{"id":"https://openalex.org/W1963536179","doi":"https://doi.org/10.1155/2014/183621","title":"Geometric Lattice Structure of Covering and Its Application to Attribute Reduction through Matroids","display_name":"Geometric Lattice Structure of Covering and Its Application to Attribute Reduction through Matroids","publication_year":2014,"publication_date":"2014-01-01","ids":{"openalex":"https://openalex.org/W1963536179","doi":"https://doi.org/10.1155/2014/183621","mag":"1963536179"},"language":"en","primary_location":{"id":"doi:10.1155/2014/183621","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2014/183621","pdf_url":"https://downloads.hindawi.com/journals/jam/2014/183621.pdf","source":{"id":"https://openalex.org/S190082376","display_name":"Journal of Applied Mathematics","issn_l":"1110-757X","issn":["1110-757X","1687-0042"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Applied Mathematics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://downloads.hindawi.com/journals/jam/2014/183621.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5101599930","display_name":"Aiping Huang","orcid":"https://orcid.org/0000-0002-6354-9039"},"institutions":[{"id":"https://openalex.org/I9356336","display_name":"Minnan 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":"Aiping Huang","raw_affiliation_strings":["Lab of Granular Computing, Minnan Normal University, Zhangzhou 363000, China","Lab of Granular Computing, Minnan Normal University, Zhangzhou, 363000, China"],"raw_orcid":"https://orcid.org/0000-0002-6354-9039","affiliations":[{"raw_affiliation_string":"Lab of Granular Computing, Minnan Normal University, Zhangzhou 363000, China","institution_ids":["https://openalex.org/I9356336"]},{"raw_affiliation_string":"Lab of Granular Computing, Minnan Normal University, Zhangzhou, 363000, 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":"Minnan 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":"William Zhu","raw_affiliation_strings":["Lab of Granular Computing, Minnan Normal University, Zhangzhou 363000, China","Lab of Granular Computing, Minnan Normal University, Zhangzhou, 363000, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Lab of Granular Computing, Minnan Normal University, Zhangzhou 363000, China","institution_ids":["https://openalex.org/I9356336"]},{"raw_affiliation_string":"Lab of Granular Computing, Minnan Normal University, Zhangzhou, 363000, China","institution_ids":["https://openalex.org/I9356336"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5078911343"],"corresponding_institution_ids":["https://openalex.org/I9356336"],"apc_list":{"value":1050,"currency":"USD","value_usd":1050},"apc_paid":{"value":1050,"currency":"USD","value_usd":1050},"fwci":1.0473,"has_fulltext":true,"cited_by_count":3,"citation_normalized_percentile":{"value":0.76027174,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":96},"biblio":{"volume":"2014","issue":null,"first_page":"1","last_page":"8"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11063","display_name":"Rough Sets and Fuzzy Logic","score":1.0,"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":1.0,"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":0.9399999976158142,"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/T11106","display_name":"Data Management and Algorithms","score":0.9096999764442444,"subfield":{"id":"https://openalex.org/subfields/1711","display_name":"Signal Processing"},"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/matroid","display_name":"Matroid","score":0.932732343673706},{"id":"https://openalex.org/keywords/lattice","display_name":"Lattice (music)","score":0.6659920811653137},{"id":"https://openalex.org/keywords/reduction","display_name":"Reduction (mathematics)","score":0.5478295683860779},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5322976112365723},{"id":"https://openalex.org/keywords/rough-set","display_name":"Rough set","score":0.5006279945373535},{"id":"https://openalex.org/keywords/lattice-reduction","display_name":"Lattice reduction","score":0.4971201717853546},{"id":"https://openalex.org/keywords/greedy-algorithm","display_name":"Greedy algorithm","score":0.48900115489959717},{"id":"https://openalex.org/keywords/geometric-data-analysis","display_name":"Geometric data analysis","score":0.4203836917877197},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3948499858379364},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.33994168043136597},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3102848529815674},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.18640118837356567},{"id":"https://openalex.org/keywords/data-mining","display_name":"Data