{"id":"https://openalex.org/W2026085750","doi":"https://doi.org/10.1109/grc.2008.4664710","title":"Quick building of fuzzy equivalence matrix in granular computing","display_name":"Quick building of fuzzy equivalence matrix in granular computing","publication_year":2008,"publication_date":"2008-08-01","ids":{"openalex":"https://openalex.org/W2026085750","doi":"https://doi.org/10.1109/grc.2008.4664710","mag":"2026085750"},"language":"en","primary_location":{"id":"doi:10.1109/grc.2008.4664710","is_oa":false,"landing_page_url":"https://doi.org/10.1109/grc.2008.4664710","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/A5063277191","display_name":"Xianquan Liu","orcid":"https://orcid.org/0000-0002-4313-3677"},"institutions":[{"id":"https://openalex.org/I10535382","display_name":"Chongqing University of Posts and Telecommunications","ror":"https://ror.org/03dgaqz26","country_code":"CN","type":"education","lineage":["https://openalex.org/I10535382"]},{"id":"https://openalex.org/I4800084","display_name":"Southwest Jiaotong University","ror":"https://ror.org/00hn7w693","country_code":"CN","type":"education","lineage":["https://openalex.org/I4800084"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Xianquan Liu","raw_affiliation_strings":["Institute of Computer Science and Technology, Chongqing University of Posts and Telecommunications, Chongqing, China","School of Information Science and Technology, Southwest Jiaotong University, Chengdu, Sichuan, China"],"affiliations":[{"raw_affiliation_string":"Institute of Computer Science and Technology, Chongqing University of Posts and Telecommunications, Chongqing, China","institution_ids":["https://openalex.org/I10535382"]},{"raw_affiliation_string":"School of Information Science and Technology, Southwest Jiaotong University, Chengdu, Sichuan, China","institution_ids":["https://openalex.org/I4800084"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5031220156","display_name":"Guoyin Wang","orcid":"https://orcid.org/0000-0002-8521-5232"},"institutions":[{"id":"https://openalex.org/I10535382","display_name":"Chongqing University of Posts and Telecommunications","ror":"https://ror.org/03dgaqz26","country_code":"CN","type":"education","lineage":["https://openalex.org/I10535382"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Guoyin Wang","raw_affiliation_strings":["Institute of Computer Science and Technology, Chongqing University of Posts and Telecommunications, Chongqing, China"],"affiliations":[{"raw_affiliation_string":"Institute of Computer Science and Technology, Chongqing University of Posts and Telecommunications, Chongqing, China","institution_ids":["https://openalex.org/I10535382"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5055297909","display_name":"Qinghua Zhang","orcid":"https://orcid.org/0000-0002-6154-4656"},"institutions":[{"id":"https://openalex.org/I4800084","display_name":"Southwest Jiaotong University","ror":"https://ror.org/00hn7w693","country_code":"CN","type":"education","lineage":["https://openalex.org/I4800084"]},{"id":"https://openalex.org/I10535382","display_name":"Chongqing University of Posts and Telecommunications","ror":"https://ror.org/03dgaqz26","country_code":"CN","type":"education","lineage":["https://openalex.org/I10535382"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Qinghua Zhang","raw_affiliation_strings":["Institute of Computer Science and Technology, Chongqing University of Posts and Telecommunications, Chongqing, China","School of Information Science and Technology, Southwest Jiaotong University, Chengdu, Sichuan, China"],"affiliations":[{"raw_affiliation_string":"Institute of Computer Science and Technology, Chongqing University of Posts and Telecommunications, Chongqing, China","institution_ids":["https://openalex.org/I10535382"]},{"raw_affiliation_string":"School of Information Science and Technology, Southwest Jiaotong University, Chengdu, Sichuan, China","institution_ids":["https://openalex.org/I4800084"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5101650811","display_name":"Jun Hu","orcid":"https://orcid.org/0000-0002-2551-7204"},"institutions":[{"id":"https://openalex.org/I10535382","display_name":"Chongqing University of Posts and Telecommunications","ror":"https://ror.org/03dgaqz26","country_code":"CN","type":"education","lineage":["https://openalex.org/I10535382"]},{"id":"https://openalex.org/I149594827","display_name":"Xidian University","ror":"https://ror.org/05s92vm98","country_code":"CN","type":"education","lineage":["https://openalex.org/I149594827"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Jun Hu","raw_affiliation_strings":["Institute of Computer Science and Technology, Chongqing University of