":0.9623000025749207,"subfield":{"id":"https://openalex.org/subfields/1707","display_name":"Computer Vision and Pattern Recognition"},"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/mathematics","display_name":"Mathematics","score":0.7644509077072144},{"id":"https://openalex.org/keywords/modularity","display_name":"Modularity (biology)","score":0.7272916436195374},{"id":"https://openalex.org/keywords/bipartite-graph","display_name":"Bipartite graph","score":0.6494237780570984},{"id":"https://openalex.org/keywords/cluster","display_name":"Cluster (spacecraft)","score":0.5647734999656677},{"id":"https://openalex.org/keywords/fuzzy-logic","display_name":"Fuzzy logic","score":0.5579577088356018},{"id":"https://openalex.org/keywords/index","display_name":"Index (typography)","score":0.5440711975097656},{"id":"https://openalex.org/keywords/cluster-analysis","display_name":"Cluster analysis","score":0.4758298695087433},{"id":"https://openalex.org/keywords/fuzzy-set","display_name":"Fuzzy set","score":0.44397589564323425},{"id":"https://openalex.org/keywords/fuzzy-clustering","display_name":"Fuzzy clustering","score":0.4311600923538208},{"id":"https://openalex.org/keywords/data-mining","display_name":"Data mining","score":0.4064875841140747},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.3843719959259033},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.25963789224624634},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.233617901802063},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.17913448810577393},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.07401731610298157}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7644509077072144},{"id":"https://openalex.org/C2779478453","wikidata":"https://www.wikidata.org/wiki/Q6889748","display_name":"Modularity (biology)","level":2,"score":0.7272916436195374},{"id":"https://openalex.org/C197657726","wikidata":"https://www.wikidata.org/wiki/Q174733","display_name":"Bipartite graph","level":3,"score":0.6494237780570984},{"id":"https://openalex.org/C164866538","wikidata":"https://www.wikidata.org/wiki/Q367351","display_name":"Cluster (spacecraft)","level":2,"score":0.5647734999656677},{"id":"https://openalex.org/C58166","wikidata":"https://www.wikidata.org/wiki/Q224821","display_name":"Fuzzy logic","level":2,"score":0.5579577088356018},{"id":"https://openalex.org/C2777382242","wikidata":"https://www.wikidata.org/wiki/Q6017816","display_name":"Index (typography)","level":2,"score":0.5440711975097656},{"id":"https://openalex.org/C73555534","wikidata":"https://www.wikidata.org/wiki/Q622825","display_name":"Cluster analysis","level":2,"score":0.4758298695087433},{"id":"https://openalex.org/C42011625","wikidata":"https://www.wikidata.org/wiki/Q1055058","display_name":"Fuzzy set","level":3,"score":0.44397589564323425},{"id":"https://openalex.org/C17212007","wikidata":"https://www.wikidata.org/wiki/Q5511111","display_name":"Fuzzy clustering","level":3,"score":0.4311600923538208},{"id":"https://openalex.org/C124101348","wikidata":"https://www.wikidata.org/wiki/Q172491","display_name":"Data mining","level":1,"score":0.4064875841140747},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.3843719959259033},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.25963789224624634},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.233617901802063},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.17913448810577393},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.07401731610298157},{"id":"https://openalex.org/C136764020","wikidata":"https://www.wikidata.org/wiki/Q466","display_name":"World Wide Web","level":1,"score":0.0},{"id":"https://openalex.org/C54355233","wikidata":"https://www.wikidata.org/wiki/Q7162","display_name":"Genetics","level":1,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1016/j.fss.2013.12.013","is_oa":false,"landing_page_url":"https://doi.org/10.1016/j.fss.2013.12.013","pdf_url":null,"source":{"id":"https://openalex.org/S169411308","display_name":"Fuzzy Sets and Systems","issn_l":"0165-0114","issn":["0165-0114","1872-6801"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Fuzzy Sets and Systems","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"score":0.5099999904632568,"display_name":"Partnerships for the goals","id":"https://metadata.un.org/sdg/17"}],"awards":[],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":36,"referenced_works":["https://openalex.org/W1963568149","https://openalex.org/W1974899343","https://openalex.org/W1978527081","https://openalex.org/W1983753875","https://openalex.org/W1987801991","https://openalex.org/W1990368529","https://openalex.org/W1996747841","https://openalex.org/W1999075329","https://openalex.org/W2001619934","https://openalex.org/W2003078486","https://openalex.org/W2014922235","https://openalex.org/W2025572017","https://openalex.org/W2025767687","https://openalex.org/W2029475565","https://openalex.org/W2029906715","https://openalex.org/W2032273054","https://openalex.org/W2039752655","https://openalex.org/W2046778278","https://openalex.org/W2051224630","https://openalex.org/W2054232099","https://openalex.org/W2071826364","https://openalex.org/W2082257952","https://openalex.org/W2094510831","https://openalex.org/W2112090702","https://openalex.org/W2113076747","https://openalex.org/W2118808755","https://openalex.org/W2137686028","https://openalex.org/W2165187708","https://openalex.org/W2171975443","https://openalex.org/W2302947639","https://openalex.org/W2395193627","https://openalex.org/W3165241807","https://openalex.org/W3176049587","https://openalex.org/W6647172677","https://openalex.org/W6668502158","https://openalex.org/W6796017329"],"related_works":["https://openalex.org/W2371352078","https://openalex.org/W2077383796","https://openalex.org/W4230687177","https://openalex.org/W2953461625","https://openalex.org/W1968829728","https://openalex.org/W2349859869","https://openalex.org/W2080136900","https://openalex.org/W2076272170","https://openalex.org/W144313889","https://openalex.org/W2008788438"],"abstract_inverted_index":null,"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":3},{"year":2020,"cited_by_count":6},{"year":2019,"cited_by_count":4},{"year":2018,"cited_by_count":10},{"year":2017,"cited_by_count":5},{"year":2016,"cited_by_count":9},{"year":2015,"cited_by_count":3}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
