{"id":"https://openalex.org/W2067746801","doi":"https://doi.org/10.1109/grc.2008.4664760","title":"On tolerant entropy regularized fuzzy c-means","display_name":"On tolerant entropy regularized fuzzy c-means","publication_year":2008,"publication_date":"2008-08-01","ids":{"openalex":"https://openalex.org/W2067746801","doi":"https://doi.org/10.1109/grc.2008.4664760","mag":"2067746801"},"language":"en","primary_location":{"id":"doi:10.1109/grc.2008.4664760","is_oa":false,"landing_page_url":"https://doi.org/10.1109/grc.2008.4664760","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2008 IEEE International Conference on Granular Computing","raw_type":"proceedings-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/A5060898444","display_name":"Yukihiro Hamasuna","orcid":null},"institutions":[{"id":"https://openalex.org/I146399215","display_name":"University of Tsukuba","ror":"https://ror.org/02956yf07","country_code":"JP","type":"education","lineage":["https://openalex.org/I146399215"]}],"countries":["JP"],"is_corresponding":true,"raw_author_name":"Yukihiro Hamasuna","raw_affiliation_strings":["Department of Risk Engineering, University of Tsukuba, Ibaraki, Japan","Dept. of Risk Eng., Univ. of Tsukuba, Tsukuba"],"affiliations":[{"raw_affiliation_string":"Department of Risk Engineering, University of Tsukuba, Ibaraki, Japan","institution_ids":["https://openalex.org/I146399215"]},{"raw_affiliation_string":"Dept. of Risk Eng., Univ. of Tsukuba, Tsukuba","institution_ids":["https://openalex.org/I146399215"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5101943648","display_name":"Yasunori Endo","orcid":"https://orcid.org/0000-0003-2968-4613"},"institutions":[{"id":"https://openalex.org/I146399215","display_name":"University of Tsukuba","ror":"https://ror.org/02956yf07","country_code":"JP","type":"education","lineage":["https://openalex.org/I146399215"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Yasunori Endo","raw_affiliation_strings":["Department of Risk Engineering, University of Tsukuba, Ibaraki, Japan","Dept. of Risk Eng., Univ. of Tsukuba, Tsukuba"],"affiliations":[{"raw_affiliation_string":"Department of Risk Engineering, University of Tsukuba, Ibaraki, Japan","institution_ids":["https://openalex.org/I146399215"]},{"raw_affiliation_string":"Dept. of Risk Eng., Univ. of Tsukuba, Tsukuba","institution_ids":["https://openalex.org/I146399215"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5022529051","display_name":"Makito Yamashiro","orcid":null},"institutions":[{"id":"https://openalex.org/I146399215","display_name":"University of Tsukuba","ror":"https://ror.org/02956yf07","country_code":"JP","type":"education","lineage":["https://openalex.org/I146399215"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Makito Yamashiro","raw_affiliation_strings":["Department of Risk Engineering, University of Tsukuba, Ibaraki, Japan","Dept. of Risk Eng., Univ. of Tsukuba, Tsukuba"],"affiliations":[{"raw_affiliation_string":"Department of Risk Engineering, University of Tsukuba, Ibaraki, Japan","institution_ids":["https://openalex.org/I146399215"]},{"raw_affiliation_string":"Dept. of Risk Eng., Univ. of Tsukuba, Tsukuba","institution_ids":["https://openalex.org/I146399215"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5060898444"],"corresponding_institution_ids":["https://openalex.org/I146399215"],"apc_list":null,"apc_paid":null,"fwci":0.6074,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.71428571,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"2","issue":null,"first_page":"244","last_page":"247"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12135","display_name":"Fuzzy Systems and Optimization","score":0.9883999824523926,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T12135","display_name":"Fuzzy Systems and Optimization","score":0.9883999824523926,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10100","display_name":"Metaheuristic Optimization Algorithms Research","score":0.9829000234603882,"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/T10050","display_name":"Multi-Criteria Decision Making","score":0.979200005531311,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/cluster-analysis","display_name":"Cluster analysis","score":0.5872158408164978},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.5700632333755493},{"id":"https://openalex.org/keywords/entropy","display_name":"Entropy (arrow