Posts and Telecommunications, Chongqing, China","School of Electronic Engineering, Xidian University, Xi'an, Shaanxi, China"],"affiliations":[{"raw_affiliation_string":"Institute of Computer Science and Technology, Chongqing University of Posts and Telecommunications, Chongqing, China","institution_ids":["https://openalex.org/I10535382"]},{"raw_affiliation_string":"School of Electronic Engineering, Xidian University, Xi'an, Shaanxi, China","institution_ids":["https://openalex.org/I149594827"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100851522","display_name":"Jiaqing Zhou","orcid":null},"institutions":[{"id":"https://openalex.org/I4800084","display_name":"Southwest Jiaotong University","ror":"https://ror.org/00hn7w693","country_code":"CN","type":"education","lineage":["https://openalex.org/I4800084"]},{"id":"https://openalex.org/I10535382","display_name":"Chongqing University of Posts and Telecommunications","ror":"https://ror.org/03dgaqz26","country_code":"CN","type":"education","lineage":["https://openalex.org/I10535382"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Jiaqing Zhou","raw_affiliation_strings":["Institute of Computer Science and Technology, Chongqing University of Posts and Telecommunications, Chongqing, China","School of Information Science and Technology, Southwest Jiaotong University, Chengdu, Sichuan, China"],"affiliations":[{"raw_affiliation_string":"Institute of Computer Science and Technology, Chongqing University of Posts and Telecommunications, Chongqing, China","institution_ids":["https://openalex.org/I10535382"]},{"raw_affiliation_string":"School of Information Science and Technology, Southwest Jiaotong University, Chengdu, Sichuan, China","institution_ids":["https://openalex.org/I4800084"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":5,"corresponding_author_ids":["https://openalex.org/A5063277191"],"corresponding_institution_ids":["https://openalex.org/I10535382","https://openalex.org/I4800084"],"apc_list":null,"apc_paid":null,"fwci":0.4233,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.66007085,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"1992","issue":null,"first_page":"466","last_page":"469"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11063","display_name":"Rough Sets and Fuzzy Logic","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"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/T11063","display_name":"Rough Sets and Fuzzy Logic","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"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/T11727","display_name":"Advanced Algebra and Logic","score":0.9955999851226807,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"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":0.9814000129699707,"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/quotient-space","display_name":"Quotient space (topology)","score":0.7844187021255493},{"id":"https://openalex.org/keywords/quotient","display_name":"Quotient","score":0.7098840475082397},{"id":"https://openalex.org/keywords/granular-computing","display_name":"Granular computing","score":0.690399706363678},{"id":"https://openalex.org/keywords/equivalence-relation","display_name":"Equivalence relation","score":0.6747662425041199},{"id":"https://openalex.org/keywords/fuzzy-logic","display_name":"Fuzzy logic","score":0.5829432010650635},{"id":"https://openalex.org/keywords/equivalence","display_name":"Equivalence (formal languages)","score":0.5790294408798218},{"id":"https://openalex.org/keywords/equivalence-class","display_name":"Equivalence class (music)","score":0.5588309168815613},{"id":"https://openalex.org/keywords/fuzzy-set","display_name":"Fuzzy set","score":0.5064836740493774},{"id":"https://openalex.org/keywords/quotient-algebra","display_name":"Quotient algebra","score":0.4830816090106964},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.46066561341285706},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.45322877168655396},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.43434953689575195},{"id":"https://openalex.org/keywords/fuzzy-set-operations","display_name":"Fuzzy set operations","score":0.42010441422462463},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.40518876910209656},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.4006916582584381},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.38654160499572754},{"id":"https://openalex.org/keywords/rough-set","display_name":"Rough set","score":0.28159600496292114},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.2629472017288208},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.20339196920394897}],"concepts":[{"id":"https://openalex.org/C40753290","wikidata":"https://www.wikidata.org/wiki/Q1139111","display_name":"Quotient