{"id":"https://openalex.org/W3038456932","doi":"https://doi.org/10.3390/a13070158","title":"Fuzzy C-Means Clustering Algorithm with Multiple Fuzzification Coefficients","display_name":"Fuzzy C-Means Clustering Algorithm with Multiple Fuzzification Coefficients","publication_year":2020,"publication_date":"2020-06-30","ids":{"openalex":"https://openalex.org/W3038456932","doi":"https://doi.org/10.3390/a13070158","mag":"3038456932"},"language":"en","primary_location":{"id":"doi:10.3390/a13070158","is_oa":true,"landing_page_url":"https://doi.org/10.3390/a13070158","pdf_url":"https://www.mdpi.com/1999-4893/13/7/158/pdf?version=1594187574","source":{"id":"https://openalex.org/S190629608","display_name":"Algorithms","issn_l":"1999-4893","issn":["1999-4893"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Algorithms","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/1999-4893/13/7/158/pdf?version=1594187574","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5011447933","display_name":"Tr\u1ea7n \u0110\u00ecnh Kh\u00e1ng","orcid":"https://orcid.org/0000-0002-2371-858X"},"institutions":[{"id":"https://openalex.org/I94518387","display_name":"Hanoi University of Science and Technology","ror":"https://ror.org/04nyv3z04","country_code":"VN","type":"education","lineage":["https://openalex.org/I94518387"]}],"countries":["VN"],"is_corresponding":true,"raw_author_name":"Tran Dinh Khang","raw_affiliation_strings":["Department of Information Systems, Hanoi University of Science and Technology, Hanoi 10000, Vietnam"],"affiliations":[{"raw_affiliation_string":"Department of Information Systems, Hanoi University of Science and Technology, Hanoi 10000, Vietnam","institution_ids":["https://openalex.org/I94518387"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5101534791","display_name":"Vuong D. Nguyen","orcid":"https://orcid.org/0000-0002-2369-8793"},"institutions":[{"id":"https://openalex.org/I94518387","display_name":"Hanoi University of Science and Technology","ror":"https://ror.org/04nyv3z04","country_code":"VN","type":"education","lineage":["https://openalex.org/I94518387"]}],"countries":["VN"],"is_corresponding":false,"raw_author_name":"Nguyen Duc Vuong","raw_affiliation_strings":["Department of Information Systems, Hanoi University of Science and Technology, Hanoi 10000, Vietnam"],"affiliations":[{"raw_affiliation_string":"Department of Information Systems, Hanoi University of Science and Technology, Hanoi 10000, Vietnam","institution_ids":["https://openalex.org/I94518387"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5012099379","display_name":"Manh\u2010Kien Tran","orcid":"https://orcid.org/0000-0001-9937-1749"},"institutions":[{"id":"https://openalex.org/I151746483","display_name":"University of Waterloo","ror":"https://ror.org/01aff2v68","country_code":"CA","type":"education","lineage":["https://openalex.org/I151746483"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Manh-Kien Tran","raw_affiliation_strings":["Department of Chemical Engineering, University of Waterloo, Waterloo, ON N2L 3G1, Canada"],"affiliations":[{"raw_affiliation_string":"Department of Chemical Engineering, University of Waterloo, Waterloo, ON N2L 3G1, Canada","institution_ids":["https://openalex.org/I151746483"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5002554251","display_name":"Michael Fowler","orcid":"https://orcid.org/0000-0002-9761-0336"},"institutions":[{"id":"https://openalex.org/I151746483","display_name":"University of Waterloo","ror":"https://ror.org/01aff2v68","country_code":"CA","type":"education","lineage":["https://openalex.org/I151746483"]}],"countries":["CA"],"is_corresponding":true,"raw_author_name":"Michael Fowler","raw_affiliation_strings":["Department of Chemical Engineering, University of Waterloo, Waterloo, ON N2L 3G1, Canada"],"affiliations":[{"raw_affiliation_string":"Department of Chemical Engineering, University of Waterloo, Waterloo, ON N2L 3G1, Canada","institution_ids":["https://openalex.org/I151746483"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5002554251","https://openalex.org/A5011447933"],"corresponding_institution_ids":["https://openalex.org/I151746483","https://openalex.org/I94518387"],"apc_list":{"value":1400,"currency":"CHF","value_usd":1515},"apc_paid":{"value":1400,"currency":"CHF","value_usd":1515},"fwci":3.7039,"has_fulltext":false,"cited_by_count":49,"citation_normalized_percentile":{"value":0.94290196,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":98,"max":99},"biblio":{"volume":"13","issue":"7","first_page":"158","last_page":"158"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10637","display_name":"Advanced Clustering Algorithms Research","score":0.9990000128746033,"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":0.9990000128746033,"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/T10057","display_name":"Face