{"id":"https://openalex.org/W62522281","doi":"https://doi.org/10.1007/978-3-642-22833-9_82","title":"Completely Compact Elements and Atoms of Rough Sets","display_name":"Completely Compact Elements and Atoms of Rough Sets","publication_year":2011,"publication_date":"2011-01-01","ids":{"openalex":"https://openalex.org/W62522281","doi":"https://doi.org/10.1007/978-3-642-22833-9_82","mag":"62522281"},"language":"en","primary_location":{"id":"doi:10.1007/978-3-642-22833-9_82","is_oa":false,"landing_page_url":"https://doi.org/10.1007/978-3-642-22833-9_82","pdf_url":null,"source":{"id":"https://openalex.org/S4210208846","display_name":"Advances in intelligent and soft computing","issn_l":"1867-5662","issn":["1867-5662","1867-5670"],"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":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Advances in Intelligent and Soft Computing","raw_type":"book-chapter"},"type":"book-chapter","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/A5088183280","display_name":"Gaolin Li","orcid":null},"institutions":[{"id":"https://openalex.org/I4210141689","display_name":"Yancheng Teachers University","ror":"https://ror.org/042k5fe81","country_code":"CN","type":"education","lineage":["https://openalex.org/I4210141689"]},{"id":"https://openalex.org/I78978612","display_name":"Yangzhou University","ror":"https://ror.org/03tqb8s11","country_code":"CN","type":"education","lineage":["https://openalex.org/I78978612"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Gaolin Li","raw_affiliation_strings":["Department of Mathematics, Yancheng Teachers College, Yancheng, 224002, China","Department of Mathematics, Yangzhou University, Yangzhou, 225002, China","Department of Mathematics, Yancheng Teachers College, Yancheng, China","Department of Mathematics, Yangzhou University, Yangzhou, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Yancheng Teachers College, Yancheng, 224002, China","institution_ids":["https://openalex.org/I4210141689"]},{"raw_affiliation_string":"Department of Mathematics, Yangzhou University, Yangzhou, 225002, China","institution_ids":["https://openalex.org/I78978612"]},{"raw_affiliation_string":"Department of Mathematics, Yancheng Teachers College, Yancheng, China","institution_ids":["https://openalex.org/I4210141689"]},{"raw_affiliation_string":"Department of Mathematics, Yangzhou University, Yangzhou, China","institution_ids":["https://openalex.org/I78978612"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5110699441","display_name":"Luoshan Xu","orcid":null},"institutions":[{"id":"https://openalex.org/I78978612","display_name":"Yangzhou University","ror":"https://ror.org/03tqb8s11","country_code":"CN","type":"education","lineage":["https://openalex.org/I78978612"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Luoshan Xu","raw_affiliation_strings":["Department of Mathematics, Yangzhou University, Yangzhou, 225002, China","Department of Mathematics, Yangzhou University, Yangzhou, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Yangzhou University, Yangzhou, 225002, China","institution_ids":["https://openalex.org/I78978612"]},{"raw_affiliation_string":"Department of Mathematics, Yangzhou University, Yangzhou, China","institution_ids":["https://openalex.org/I78978612"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.04134615,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":"675","last_page":"682"},"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":0.9054999947547913,"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/T11727","display_name":"Advanced Algebra and Logic","score":0.9050999879837036,"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/mathematics","display_name":"Mathematics","score":0.6880211234092712},{"id":"https://openalex.org/keywords/equivalence-relation","display_name":"Equivalence relation","score":0.588224470615387},{"id":"https://openalex.org/keywords/pointwise","display_name":"Pointwise","score":0.5820155143737793},{"id":"https://openalex.org/keywords/rough-set","display_name":"Rough set","score":0.48936837911605835},{"id":"https://openalex.org/keywords/lattice","display_name":"Lattice (music)","score":0.482820600271225},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.47393447160720825},{"id":"https://openalex.org/keywords/distributivity","display_name":"Distributivity","score":0.47127339243888855},{"id":"https://openalex.org/keywords/algebraic-number","display_name":"Algebraic number","score":0.46977490186691284},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.46082744002342224},{"id":"https://openalex.org/keywords/distributive-property","display_name":"Distributive property","score":0.3889024555683136},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.2702042758464813},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.12480607628822327},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.09112176299095154}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6880211234092712},{"id":"https://openalex.org/C156103551","wikidata":"https://www.wikidata.org/wiki/Q130998","display_name":"Equivalence relation","level":2,"score":0.588224470615387},{"id":"https://openalex.org/C2777984123","wikidata":"https://www.wikidata.org/wiki/Q9248237","display_name":"Pointwise","level":2,"score":0.5820155143737793},{"id":"https://openalex.org/C111012933","wikidata":"https://www.wikidata.org/wiki/Q3137210","display_name":"Rough set","level":2,"score":0.48936837911605835},{"id":"https://openalex.org/C2781204021","wikidata":"https://www.wikidata.org/wiki/Q6497091","display_name":"Lattice (music)","level":2,"score":0.482820600271225},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.47393447160720825},{"id":"https://openalex.org/C138390121","wikidata":"https://www.wikidata.org/wiki/Q5283219","display_name":"Distributivity","level":3,"score":0.47127339243888855},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.46977490186691284},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.46082744002342224},{"id":"https://openalex.org/C11821877","wikidata":"https://www.wikidata.org/wiki/Q187959","display_name":"Distributive property","level":2,"score":0.3889024555683136},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.2702042758464813},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.12480607628822327},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.09112176299095154},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.0},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.0},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/978-3-642-22833-9_82","is_oa":false,"landing_page_url":"https://doi.org/10.1007/978-3-642-22833-9_82","pdf_url":null,"source":{"id":"https://openalex.org/S4210208846","display_name":"Advances in intelligent and soft computing","issn_l":"1867-5662","issn":["1867-5662","1867-5670"],"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":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Advances in Intelligent and Soft Computing","raw_type":"book-chapter"}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/10","display_name":"Reduced inequalities","score":0.47999998927116394}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":23,"referenced_works":["https://openalex.org/W116608051","https://openalex.org/W179988417","https://openalex.org/W1525647423","https://openalex.org/W1535538569","https://openalex.org/W1536630500","https://openalex.org/W1587782513","https://openalex.org/W1931213803","https://openalex.org/W1969463949","https://openalex.org/W1987251161","https://openalex.org/W2001692054","https://openalex.org/W2028095785","https://openalex.org/W2052691716","https://openalex.org/W2053749030","https://openalex.org/W2072493552","https://openalex.org/W2116509046","https://openalex.org/W2163982943","https://openalex.org/W2494528959","https://openalex.org/W2500062327","https://openalex.org/W2912565176","https://openalex.org/W3023422795","https://openalex.org/W4211007335","https://openalex.org/W4255833381","https://openalex.org/W4285719527"],"related_works":["https://openalex.org/W4235162539","https://openalex.org/W2099647936","https://openalex.org/W2094667621","https://openalex.org/W2962966399","https://openalex.org/W2611849467","https://openalex.org/W3001184693","https://openalex.org/W2389398758","https://openalex.org/W1975379066","https://openalex.org/W2330170983","https://openalex.org/W2615041368"],"abstract_inverted_index":null,"counts_by_year":[],"updated_date":"2026-08-04T08:18:43.703281","created_date":"2025-10-10T00:00:00"}
