{"id":"https://openalex.org/W2048596282","doi":"https://doi.org/10.1109/tpami.1981.4767051","title":"A Clustering Performance Measure Based on Fuzzy Set Decomposition","display_name":"A Clustering Performance Measure Based on Fuzzy Set Decomposition","publication_year":1981,"publication_date":"1981-01-01","ids":{"openalex":"https://openalex.org/W2048596282","doi":"https://doi.org/10.1109/tpami.1981.4767051","mag":"2048596282","pmid":"https://pubmed.ncbi.nlm.nih.gov/21868919"},"language":"en","primary_location":{"id":"doi:10.1109/tpami.1981.4767051","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tpami.1981.4767051","pdf_url":null,"source":{"id":"https://openalex.org/S199944782","display_name":"IEEE Transactions on Pattern Analysis and Machine Intelligence","issn_l":"0162-8828","issn":["0162-8828","1939-3539","2160-9292"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320439","host_organization_name":"IEEE Computer Society","host_organization_lineage":["https://openalex.org/P4310320439","https://openalex.org/P4310319808"],"host_organization_lineage_names":["IEEE Computer Society","Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Pattern Analysis and Machine Intelligence","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","pubmed"],"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/A5055486665","display_name":"E. Backer","orcid":null},"institutions":[{"id":"https://openalex.org/I98358874","display_name":"Delft University of Technology","ror":"https://ror.org/02e2c7k09","country_code":"NL","type":"education","lineage":["https://openalex.org/I98358874"]}],"countries":["NL"],"is_corresponding":false,"raw_author_name":"Eric Backer","raw_affiliation_strings":["MEMBER, IEEE, Information Theory Group, Delft University of Technology, Delft, The Netherlands"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"MEMBER, IEEE, Information Theory Group, Delft University of Technology, Delft, The Netherlands","institution_ids":["https://openalex.org/I98358874"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100613677","display_name":"Anil K. Jain","orcid":"https://orcid.org/0000-0002-6369-6995"},"institutions":[{"id":"https://openalex.org/I87216513","display_name":"Michigan State University","ror":"https://ror.org/05hs6h993","country_code":"US","type":"education","lineage":["https://openalex.org/I87216513"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Anil K. Jain","raw_affiliation_strings":["Department of Computer Science, Michigan State University, East Lansing, MI, USA","MEMBER, IEEE, Department of Computer Science, Michigan State University, East Lansing, MI 48823.#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computer Science, Michigan State University, East Lansing, MI, USA","institution_ids":["https://openalex.org/I87216513"]},{"raw_affiliation_string":"MEMBER, IEEE, Department of Computer Science, Michigan State University, East Lansing, MI 48823.#TAB#","institution_ids":["https://openalex.org/I87216513"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":186,"citation_normalized_percentile":{"value":0.09731615,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":91,"max":99},"biblio":{"volume":"PAMI-3","issue":"1","first_page":"66","last_page":"75"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10637","display_name":"Advanced Clustering Algorithms Research","score":0.9950000047683716,"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":0.9950000047683716,"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/T11106","display_name":"Data Management and Algorithms","score":0.9750999808311462,"subfield":{"id":"https://openalex.org/subfields/1711","display_name":"Signal Processing"},"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":0.9718999862670898,"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/cluster-analysis","display_name":"Cluster analysis","score":0.759052574634552},{"id":"https://openalex.org/keywords/fuzzy-clustering","display_name":"Fuzzy clustering","score":0.6970098614692688},{"id":"https://openalex.org/keywords/data-mining","display_name":"Data mining","score":0.6016075015068054},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5735051035881042},{"id":"https://openalex.org/keywords/fuzzy-set","display_name":"Fuzzy set","score":0.5265127420425415},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.5224370360374451},{"id":"https://openalex.org/keywords/measure","display_name":"Measure (data warehouse)","score":0.5070054531097412},{"id":"https://openalex.org/keywords/pattern-recognition","display_name":"Pattern recognition (psychology)","score":0.49313563108444214},{"id":"https://openalex.org/keywords/correlation-clustering","display_name":"Correlation clustering","score":0.45946192741394043},{"id":"https://openalex.org/keywords/partition","display_name":"Partition (number theory)","score":0.44663190841674805},{"id":"https://openalex.org/keywords/single-linkage-clustering","display_name":"Single-linkage clustering","score":0.44615182280540466},{"id":"https://openalex.org/keywords/determining-the-number-of-clusters-in-a-data-set","display_name":"Determining the number of clusters in a data set","score":0.4144717752933502},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4035395383834839},{"id":"https://openalex.org/keywords/fuzzy-logic","display_name":"Fuzzy logic","score":0.39461439847946167},{"id":"https://openalex.org/keywords/cure-data-clustering-algorithm","display_name":"CURE data clustering algorithm","score":0.3433602452278137}],"concepts":[{"id":"https://openalex.org/C73555534","wikidata":"https://www.wikidata.org/wiki/Q622825","display_name":"Cluster