and Expression Recognition","score":0.986299991607666,"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"}},{"id":"https://openalex.org/T10100","display_name":"Metaheuristic Optimization Algorithms Research","score":0.9825000166893005,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/cluster-analysis","display_name":"Cluster analysis","score":0.7734472751617432},{"id":"https://openalex.org/keywords/fuzzy-clustering","display_name":"Fuzzy clustering","score":0.6949020624160767},{"id":"https://openalex.org/keywords/correlation-clustering","display_name":"Correlation clustering","score":0.6356645226478577},{"id":"https://openalex.org/keywords/cure-data-clustering-algorithm","display_name":"CURE data clustering algorithm","score":0.6101706027984619},{"id":"https://openalex.org/keywords/canopy-clustering-algorithm","display_name":"Canopy clustering algorithm","score":0.601053774356842},{"id":"https://openalex.org/keywords/data-mining","display_name":"Data mining","score":0.5846132636070251},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.532331109046936},{"id":"https://openalex.org/keywords/flame-clustering","display_name":"FLAME clustering","score":0.4907587468624115},{"id":"https://openalex.org/keywords/fuzzy-set","display_name":"Fuzzy set","score":0.47227558493614197},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.4444628059864044},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.4409824311733246},{"id":"https://openalex.org/keywords/data-stream-clustering","display_name":"Data stream clustering","score":0.4332556426525116},{"id":"https://openalex.org/keywords/fuzzy-logic","display_name":"Fuzzy logic","score":0.4129006862640381},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4083375930786133},{"id":"https://openalex.org/keywords/pattern-recognition","display_name":"Pattern recognition (psychology)","score":0.4034436047077179}],"concepts":[{"id":"https://openalex.org/C73555534","wikidata":"https://www.wikidata.org/wiki/Q622825","display_name":"Cluster analysis","level":2,"score":0.7734472751617432},{"id":"https://openalex.org/C17212007","wikidata":"https://www.wikidata.org/wiki/Q5511111","display_name":"Fuzzy clustering","level":3,"score":0.6949020624160767},{"id":"https://openalex.org/C94641424","wikidata":"https://www.wikidata.org/wiki/Q5172845","display_name":"Correlation clustering","level":3,"score":0.6356645226478577},{"id":"https://openalex.org/C33704608","wikidata":"https://www.wikidata.org/wiki/Q5014717","display_name":"CURE data clustering algorithm","level":4,"score":0.6101706027984619},{"id":"https://openalex.org/C104047586","wikidata":"https://www.wikidata.org/wiki/Q5033439","display_name":"Canopy clustering algorithm","level":4,"score":0.601053774356842},{"id":"https://openalex.org/C124101348","wikidata":"https://www.wikidata.org/wiki/Q172491","display_name":"Data mining","level":1,"score":0.5846132636070251},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.532331109046936},{"id":"https://openalex.org/C44859942","wikidata":"https://www.wikidata.org/wiki/Q5426511","display_name":"FLAME clustering","level":5,"score":0.4907587468624115},{"id":"https://openalex.org/C42011625","wikidata":"https://www.wikidata.org/wiki/Q1055058","display_name":"Fuzzy set","level":3,"score":0.47227558493614197},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.4444628059864044},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4409824311733246},{"id":"https://openalex.org/C193143536","wikidata":"https://www.wikidata.org/wiki/Q5227360","display_name":"Data stream clustering","level":5,"score":0.4332556426525116},{"id":"https://openalex.org/C58166","wikidata":"https://www.wikidata.org/wiki/Q224821","display_name":"Fuzzy logic","level":2,"score":0.4129006862640381},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4083375930786133},{"id":"https://openalex.org/C153180895","wikidata":"https://www.wikidata.org/wiki/Q7148389","display_name":"Pattern recognition (psychology)","level":2,"score":0.4034436047077179}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.3390/a13070158","is_oa":true,"landing_page_url":"https://doi.org/10.3390/a13070158","pdf_url":"https://www.mdpi.com/1999-4893/13/7/158/pdf?version=1594187574","source":{"id":"https://openalex.org/S190629608","display_name":"Algorithms","issn_l":"1999-4893","issn":["1999-4893"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Algorithms","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:d392a0187b8f493dbdfdb10ddb2c9205","is_oa":true,"landing_page_url":"https://doaj.org/article/d392a0187b8f493dbdfdb10ddb2c9205","pdf_url":null,"source":{"id":"https://openalex.org/S112646816","display_name":"SHILAP Revista de lepidopterolog\u00eda","issn_l":"0300-5267","issn":["0300-5267","2340-4078"],"is_oa":true,"is_in_doaj":true,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Algorithms, Vol 