{"id":"https://openalex.org/W2070064710","doi":"https://doi.org/10.1109/grc.2009.5255022","title":"Generalized fuzzy equivalent relations","display_name":"Generalized fuzzy equivalent relations","publication_year":2009,"publication_date":"2009-08-01","ids":{"openalex":"https://openalex.org/W2070064710","doi":"https://doi.org/10.1109/grc.2009.5255022","mag":"2070064710"},"language":"en","primary_location":{"id":"doi:10.1109/grc.2009.5255022","is_oa":false,"landing_page_url":"https://doi.org/10.1109/grc.2009.5255022","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2009 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/A5102091769","display_name":"Xue-hai Yuan","orcid":null},"institutions":[{"id":"https://openalex.org/I4210092944","display_name":"Dalian University","ror":"https://ror.org/00g2ypp58","country_code":"CN","type":"education","lineage":["https://openalex.org/I4210092944"]},{"id":"https://openalex.org/I27357992","display_name":"Dalian University of Technology","ror":"https://ror.org/023hj5876","country_code":"CN","type":"education","lineage":["https://openalex.org/I27357992"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Xue-Hai Yuan","raw_affiliation_strings":["School of Electronic and Information Engineering, Dalian University of Technology, Dalian, China","School of Electronic and Information Engineering, Dalian University of Technology, 116024, China"],"affiliations":[{"raw_affiliation_string":"School of Electronic and Information Engineering, Dalian University of Technology, Dalian, China","institution_ids":["https://openalex.org/I4210092944","https://openalex.org/I27357992"]},{"raw_affiliation_string":"School of Electronic and Information Engineering, Dalian University of Technology, 116024, China","institution_ids":["https://openalex.org/I4210092944","https://openalex.org/I27357992"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100642285","display_name":"Hongxing Li","orcid":"https://orcid.org/0000-0001-9251-6079"},"institutions":[{"id":"https://openalex.org/I27357992","display_name":"Dalian University of Technology","ror":"https://ror.org/023hj5876","country_code":"CN","type":"education","lineage":["https://openalex.org/I27357992"]},{"id":"https://openalex.org/I4210092944","display_name":"Dalian University","ror":"https://ror.org/00g2ypp58","country_code":"CN","type":"education","lineage":["https://openalex.org/I4210092944"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Hong-xing Li","raw_affiliation_strings":["School of Electronic and Information Engineering, Dalian University of Technology, Dalian, China","School of Electronic and Information Engineering, Dalian University of Technology, 116024, China"],"affiliations":[{"raw_affiliation_string":"School of Electronic and Information Engineering, Dalian University of Technology, Dalian, China","institution_ids":["https://openalex.org/I4210092944","https://openalex.org/I27357992"]},{"raw_affiliation_string":"School of Electronic and Information Engineering, Dalian University of Technology, 116024, China","institution_ids":["https://openalex.org/I4210092944","https://openalex.org/I27357992"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5102091769"],"corresponding_institution_ids":["https://openalex.org/I27357992","https://openalex.org/I4210092944"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.16180884,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"37","issue":null,"first_page":"739","last_page":"742"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11671","display_name":"Fuzzy and Soft Set Theory","score":0.9977999925613403,"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/T11671","display_name":"Fuzzy and Soft Set Theory","score":0.9977999925613403,"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/T10050","display_name":"Multi-Criteria Decision Making","score":0.9947999715805054,"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/T11727","display_name":"Advanced Algebra and Logic","score":0.9868000149726868,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/relation","display_name":"Relation (database)","score":0.8213704824447632},{"id":"https://openalex.org/keywords/fuzzy-logic","display_name":"Fuzzy logic","score":0.7171374559402466},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6922721266746521},{"id":"https://openalex.org/keywords/lambda","display_name":"Lambda","score":0.5113343596458435},{"id":"https://openalex.org/keywords/fuzzy-set","display_name":"Fuzzy