{"id":"https://openalex.org/W2025905372","doi":"https://doi.org/10.1109/grc.2012.6468666","title":"Rough fuzzy subspaces based on subspaces in the vector space","display_name":"Rough fuzzy subspaces based on subspaces in the vector space","publication_year":2012,"publication_date":"2012-08-01","ids":{"openalex":"https://openalex.org/W2025905372","doi":"https://doi.org/10.1109/grc.2012.6468666","mag":"2025905372"},"language":"en","primary_location":{"id":"doi:10.1109/grc.2012.6468666","is_oa":false,"landing_page_url":"https://doi.org/10.1109/grc.2012.6468666","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2012 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/A5047354828","display_name":"Mingfen Wu","orcid":"https://orcid.org/0000-0002-2761-2299"},"institutions":[{"id":"https://openalex.org/I19820366","display_name":"Chinese Academy of Sciences","ror":"https://ror.org/034t30j35","country_code":"CN","type":"funder","lineage":["https://openalex.org/I19820366"]},{"id":"https://openalex.org/I4210151615","display_name":"Wuyi University","ror":"https://ror.org/0488wz367","country_code":"CN","type":"education","lineage":["https://openalex.org/I4210151615"]},{"id":"https://openalex.org/I4210090176","display_name":"Institute of Computing Technology","ror":"https://ror.org/0090r4d87","country_code":"CN","type":"facility","lineage":["https://openalex.org/I19820366","https://openalex.org/I4210090176"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Mingfen Wu","raw_affiliation_strings":["Key Laboratory of Intelligent Information Processing, Institute of Computing Technology, Chinese Academy of Sciences, Beijing, China","School of Computer Science, Wuyi University, Guangdong, China"],"affiliations":[{"raw_affiliation_string":"Key Laboratory of Intelligent Information Processing, Institute of Computing Technology, Chinese Academy of Sciences, Beijing, China","institution_ids":["https://openalex.org/I4210090176","https://openalex.org/I19820366"]},{"raw_affiliation_string":"School of Computer Science, Wuyi University, Guangdong, China","institution_ids":["https://openalex.org/I4210151615"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100357748","display_name":"Tao Chen","orcid":"https://orcid.org/0000-0002-3941-1603"},"institutions":[{"id":"https://openalex.org/I98834328","display_name":"Wuyi University","ror":"https://ror.org/059djzq42","country_code":"CN","type":"education","lineage":["https://openalex.org/I98834328"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Tao Chen","raw_affiliation_strings":["School of Computer Science, Wuyi University, China"],"affiliations":[{"raw_affiliation_string":"School of Computer Science, Wuyi University, China","institution_ids":["https://openalex.org/I98834328"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5047354828"],"corresponding_institution_ids":["https://openalex.org/I19820366","https://openalex.org/I4210090176","https://openalex.org/I4210151615"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.10097179,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"176","issue":null,"first_page":"400","last_page":"405"},"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"}}],"keywords":[{"id":"https://openalex.org/keywords/linear-subspace","display_name":"Linear subspace","score":0.8788555860519409},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7280213236808777},{"id":"https://openalex.org/keywords/fuzzy-set","display_name":"Fuzzy set","score":0.5695945620536804},{"id":"https://openalex.org/keywords/subspace-topology","display_name":"Subspace topology","score":0.5641859173774719},{"id":"https://openalex.org/keywords/fuzzy-logic","display_name":"Fuzzy logic","score":0.5294515490531921},{"id":"https://openalex.org/keywords/fuzzy-set-operations","display_name":"Fuzzy set operations","score":0.511086106300354},{"id":"https://openalex.org/keywords/vector-space","display_name":"Vector space","score":0.5097100734710693},{"id":"https://openalex.org/keywords/fuzzy-classification","display_name":"Fuzzy classification","score":0.5094016194343567},{"id":"https://openalex.org/keywords/fuzzy-number","display_name":"Fuzzy number","score":0.5070207118988037},{"id":"https://openalex.org/keywords/fuzzy-subalgebra","display_name":"Fuzzy subalgebra","score":0.49199387431144714},{"id":"https://openalex.org/keywords/rough-set","display_name":"Rough set","score":0.47591835260391235},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.38252657651901245},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.3620620667934418},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.24752551317214966},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.23521438241004944},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.19420063495635986},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.11810031533241272}],"concepts":[{"id":"https://openalex.org/C12362212","wikidata":"https://www.wikidata.org/wiki/Q728435","display_name":"Linear