analysis","level":2,"score":0.759052574634552},{"id":"https://openalex.org/C17212007","wikidata":"https://www.wikidata.org/wiki/Q5511111","display_name":"Fuzzy clustering","level":3,"score":0.6970098614692688},{"id":"https://openalex.org/C124101348","wikidata":"https://www.wikidata.org/wiki/Q172491","display_name":"Data mining","level":1,"score":0.6016075015068054},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5735051035881042},{"id":"https://openalex.org/C42011625","wikidata":"https://www.wikidata.org/wiki/Q1055058","display_name":"Fuzzy set","level":3,"score":0.5265127420425415},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.5224370360374451},{"id":"https://openalex.org/C2780009758","wikidata":"https://www.wikidata.org/wiki/Q6804172","display_name":"Measure (data warehouse)","level":2,"score":0.5070054531097412},{"id":"https://openalex.org/C153180895","wikidata":"https://www.wikidata.org/wiki/Q7148389","display_name":"Pattern recognition (psychology)","level":2,"score":0.49313563108444214},{"id":"https://openalex.org/C94641424","wikidata":"https://www.wikidata.org/wiki/Q5172845","display_name":"Correlation clustering","level":3,"score":0.45946192741394043},{"id":"https://openalex.org/C42812","wikidata":"https://www.wikidata.org/wiki/Q1082910","display_name":"Partition (number theory)","level":2,"score":0.44663190841674805},{"id":"https://openalex.org/C22648726","wikidata":"https://www.wikidata.org/wiki/Q7523744","display_name":"Single-linkage clustering","level":5,"score":0.44615182280540466},{"id":"https://openalex.org/C149872217","wikidata":"https://www.wikidata.org/wiki/Q5265701","display_name":"Determining the number of clusters in a data set","level":5,"score":0.4144717752933502},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4035395383834839},{"id":"https://openalex.org/C58166","wikidata":"https://www.wikidata.org/wiki/Q224821","display_name":"Fuzzy logic","level":2,"score":0.39461439847946167},{"id":"https://openalex.org/C33704608","wikidata":"https://www.wikidata.org/wiki/Q5014717","display_name":"CURE data clustering algorithm","level":4,"score":0.3433602452278137},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/tpami.1981.4767051","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tpami.1981.4767051","pdf_url":null,"source":{"id":"https://openalex.org/S199944782","display_name":"IEEE Transactions on Pattern Analysis and Machine Intelligence","issn_l":"0162-8828","issn":["0162-8828","1939-3539","2160-9292"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320439","host_organization_name":"IEEE Computer Society","host_organization_lineage":["https://openalex.org/P4310320439","https://openalex.org/P4310319808"],"host_organization_lineage_names":["IEEE Computer Society","Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Pattern Analysis and Machine Intelligence","raw_type":"journal-article"},{"id":"pmid:21868919","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/21868919","pdf_url":null,"source":{"id":"https://openalex.org/S4306525036","display_name":"PubMed","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE transactions on pattern analysis and machine intelligence","raw_type":null}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":5,"referenced_works":["https://openalex.org/W1537579017","https://openalex.org/W2046778278","https://openalex.org/W2070771945","https://openalex.org/W2081206009","https://openalex.org/W2118587067"],"related_works":["https://openalex.org/W2406185607","https://openalex.org/W4308301473","https://openalex.org/W4298005308","https://openalex.org/W2982243238","https://openalex.org/W2389934482","https://openalex.org/W4241252752","https://openalex.org/W3209217468","https://openalex.org/W3176177124","https://openalex.org/W2553999514","https://openalex.org/W2058604213"],"abstract_inverted_index":{"Clustering":[0],"is":[1,20,57,99],"primarily":[2],"used":[3],"to":[4,22,27,35],"uncover":[5],"the":[6,24,40,72,84,95,102,110,113],"true":[7],"underlying":[8],"structure":[9],"of":[10,43,54,61,71,94,105,112],"a":[11,44,62,67,106],"given":[12],"data":[13,26,45,73,97],"set":[14,46,69,74],"and,":[15],"for":[16],"this":[17],"purpose,":[18],"it":[19],"desirable":[21],"subject":[23],"same":[25,96],"several":[28],"different":[29,49,92],"clustering":[30,50],"algorithms.":[31,51],"This":[32],"paper":[33],"attempts":[34],"put":[36],"an":[37,89],"order":[38,90],"on":[39,66,91,109],"various":[41],"partitions":[42,93],"obtained":[47,114],"from":[48],"The":[52],"goodness":[53],"each":[55],"partition":[56],"expressed":[58],"by":[59],"means":[60],"performance":[63,86],"measure":[64,87],"based":[65],"fuzzy":[68],"decomposition":[70],"under":[75],"consideration.":[76],"Several":[77],"experiments":[78],"reported":[79],"in":[80],"here":[81],"show":[82],"that":[83],"proposed":[85],"puts":[88],"which":[98],"consistent":[100],"with":[101],"error":[103],"rate":[104],"classifier":[107],"designed":[108],"basis":[111],"cluster":[115],"labelings.":[116]},"counts_by_year":[{"year":2026,"cited_by_count":4},{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":7},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":4},{"year":2021,"cited_by_count":3},{"year":2020,"cited_by_count":5},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":5},{"year":2017,"cited_by_count":3},{"year":2016,"cited_by_count":8},{"year":2015,"cited_by_count":4},{"year":2014,"cited_by_count":5},{"year":2013,"cited_by_count":7},{"year":2012,"cited_by_count":10}],"updated_date":"2026-07-22T07:51:19.307946","created_date":"2025-10-10T00:00:00"}