space (topology)","level":3,"score":0.7844187021255493},{"id":"https://openalex.org/C199422724","wikidata":"https://www.wikidata.org/wiki/Q41118","display_name":"Quotient","level":2,"score":0.7098840475082397},{"id":"https://openalex.org/C17209119","wikidata":"https://www.wikidata.org/wiki/Q5596712","display_name":"Granular computing","level":3,"score":0.690399706363678},{"id":"https://openalex.org/C156103551","wikidata":"https://www.wikidata.org/wiki/Q130998","display_name":"Equivalence relation","level":2,"score":0.6747662425041199},{"id":"https://openalex.org/C58166","wikidata":"https://www.wikidata.org/wiki/Q224821","display_name":"Fuzzy logic","level":2,"score":0.5829432010650635},{"id":"https://openalex.org/C2780069185","wikidata":"https://www.wikidata.org/wiki/Q7977945","display_name":"Equivalence (formal languages)","level":2,"score":0.5790294408798218},{"id":"https://openalex.org/C2777044963","wikidata":"https://www.wikidata.org/wiki/Q5384707","display_name":"Equivalence class (music)","level":2,"score":0.5588309168815613},{"id":"https://openalex.org/C42011625","wikidata":"https://www.wikidata.org/wiki/Q1055058","display_name":"Fuzzy set","level":3,"score":0.5064836740493774},{"id":"https://openalex.org/C51287006","wikidata":"https://www.wikidata.org/wiki/Q63565120","display_name":"Quotient algebra","level":4,"score":0.4830816090106964},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.46066561341285706},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.45322877168655396},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.43434953689575195},{"id":"https://openalex.org/C148671577","wikidata":"https://www.wikidata.org/wiki/Q5511133","display_name":"Fuzzy set operations","level":4,"score":0.42010441422462463},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.40518876910209656},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.4006916582584381},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.38654160499572754},{"id":"https://openalex.org/C111012933","wikidata":"https://www.wikidata.org/wiki/Q3137210","display_name":"Rough set","level":2,"score":0.28159600496292114},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.2629472017288208},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.20339196920394897},{"id":"https://openalex.org/C14394260","wikidata":"https://www.wikidata.org/wiki/Q4723980","display_name":"Algebra representation","level":3,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/grc.2008.4664710","is_oa":false,"landing_page_url":"https://doi.org/10.1109/grc.2008.4664710","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":13,"referenced_works":["https://openalex.org/W1521708037","https://openalex.org/W1655990431","https://openalex.org/W1829880586","https://openalex.org/W2019508321","https://openalex.org/W2019529630","https://openalex.org/W2034094790","https://openalex.org/W2055375485","https://openalex.org/W2129559955","https://openalex.org/W2147061787","https://openalex.org/W2153676086","https://openalex.org/W2189423551","https://openalex.org/W4239045871","https://openalex.org/W6987621453"],"related_works":["https://openalex.org/W2977467206","https://openalex.org/W4311904535","https://openalex.org/W2362545535","https://openalex.org/W4298221493","https://openalex.org/W2621644573","https://openalex.org/W3122722170","https://openalex.org/W4251197167","https://openalex.org/W1576779296","https://openalex.org/W2388332169","https://openalex.org/W1974325786"],"abstract_inverted_index":{"The":[0],"fuzzy":[1,14,31,44,55],"quotient":[2,10],"space":[3,11,65],"model":[4,8],"is":[5,28,50,67],"a":[6],"hybrid":[7],"between":[9],"theory":[12],"and":[13,26,61,64],"set":[15],"theory,":[16],"which":[17],"are":[18,35],"two":[19],"important":[20],"methods":[21],"in":[22,58],"granular":[23],"computing":[24,42],"models,":[25],"it":[27],"based":[29],"on":[30],"equivalence":[32,45,56],"relation.":[33],"There":[34],"many":[36],"algorithms":[37,88],"with":[38],"high":[39],"complexity":[40,66],"for":[41,85,89],"the":[43,54],"matrices.":[46],"A":[47],"new":[48],"algorithm":[49],"proposed":[51],"to":[52],"compute":[53],"matrices":[57],"this":[59,77],"paper,":[60],"its":[62],"time":[63],"o(n":[68],"<sup":[69],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[70],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">2</sup>":[71],").":[72],"An":[73],"example":[74],"also":[75],"illustrates":[76],"algorithm.":[78],"This":[79],"result":[80],"would":[81],"be":[82],"very":[83],"helpful":[84],"designing":[86],"efficient":[87],"huge":[90],"data":[91],"processing.":[92]},"counts_by_year":[],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}