of time)","score":0.5268981456756592},{"id":"https://openalex.org/keywords/optimization-problem","display_name":"Optimization problem","score":0.5263277888298035},{"id":"https://openalex.org/keywords/fuzzy-logic","display_name":"Fuzzy logic","score":0.5124295353889465},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.46867284178733826},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.45783567428588867},{"id":"https://openalex.org/keywords/vector-optimization","display_name":"Vector optimization","score":0.42418718338012695},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.40973666310310364},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.1573430895805359},{"id":"https://openalex.org/keywords/multi-swarm-optimization","display_name":"Multi-swarm optimization","score":0.15354454517364502}],"concepts":[{"id":"https://openalex.org/C73555534","wikidata":"https://www.wikidata.org/wiki/Q622825","display_name":"Cluster analysis","level":2,"score":0.5872158408164978},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.5700632333755493},{"id":"https://openalex.org/C106301342","wikidata":"https://www.wikidata.org/wiki/Q4117933","display_name":"Entropy (arrow of time)","level":2,"score":0.5268981456756592},{"id":"https://openalex.org/C137836250","wikidata":"https://www.wikidata.org/wiki/Q984063","display_name":"Optimization problem","level":2,"score":0.5263277888298035},{"id":"https://openalex.org/C58166","wikidata":"https://www.wikidata.org/wiki/Q224821","display_name":"Fuzzy logic","level":2,"score":0.5124295353889465},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.46867284178733826},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.45783567428588867},{"id":"https://openalex.org/C164088818","wikidata":"https://www.wikidata.org/wiki/Q7917833","display_name":"Vector optimization","level":4,"score":0.42418718338012695},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.40973666310310364},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.1573430895805359},{"id":"https://openalex.org/C122357587","wikidata":"https://www.wikidata.org/wiki/Q6934508","display_name":"Multi-swarm optimization","level":3,"score":0.15354454517364502},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","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}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/grc.2008.4664760","is_oa":false,"landing_page_url":"https://doi.org/10.1109/grc.2008.4664760","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2008 IEEE International Conference on Granular Computing","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":8,"referenced_works":["https://openalex.org/W1584532972","https://openalex.org/W2070541424","https://openalex.org/W2099413512","https://openalex.org/W2106582507","https://openalex.org/W2106780461","https://openalex.org/W2113076747","https://openalex.org/W2278532921","https://openalex.org/W6694777023"],"related_works":["https://openalex.org/W2565276936","https://openalex.org/W2766340440","https://openalex.org/W4385713703","https://openalex.org/W4384574993","https://openalex.org/W109016340","https://openalex.org/W188711498","https://openalex.org/W2390455111","https://openalex.org/W3199277564","https://openalex.org/W4230074750","https://openalex.org/W2184300223"],"abstract_inverted_index":{"This":[0,48],"paper":[1],"presents":[2],"a":[3,19,26,38],"new":[4,20,39,73],"type":[5],"of":[6,41,86,93],"clustering":[7,74],"algorithm":[8,75,96],"by":[9,67],"using":[10,68],"tolerance":[11,14,42,64],"vector.":[12],"The":[13],"vector":[15,24],"is":[16,43,51,65,76,97],"considered":[17],"from":[18],"viewpoint":[21],"that":[22],"the":[23,59,63,69,80,87,91,94],"shows":[25],"correlation":[27],"between":[28],"each":[29],"data":[30],"and":[31,82],"cluster":[32],"centers":[33],"in":[34],"proposed":[35,95],"algorithm.":[36],"First,":[37],"concept":[40],"introduced":[44],"into":[45],"optimization":[46,49,60,88],"problem.":[47,89],"problem":[50,61],"based":[52,78],"on":[53,79],"entropy":[54],"regularized":[55],"fuzzy":[56],"c-means.":[57],"Second,":[58],"with":[62],"solved":[66],"Karush-Kuhn-Tucker":[70],"conditions.":[71],"Next,":[72],"constructed":[77],"unique":[81],"explicit":[83],"optimal":[84],"solutions":[85],"Finally,":[90],"effectiveness":[92],"verified":[98],"through":[99],"some":[100],"numerical":[101],"examples.":[102]},"counts_by_year":[],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}