{"id":"https://openalex.org/W2162912744","doi":"https://doi.org/10.1109/grc.2012.6468665","title":"Covering-based approximation operators by boolean matrix","display_name":"Covering-based approximation operators by boolean matrix","publication_year":2012,"publication_date":"2012-08-01","ids":{"openalex":"https://openalex.org/W2162912744","doi":"https://doi.org/10.1109/grc.2012.6468665","mag":"2162912744"},"language":"en","primary_location":{"id":"doi:10.1109/grc.2012.6468665","is_oa":false,"landing_page_url":"https://doi.org/10.1109/grc.2012.6468665","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/A5101936916","display_name":"Qingyin Li","orcid":null},"institutions":[{"id":"https://openalex.org/I9356336","display_name":"Zhangzhou Normal University","ror":"https://ror.org/02vj1vm13","country_code":"CN","type":"education","lineage":["https://openalex.org/I9356336"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Qingyin Li","raw_affiliation_strings":["Laboratory of Granular Computing, Zhangzhou Normal University, Zhangzhou, China"],"affiliations":[{"raw_affiliation_string":"Laboratory of Granular Computing, Zhangzhou Normal University, Zhangzhou, China","institution_ids":["https://openalex.org/I9356336"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5078911343","display_name":"William Zhu","orcid":"https://orcid.org/0000-0001-8898-9244"},"institutions":[{"id":"https://openalex.org/I9356336","display_name":"Zhangzhou Normal University","ror":"https://ror.org/02vj1vm13","country_code":"CN","type":"education","lineage":["https://openalex.org/I9356336"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"William Zhu","raw_affiliation_strings":["Laboratory of Granular Computing, Zhangzhou Normal University, Zhangzhou, China"],"affiliations":[{"raw_affiliation_string":"Laboratory of Granular Computing, Zhangzhou Normal University, Zhangzhou, China","institution_ids":["https://openalex.org/I9356336"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5101936916"],"corresponding_institution_ids":["https://openalex.org/I9356336"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.17289838,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"33","issue":null,"first_page":"236","last_page":"241"},"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/T11245","display_name":"Advanced Numerical Analysis Techniques","score":0.9496999979019165,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10181","display_name":"Natural Language Processing Techniques","score":0.9129999876022339,"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/mathematics","display_name":"Mathematics","score":0.6229233741760254},{"id":"https://openalex.org/keywords/generalization","display_name":"Generalization","score":0.6156681776046753},{"id":"https://openalex.org/keywords/approximation-algorithm","display_name":"Approximation algorithm","score":0.5629106163978577},{"id":"https://openalex.org/keywords/approximation-theory","display_name":"Approximation theory","score":0.5438514351844788},{"id":"https://openalex.org/keywords/operator","display_name":"Operator (biology)","score":0.5349783897399902},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.5053873062133789},{"id":"https://openalex.org/keywords/spouges-approximation","display_name":"Spouge's approximation","score":0.5011231899261475},{"id":"https://openalex.org/keywords/matrix-multiplication","display_name":"Matrix multiplication","score":0.4265679121017456},{"id":"https://openalex.org/keywords/operator-theory","display_name":"Operator theory","score":0.4254564940929413},{"id":"https://openalex.org/keywords/type","display_name":"Type (biology)","score":0.420623779296875},{"id":"https://openalex.org/keywords/approximation-error","display_name":"Approximation error","score":0.4097459018230438},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.35686811804771423},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.35648518800735474},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.2682744562625885},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.24843141436576843},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.240828275680542},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.12384364008903503}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6229233741760254},{"id":"https://openalex.org/C177148314","wikidata":"https://www.wikidata.org/wiki/Q170084","display_name":"Generalization","level":2,"score":0.6156681776046753},{"id":"https://openalex.org/C148764684","wikidata":"https://www.wikidata.org/wiki/Q621751","display_name":"Approximation algorithm","level":2,"score":0.5629106163978577},{"id":"https://openalex.org/C145242015","wikidata":"https://www.wikidata.org/wiki/Q774123","display_name":"Approximation theory","level":2,"score":0.5438514351844788},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.5349783897399902},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.5053873062133789},{"id":"https://openalex.org/C62376455","wikidata":"https://www.wikidata.org/wiki/Q935210","display_name":"Spouge's approximation","level":3,"score":0.5011231899261475},{"id":"https://openalex.org/C17349429","wikidata":"https://www.wikidata.org/wiki/Q1049914","display_name":"Matrix