subspace","level":2,"score":0.8788555860519409},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7280213236808777},{"id":"https://openalex.org/C42011625","wikidata":"https://www.wikidata.org/wiki/Q1055058","display_name":"Fuzzy set","level":3,"score":0.5695945620536804},{"id":"https://openalex.org/C32834561","wikidata":"https://www.wikidata.org/wiki/Q660730","display_name":"Subspace topology","level":2,"score":0.5641859173774719},{"id":"https://openalex.org/C58166","wikidata":"https://www.wikidata.org/wiki/Q224821","display_name":"Fuzzy logic","level":2,"score":0.5294515490531921},{"id":"https://openalex.org/C148671577","wikidata":"https://www.wikidata.org/wiki/Q5511133","display_name":"Fuzzy set operations","level":4,"score":0.511086106300354},{"id":"https://openalex.org/C13336665","wikidata":"https://www.wikidata.org/wiki/Q125977","display_name":"Vector space","level":2,"score":0.5097100734710693},{"id":"https://openalex.org/C127385683","wikidata":"https://www.wikidata.org/wiki/Q1475696","display_name":"Fuzzy classification","level":4,"score":0.5094016194343567},{"id":"https://openalex.org/C1883856","wikidata":"https://www.wikidata.org/wiki/Q3407463","display_name":"Fuzzy number","level":4,"score":0.5070207118988037},{"id":"https://openalex.org/C115740575","wikidata":"https://www.wikidata.org/wiki/Q5511136","display_name":"Fuzzy subalgebra","level":5,"score":0.49199387431144714},{"id":"https://openalex.org/C111012933","wikidata":"https://www.wikidata.org/wiki/Q3137210","display_name":"Rough set","level":2,"score":0.47591835260391235},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.38252657651901245},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.3620620667934418},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.24752551317214966},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.23521438241004944},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.19420063495635986},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.11810031533241272}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/grc.2012.6468666","is_oa":false,"landing_page_url":"https://doi.org/10.1109/grc.2012.6468666","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2012 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":21,"referenced_works":["https://openalex.org/W1557923305","https://openalex.org/W1964228588","https://openalex.org/W1973375121","https://openalex.org/W1976043415","https://openalex.org/W1978202330","https://openalex.org/W1978787534","https://openalex.org/W2007638857","https://openalex.org/W2024133240","https://openalex.org/W2027654459","https://openalex.org/W2043904881","https://openalex.org/W2049730750","https://openalex.org/W2050628546","https://openalex.org/W2066953061","https://openalex.org/W2075377471","https://openalex.org/W2078975878","https://openalex.org/W2362080168","https://openalex.org/W2506703326","https://openalex.org/W2570343052","https://openalex.org/W4211007335","https://openalex.org/W4255833381","https://openalex.org/W6669175316"],"related_works":["https://openalex.org/W2466052371","https://openalex.org/W1489009679","https://openalex.org/W2037428035","https://openalex.org/W2120855914","https://openalex.org/W2141926946","https://openalex.org/W2366798457","https://openalex.org/W2586653035","https://openalex.org/W2893993940","https://openalex.org/W2121560876","https://openalex.org/W1561699096"],"abstract_inverted_index":{"Rough":[0],"set":[1,5,12],"theory":[2,6],"and":[3,20,37,66,102,109,126,133,156,168],"fuzzy":[4,26,56,76,80,95,114,120,131,136,146,152,160,165],"are":[7,162],"complementary":[8],"generalizations":[9],"of":[10,33,59,70,90,94,106,113,122,138,158],"classical":[11],"theory.This":[13],"paper":[14],"concerns":[15],"with":[16,97],"rough":[17,25,130,135,151,164],"sets,fuzzy":[18],"sets":[19,27],"vector":[21,35,46,61,84,124,140],"spaces.We":[22],"construct":[23,73],"a":[24,31,34,45,52,64,68,83,100,145,150],"model":[28],"based":[29],"on":[30,119],"congruence":[32],"space":[36,47,62],"it":[38],"is":[39,148],"assumed":[40],"that":[41,144],"the":[42,60,74,91,107,110,123,128,134,139,154],"knowledge":[43],"about":[44],"should":[48],"be":[49],"restricted":[50],"by":[51],"congruence.Firstly,":[53],"we":[54,87,117],"research":[55],"subs":[57,166],"paces":[58,167],"over":[63],"field,":[65],"get":[67],"series":[69],"properties.":[71],"Specifically,we":[72],"minimum":[75],"subspace":[77,147],"containing":[78],"two":[79,159],"subspaces":[81,121,132,137,161],"in":[82],"space.":[85,141],"Secondly,":[86],"define":[88,127],"concepts":[89],"lower(upper)":[92,129],"approximations":[93,112],"subsets":[96],"respect":[98],"to":[99],"subspace,":[101,153],"give":[103],"some":[104],"properties":[105],"lower":[108],"upper":[111],"subsets.":[115],"Finally,":[116],"focus":[118],"space,":[125],"We":[142],"obtain":[143],"certainly":[149],"intersection":[155],"sum":[157],"also":[163],"other":[169],"valuable":[170],"results.":[171]},"counts_by_year":[],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
