{"id":"https://openalex.org/W2292048788","doi":"https://doi.org/10.1007/978-3-319-25754-9_19","title":"Matrix Approaches for Variable Precision Rough Approximations","display_name":"Matrix Approaches for Variable Precision Rough Approximations","publication_year":2015,"publication_date":"2015-01-01","ids":{"openalex":"https://openalex.org/W2292048788","doi":"https://doi.org/10.1007/978-3-319-25754-9_19","mag":"2292048788"},"language":"en","primary_location":{"id":"doi:10.1007/978-3-319-25754-9_19","is_oa":true,"landing_page_url":"https://doi.org/10.1007/978-3-319-25754-9_19","pdf_url":null,"source":{"id":"https://openalex.org/S106296714","display_name":"Lecture notes in computer science","issn_l":"0302-9743","issn":["0302-9743","1611-3349"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"book series"},"license":"cc-by-nc","license_id":"https://openalex.org/licenses/cc-by-nc","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Lecture Notes in Computer Science","raw_type":"book-chapter"},"type":"book-chapter","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://doi.org/10.1007/978-3-319-25754-9_19","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5101872364","display_name":"Guilong Liu","orcid":"https://orcid.org/0000-0001-6861-0639"},"institutions":[{"id":"https://openalex.org/I115212828","display_name":"Beijing Language and Culture University","ror":"https://ror.org/03te2zs36","country_code":"CN","type":"education","lineage":["https://openalex.org/I115212828"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Guilong Liu","raw_affiliation_strings":["School of Information Science, Beijing Language and Culture University, Beijing, 100083, China"],"affiliations":[{"raw_affiliation_string":"School of Information Science, Beijing Language and Culture University, Beijing, 100083, China","institution_ids":["https://openalex.org/I115212828"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5101872364"],"corresponding_institution_ids":["https://openalex.org/I115212828"],"apc_list":{"value":5000,"currency":"EUR","value_usd":5392},"apc_paid":{"value":5000,"currency":"EUR","value_usd":5392},"fwci":0.8512,"has_fulltext":false,"cited_by_count":5,"citation_normalized_percentile":{"value":0.73432545,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":null,"issue":null,"first_page":"214","last_page":"221"},"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/T10538","display_name":"Data Mining Algorithms and Applications","score":0.9593999981880188,"subfield":{"id":"https://openalex.org/subfields/1710","display_name":"Information Systems"},"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/T14339","display_name":"Image Processing and 3D Reconstruction","score":0.9430999755859375,"subfield":{"id":"https://openalex.org/subfields/1707","display_name":"Computer Vision and Pattern Recognition"},"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/rough-set","display_name":"Rough set","score":0.9609845876693726},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.6164646744728088},{"id":"https://openalex.org/keywords/variable","display_name":"Variable (mathematics)","score":0.5446703433990479},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.49032285809516907},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.4766274690628052},{"id":"https://openalex.org/keywords/approximations-of-\u03c0","display_name":"Approximations of \u03c0","score":0.47439172863960266},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.4564928412437439},{"id":"https://openalex.org/keywords/data-mining","display_name":"Data mining","score":0.45328453183174133},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.360534131526947},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.34150078892707825},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.09940028190612793},{"id":"https://openalex.org/keywords/materials-science","display_name":"Materials science","score":0.054803043603897095}],"concepts":[{"id":"https://openalex.org/C111012933","wikidata":"https://www.wikidata.org/wiki/Q3137210","display_name":"Rough set","level":2,"score":0.9609845876693726},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.6164646744728088},{"id":"https://openalex.org/C182365436","wikidata":"https://www.wikidata.org/wiki/Q50701","display_name":"Variable (mathematics)","level":2,"score":0.5446703433990479},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.49032285809516907},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.4766274690628052},{"id":"https://openalex.org/C193386753","wikidata":"https://www.wikidata.org/wiki/Q1130396","display_name":"Approximations of \u03c0","level":2,"score":0.47439172863960266},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4564928412437439},{"id":"https://openalex.org/C124101348","wikidata":"https://www.wikidata.org/wiki/Q172491","display_name":"Data mining","level":1,"score":0.45328453183174133},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.360534131526947},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.34150078892707825},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.09940028190612793},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.054803043603897095},{"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/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/978-3-319-25754-9_19","is_oa":true,"landing_page_url":"https://doi.org/10.1007/978-3-319-25754-9_19","pdf_url":null,"source":{"id":"https://openalex.org/S106296714","display_name":"Lecture notes in computer science","issn_l":"0302-9743","issn":["0302-9743","1611-3349"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"book series"},"license":"cc-by-nc","license_id":"https://openalex.org/licenses/cc-by-nc","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Lecture Notes in Computer Science","raw_type":"book-chapter"}],"best_oa_location":{"id":"doi:10.1007/978-3-319-25754-9_19","is_oa":true,"landing_page_url":"https://doi.org/10.1007/978-3-319-25754-9_19","pdf_url":null,"source":{"id":"https://openalex.org/S106296714","display_name":"Lecture notes in computer science","issn_l":"0302-9743","issn":["0302-9743","1611-3349"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"book series"},"license":"cc-by-nc","license_id":"https://openalex.org/licenses/cc-by-nc","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Lecture Notes in Computer Science","raw_type":"book-chapter"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":19,"referenced_works":["https://openalex.org/W1490178817","https://openalex.org/W1523763698","https://openalex.org/W1557923305","https://openalex.org/W1786569510","https://openalex.org/W1997362234","https://openalex.org/W2008761105","https://openalex.org/W2032262272","https://openalex.org/W2038801403","https://openalex.org/W2040989072","https://openalex.org/W2056172554","https://openalex.org/W2065794423","https://openalex.org/W2071725732","https://openalex.org/W2077183117","https://openalex.org/W2078975878","https://openalex.org/W2095324437","https://openalex.org/W2110787332","https://openalex.org/W2116509046","https://openalex.org/W4232953319","https://openalex.org/W4255833381"],"related_works":["https://openalex.org/W1998730025","https://openalex.org/W1985015628","https://openalex.org/W2369031945","https://openalex.org/W2204496524","https://openalex.org/W2388587252","https://openalex.org/W2354040054","https://openalex.org/W1970534408","https://openalex.org/W2350442377","https://openalex.org/W2355835716","https://openalex.org/W2390930446"],"abstract_inverted_index":{"Many":[0],"generalizations":[1],"of":[2,20,28,40,48,50],"variable":[3],"precision":[4],"rough":[5],"set":[6],"models(VPRS)":[7],"have":[8],"been":[9],"proposed":[10],"since":[11],"Ziarko":[12],"introduced":[13],"VPRS.":[14,41,51],"This":[15,42],"paper":[16],"proposes":[17],"the":[18,46],"concept":[19],"general":[21],"VPRS":[22,30],"approximations":[23,39,49],"which":[24],"unifies":[25],"earlier":[26],"definitions":[27],"variant":[29],"and":[31],"gives":[32],"an":[33],"efficient":[34],"matrix":[35],"formulae":[36,43],"for":[37],"computing":[38],"can":[44],"simplify":[45],"calculation":[47]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2017,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}