multiplication","level":3,"score":0.4265679121017456},{"id":"https://openalex.org/C43929395","wikidata":"https://www.wikidata.org/wiki/Q1198874","display_name":"Operator theory","level":2,"score":0.4254564940929413},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.420623779296875},{"id":"https://openalex.org/C122383733","wikidata":"https://www.wikidata.org/wiki/Q865920","display_name":"Approximation error","level":2,"score":0.4097459018230438},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.35686811804771423},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.35648518800735474},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.2682744562625885},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.24843141436576843},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.240828275680542},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.12384364008903503},{"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/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0},{"id":"https://openalex.org/C158448853","wikidata":"https://www.wikidata.org/wiki/Q425218","display_name":"Repressor","level":4,"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/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C86339819","wikidata":"https://www.wikidata.org/wiki/Q407384","display_name":"Transcription factor","level":3,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","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},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C84114770","wikidata":"https://www.wikidata.org/wiki/Q46344","display_name":"Quantum","level":2,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/grc.2012.6468665","is_oa":false,"landing_page_url":"https://doi.org/10.1109/grc.2012.6468665","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":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":38,"referenced_works":["https://openalex.org/W1506662207","https://openalex.org/W1523763698","https://openalex.org/W1591618909","https://openalex.org/W1889630404","https://openalex.org/W1973375121","https://openalex.org/W1973689533","https://openalex.org/W1978202330","https://openalex.org/W1982790962","https://openalex.org/W1983426508","https://openalex.org/W1997362234","https://openalex.org/W2007247975","https://openalex.org/W2007262119","https://openalex.org/W2008761105","https://openalex.org/W2024638676","https://openalex.org/W2031978194","https://openalex.org/W2033857698","https://openalex.org/W2041596646","https://openalex.org/W2042475680","https://openalex.org/W2045260678","https://openalex.org/W2053749030","https://openalex.org/W2075340829","https://openalex.org/W2078975878","https://openalex.org/W2082266564","https://openalex.org/W2088499853","https://openalex.org/W2095290023","https://openalex.org/W2119343539","https://openalex.org/W2134866037","https://openalex.org/W2165267798","https://openalex.org/W2244247816","https://openalex.org/W2305735113","https://openalex.org/W2340020088","https://openalex.org/W2392673480","https://openalex.org/W4255833381","https://openalex.org/W6646232809","https://openalex.org/W6652154569","https://openalex.org/W6661024302","https://openalex.org/W6677883485","https://openalex.org/W7052012358"],"related_works":["https://openalex.org/W1970691912","https://openalex.org/W2737349826","https://openalex.org/W2365442605","https://openalex.org/W2014137052","https://openalex.org/W4318613422","https://openalex.org/W2025555457","https://openalex.org/W4254073641","https://openalex.org/W2044115164","https://openalex.org/W2096450101","https://openalex.org/W2108297731"],"abstract_inverted_index":{"Covering-based":[0],"rough":[1,10],"approximation":[2,11,43,58,80,91,119,130],"space":[3],"is":[4,14,93,99],"an":[5],"important":[6],"generalization":[7],"of":[8,41,57,68,75,79,118,127],"classical":[9,18],"space.":[12],"Matrix":[13],"not":[15],"only":[16],"a":[17,24,102,106,137],"field":[19],"in":[20,27],"mathematics,":[21],"but":[22],"also":[23],"powerful":[25],"tool":[26],"computer":[28],"science.":[29],"Recently,":[30],"boolean":[31,69],"matrices":[32,50],"have":[33],"been":[34],"employed":[35],"to":[36,51,123],"define":[37],"the":[38,53,76,112,115,125],"sixth":[39],"type":[40,78,117],"covering-based":[42,89,142],"operators.":[44,59],"In":[45],"this":[46],"paper,":[47],"we":[48],"use":[49],"describe":[52],"other":[54],"five":[55],"types":[56,67],"These":[60,108],"descriptions":[61,74,110],"can":[62],"be":[63],"obtained":[64],"via":[65],"two":[66],"product":[70],"operations.":[71],"The":[72,87],"equivalent":[73,109],"first":[77,116],"operators":[81,120,131],"with":[82],"indiscernible":[83],"neighborhood":[84],"are":[85,121],"studied.":[86],"fourth":[88,113],"upper":[90],"operator":[92],"described":[94],"by":[95,105,132],"predecessor":[96],"neighborhood,":[97],"which":[98],"generated":[100],"from":[101],"relation":[103],"induced":[104],"covering.":[107],"about":[111],"and":[114],"used":[122],"obtain":[124],"representations":[126],"these":[128],"three":[129],"matrices.":[133],"This":[134],"work":[135],"provides":[136],"more":[138],"general":[139],"approach":[140],"for":[141],"approximations":[143],"through":[144],"matrix.":[145]},"counts_by_year":[],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
