{"id":"https://openalex.org/W1977233649","doi":"https://doi.org/10.1016/0031-3203(86)90048-8","title":"Fuzzy c-means: Optimality of solutions and effective termination of the algorithm","display_name":"Fuzzy c-means: Optimality of solutions and effective termination of the algorithm","publication_year":1986,"publication_date":"1986-01-01","ids":{"openalex":"https://openalex.org/W1977233649","doi":"https://doi.org/10.1016/0031-3203(86)90048-8","mag":"1977233649"},"language":"en","primary_location":{"id":"doi:10.1016/0031-3203(86)90048-8","is_oa":false,"landing_page_url":"https://doi.org/10.1016/0031-3203(86)90048-8","pdf_url":null,"source":{"id":"https://openalex.org/S414566","display_name":"Pattern Recognition","issn_l":"0031-3203","issn":["0031-3203","1873-5142"],"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":"Pattern Recognition","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/A5022527760","display_name":"Mohamed A. Ismail","orcid":"https://orcid.org/0000-0001-8674-3232"},"institutions":[{"id":"https://openalex.org/I74413500","display_name":"University of Windsor","ror":"https://ror.org/01gw3d370","country_code":"CA","type":"education","lineage":["https://openalex.org/I74413500"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"M.A. Ismail","raw_affiliation_strings":["School of Computer Science, University of Windsor, Windsor, Ontario, Canada N9B 3P4","School of Computer Science, University of Windsor, Windsor, Ontario, Canada N9B 3P4,"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Computer Science, University of Windsor, Windsor, Ontario, Canada N9B 3P4","institution_ids":["https://openalex.org/I74413500"]},{"raw_affiliation_string":"School of Computer Science, University of Windsor, Windsor, Ontario, Canada N9B 3P4,","institution_ids":["https://openalex.org/I74413500"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5058646758","display_name":"Shokri Z. Selim","orcid":"https://orcid.org/0000-0002-1239-5471"},"institutions":[{"id":"https://openalex.org/I134085113","display_name":"King Fahd University of Petroleum and Minerals","ror":"https://ror.org/03yez3163","country_code":"SA","type":"education","lineage":["https://openalex.org/I134085113"]}],"countries":["SA"],"is_corresponding":false,"raw_author_name":"Shokri Z. Selim","raw_affiliation_strings":["Department of Systems Engineering, University of Petroleum and Minerals, Dhahran 31261, Saudi Arabia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Systems Engineering, University of Petroleum and Minerals, Dhahran 31261, Saudi Arabia","institution_ids":["https://openalex.org/I134085113"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":{"value":2850,"currency":"USD","value_usd":2850},"apc_paid":null,"fwci":1.2192,"has_fulltext":false,"cited_by_count":62,"citation_normalized_percentile":{"value":0.76553931,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"19","issue":"6","first_page":"481","last_page":"485"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10050","display_name":"Multi-Criteria Decision Making","score":0.9861000180244446,"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":0.9861000180244446,"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/T10100","display_name":"Metaheuristic Optimization Algorithms Research","score":0.9745000004768372,"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/T10637","display_name":"Advanced Clustering Algorithms Research","score":0.9689000248908997,"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/hessian-matrix","display_name":"Hessian matrix","score":0.8675849437713623},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.692295491695404},{"id":"https://openalex.org/keywords/positive-definiteness","display_name":"Positive definiteness","score":0.6697777509689331},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.5609602332115173},{"id":"https://openalex.org/keywords/simple","display_name":"Simple (philosophy)","score":0.5081455707550049},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.5050531029701233},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.4780873954296112},{"id":"https://openalex.org/keywords/fuzzy-logic","display_name":"Fuzzy logic","score":0.4543225169181824},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.43683600425720215},{"id":"https://openalex.org/keywords/point","display_name":"Point (geometry)","score":0.4307393431663513},{"id":"https://openalex.org/keywords/positive-definite-matrix","display_name":"Positive-definite matrix","score":0.38226914405822754},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.23932728171348572},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.23197489976882935},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.07609617710113525},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.06974983215332031}],"concepts":[{"id":"https://openalex.org/C203616005","wikidata":"https://www.wikidata.org/wiki/Q620495","display_name":"Hessian matrix","level":2,"score":0.8675849437713623},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.692295491695404},{"id":"https://openalex.org/C2778265155","wikidata":"https://www.wikidata.org/wiki/Q7233276","display_name":"Positive definiteness","level":4,"score":0.6697777509689331},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.5609602332115173},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.5081455707550049},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.5050531029701233},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4780873954296112},{"id":"https://openalex.org/C58166","wikidata":"https://www.wikidata.org/wiki/Q224821","display_name":"Fuzzy logic","level":2,"score":0.4543225169181824},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.43683600425720215},{"id":"https://openalex.org/C28719098","wikidata":"https://www.wikidata.org/wiki/Q44946","display_name":"Point (geometry)","level":2,"score":0.4307393431663513},{"id":"https://openalex.org/C49712288","wikidata":"https://www.wikidata.org/wiki/Q77601250","display_name":"Positive-definite matrix","level":3,"score":0.38226914405822754},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.23932728171348572},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.23197489976882935},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.07609617710113525},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.06974983215332031},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","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/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","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},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1016/0031-3203(86)90048-8","is_oa":false,"landing_page_url":"https://doi.org/10.1016/0031-3203(86)90048-8","pdf_url":null,"source":{"id":"https://openalex.org/S414566","display_name":"Pattern Recognition","issn_l":"0031-3203","issn":["0031-3203","1873-5142"],"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":"Pattern Recognition","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":10,"referenced_works":["https://openalex.org/W125870180","https://openalex.org/W646851550","https://openalex.org/W1990368529","https://openalex.org/W2038614136","https://openalex.org/W2073849744","https://openalex.org/W2080769860","https://openalex.org/W2335127210","https://openalex.org/W2802627035","https://openalex.org/W4285719527","https://openalex.org/W6605154018"],"related_works":["https://openalex.org/W2369793817","https://openalex.org/W2364489971","https://openalex.org/W2361979571","https://openalex.org/W3208377712","https://openalex.org/W2043819621","https://openalex.org/W2063005030","https://openalex.org/W2147922812","https://openalex.org/W4205226845","https://openalex.org/W2373372131","https://openalex.org/W1982955687"],"abstract_inverted_index":null,"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2020,"cited_by_count":2},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":2},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":1},{"year":2012,"cited_by_count":3}],"updated_date":"2026-07-29T09:40:50.615796","created_date":"2025-10-10T00:00:00"}