set","score":0.4761357605457306},{"id":"https://openalex.org/keywords/fuzzy-number","display_name":"Fuzzy number","score":0.41055387258529663},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4083445072174072},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.3122731149196625},{"id":"https://openalex.org/keywords/data-mining","display_name":"Data mining","score":0.25376924872398376},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.22926852107048035}],"concepts":[{"id":"https://openalex.org/C25343380","wikidata":"https://www.wikidata.org/wiki/Q277521","display_name":"Relation (database)","level":2,"score":0.8213704824447632},{"id":"https://openalex.org/C58166","wikidata":"https://www.wikidata.org/wiki/Q224821","display_name":"Fuzzy logic","level":2,"score":0.7171374559402466},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6922721266746521},{"id":"https://openalex.org/C2778113609","wikidata":"https://www.wikidata.org/wiki/Q10897","display_name":"Lambda","level":2,"score":0.5113343596458435},{"id":"https://openalex.org/C42011625","wikidata":"https://www.wikidata.org/wiki/Q1055058","display_name":"Fuzzy set","level":3,"score":0.4761357605457306},{"id":"https://openalex.org/C1883856","wikidata":"https://www.wikidata.org/wiki/Q3407463","display_name":"Fuzzy number","level":4,"score":0.41055387258529663},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4083445072174072},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.3122731149196625},{"id":"https://openalex.org/C124101348","wikidata":"https://www.wikidata.org/wiki/Q172491","display_name":"Data mining","level":1,"score":0.25376924872398376},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.22926852107048035},{"id":"https://openalex.org/C120665830","wikidata":"https://www.wikidata.org/wiki/Q14620","display_name":"Optics","level":1,"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:10.1109/grc.2009.5255022","is_oa":false,"landing_page_url":"https://doi.org/10.1109/grc.2009.5255022","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2009 IEEE International Conference on Granular Computing","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[{"display_name":"Sustainable cities and communities","id":"https://metadata.un.org/sdg/11","score":0.5099999904632568}],"awards":[],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":17,"referenced_works":["https://openalex.org/W648107711","https://openalex.org/W1928359990","https://openalex.org/W1967830768","https://openalex.org/W1969034054","https://openalex.org/W1984050637","https://openalex.org/W1987005259","https://openalex.org/W2015068234","https://openalex.org/W2029821599","https://openalex.org/W2076516296","https://openalex.org/W2094223942","https://openalex.org/W2119562573","https://openalex.org/W2141151134","https://openalex.org/W2160642493","https://openalex.org/W4210778630","https://openalex.org/W4302124982","https://openalex.org/W6640375979","https://openalex.org/W6683408593"],"related_works":["https://openalex.org/W2951695430","https://openalex.org/W4234874385","https://openalex.org/W2541537839","https://openalex.org/W1486684451","https://openalex.org/W2116249946","https://openalex.org/W2801459815","https://openalex.org/W2099285375","https://openalex.org/W4361273540","https://openalex.org/W4361984403","https://openalex.org/W4317826560"],"abstract_inverted_index":{"In":[0],"the":[1,4,7,16,28,37,57,62,69,77,102],"paper,":[2],"by":[3],"use":[5],"of":[6,18],"neighborhood":[8],"relations":[9],"between":[10],"fuzzy":[11,14],"points":[12],"and":[13,47,68,93],"relations,":[15],"concept":[17],"(betamacr,alphamacr)-fuzzy":[19],"equivalent":[20,40,45,51,60,66,74,80,90,111],"relation":[21,46,67,75,91,104],"is":[22,86,109],"presented.":[23],"Firstly,":[24],"we":[25,54],"derived":[26],"that":[27,56,84],"acceptable":[29],"non-trivial":[30],"concepts":[31],"obtained":[32],"in":[33],"this":[34],"manner":[35],"are":[36],"(isin,":[38,42,58,63],"isin)-fuzzy":[39,59],"relation,":[41,61],"isin":[43,64,99],"Vq)-fuzzy":[44,50,65],"(isinmacr,":[48,70],"isinmacr":[49,71],"relation.":[52,81,112],"Secondly,":[53],"generalized":[55],"V":[72],"qmacr)-fuzzy":[73],"to":[76],"(lambda,":[78,88,100],"mu]-fuzzy":[79,89],"We":[82],"proved":[83],"R":[85,105],"a":[87,110],"if":[92],"only":[94],"if,":[95],"for":[96],"any":[97],"t":[98],"mu],":[101],"cut":[103],"<sub":[106],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[107],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">t</sub>":[108]},"counts_by_year":[],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}