13, Iss 7, p 158 (2020)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/1999-4893/13/7/158/","is_oa":true,"landing_page_url":"http://dx.doi.org/10.3390/a13070158","pdf_url":null,"source":{"id":"https://openalex.org/S4306400947","display_name":"MDPI (MDPI AG)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210097602","host_organization_name":"Multidisciplinary Digital Publishing Institute (Switzerland)","host_organization_lineage":["https://openalex.org/I4210097602"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Algorithms","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/a13070158","is_oa":true,"landing_page_url":"https://doi.org/10.3390/a13070158","pdf_url":"https://www.mdpi.com/1999-4893/13/7/158/pdf?version=1594187574","source":{"id":"https://openalex.org/S190629608","display_name":"Algorithms","issn_l":"1999-4893","issn":["1999-4893"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Algorithms","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G2078499933","display_name":null,"funder_award_id":"102.05-2018.02","funder_id":"https://openalex.org/F4320309617","funder_display_name":"National Foundation for Science and Technology Development"}],"funders":[{"id":"https://openalex.org/F4320309617","display_name":"National Foundation for Science and Technology Development","ror":"https://ror.org/04rw64z44"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3038456932.pdf","grobid_xml":"https://content.openalex.org/works/W3038456932.grobid-xml"},"referenced_works_count":18,"referenced_works":["https://openalex.org/W1936837682","https://openalex.org/W1989907351","https://openalex.org/W1995450389","https://openalex.org/W2013900754","https://openalex.org/W2071300659","https://openalex.org/W2077061001","https://openalex.org/W2103535990","https://openalex.org/W2106650695","https://openalex.org/W2125094706","https://openalex.org/W2319017187","https://openalex.org/W2479531384","https://openalex.org/W2586696502","https://openalex.org/W2588865889","https://openalex.org/W2810183518","https://openalex.org/W2911008619","https://openalex.org/W2914820851","https://openalex.org/W3083424454","https://openalex.org/W6640331532"],"related_works":["https://openalex.org/W2491448268","https://openalex.org/W2892323093","https://openalex.org/W2394193399","https://openalex.org/W2374506950","https://openalex.org/W3071522575","https://openalex.org/W2352139139","https://openalex.org/W2054669762","https://openalex.org/W2399084168","https://openalex.org/W2556490192","https://openalex.org/W1985667446"],"abstract_inverted_index":{"Clustering":[0],"is":[1,27,124,145,162],"an":[2],"unsupervised":[3],"machine":[4],"learning":[5],"technique":[6],"with":[7,108,148],"many":[8,40],"practical":[9],"applications":[10],"that":[11,158],"has":[12,102],"gathered":[13],"extensive":[14],"research":[15],"interest.":[16],"Aside":[17],"from":[18],"deterministic":[19],"or":[20,62],"probabilistic":[21],"techniques,":[22,67],"fuzzy":[23,81,99],"C-means":[24],"clustering":[25,31,47,82,100,174],"(FCM)":[26],"also":[28],"a":[29,79],"common":[30,152],"technique.":[32],"Since":[33],"the":[34,37,54,60,71,91,125,138,155,159,167],"advent":[35],"of":[36,57,93,121,127],"FCM":[38,107,140,169],"method,":[39],"improvements":[41,50],"have":[42],"been":[43],"made":[44],"to":[45,106,115,133,166],"increase":[46],"efficiency.":[48],"These":[49],"focus":[51],"on":[52,63,90,150],"adjusting":[53],"membership":[55],"representation":[56],"elements":[58],"in":[59,137],"clusters,":[61],"fuzzifying":[64],"and":[65,154],"defuzzifying":[66],"as":[68,70,131,170,172],"well":[69,171],"distance":[72],"function":[73],"between":[74],"elements.":[75],"This":[76],"study":[77],"proposes":[78],"novel":[80],"algorithm":[83,144,161],"using":[84],"multiple":[85,128],"different":[86],"fuzzification":[87,129],"coefficients":[88,130],"depending":[89],"characteristics":[92],"each":[94],"data":[95],"sample.":[96],"The":[97,111,118,142],"proposed":[98,160],"method":[101],"similar":[103],"calculation":[104],"steps":[105],"some":[109],"modifications.":[110],"formulas":[112],"are":[113],"derived":[114],"ensure":[116],"convergence.":[117],"main":[119],"contribution":[120],"this":[122],"approach":[123],"utilization":[126],"opposed":[132],"only":[134],"one":[135],"coefficient":[136],"original":[139,168],"algorithm.":[141],"new":[143],"then":[146],"evaluated":[147],"experiments":[149],"several":[151],"datasets":[153],"results":[156],"show":[157],"more":[163],"efficient":[164],"compared":[165],"other":[173],"methods.":[175]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":6},{"year":2024,"cited_by_count":14},{"year":2023,"cited_by_count":8},{"year":2022,"cited_by_count":11},{"year":2021,"cited_by_count":8}],"updated_date":"2026-03-27T05:58:40.876381","created_date":"2025-10-10T00:00:00"}