mining","score":0.17153513431549072}],"concepts":[{"id":"https://openalex.org/C106286213","wikidata":"https://www.wikidata.org/wiki/Q898572","display_name":"Matroid","level":2,"score":0.932732343673706},{"id":"https://openalex.org/C2781204021","wikidata":"https://www.wikidata.org/wiki/Q6497091","display_name":"Lattice (music)","level":2,"score":0.6659920811653137},{"id":"https://openalex.org/C111335779","wikidata":"https://www.wikidata.org/wiki/Q3454686","display_name":"Reduction (mathematics)","level":2,"score":0.5478295683860779},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5322976112365723},{"id":"https://openalex.org/C111012933","wikidata":"https://www.wikidata.org/wiki/Q3137210","display_name":"Rough set","level":2,"score":0.5006279945373535},{"id":"https://openalex.org/C44274781","wikidata":"https://www.wikidata.org/wiki/Q6497132","display_name":"Lattice reduction","level":4,"score":0.4971201717853546},{"id":"https://openalex.org/C51823790","wikidata":"https://www.wikidata.org/wiki/Q504353","display_name":"Greedy algorithm","level":2,"score":0.48900115489959717},{"id":"https://openalex.org/C136520226","wikidata":"https://www.wikidata.org/wiki/Q302814","display_name":"Geometric data analysis","level":2,"score":0.4203836917877197},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3948499858379364},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.33994168043136597},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3102848529815674},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.18640118837356567},{"id":"https://openalex.org/C124101348","wikidata":"https://www.wikidata.org/wiki/Q172491","display_name":"Data mining","level":1,"score":0.17153513431549072},{"id":"https://openalex.org/C207987634","wikidata":"https://www.wikidata.org/wiki/Q176862","display_name":"MIMO","level":3,"score":0.0},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0},{"id":"https://openalex.org/C54197355","wikidata":"https://www.wikidata.org/wiki/Q5782992","display_name":"Beamforming","level":2,"score":0.0},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","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":4,"locations":[{"id":"doi:10.1155/2014/183621","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2014/183621","pdf_url":"https://downloads.hindawi.com/journals/jam/2014/183621.pdf","source":{"id":"https://openalex.org/S190082376","display_name":"Journal of Applied Mathematics","issn_l":"1110-757X","issn":["1110-757X","1687-0042"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Applied Mathematics","raw_type":"journal-article"},{"id":"pmh:oai:CULeuclid:euclid.jam/1425305524","is_oa":false,"landing_page_url":"https://projecteuclid.org/euclid.jam/1425305524","pdf_url":null,"source":{"id":"https://openalex.org/S4306400787","display_name":"Project Euclid (Cornell University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Text"},{"id":"pmh:oai:RePEc:hin:jnljam:183621","is_oa":false,"landing_page_url":"http://downloads.hindawi.com/journals/JAM/2014/183621.xml","pdf_url":null,"source":{"id":"https://openalex.org/S4306401271","display_name":"RePEc: Research Papers in Economics","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I77793887","host_organization_name":"Federal Reserve Bank of St. Louis","host_organization_lineage":["https://openalex.org/I77793887"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article"},{"id":"pmh:oai:doaj.org/article:f386b593784c42f98a795bac1586e1d3","is_oa":true,"landing_page_url":"https://doaj.org/article/f386b593784c42f98a795bac1586e1d3","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Journal of Applied Mathematics, Vol 2014 (2014)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.1155/2014/183621","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2014/183621","pdf_url":"https://downloads.hindawi.com/journals/jam/2014/183621.pdf","source":{"id":"https://openalex.org/S190082376","display_name":"Journal of Applied Mathematics","issn_l":"1110-757X","issn":["1110-757X","1687-0042"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Applied Mathematics","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1225831505","display_name":null,"funder_award_id":"Z2011001","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G1904872545","display_name":null,"funder_award_id":"61379089","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G3294029364","display_name":null,"funder_award_id":"61170128","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G3626310088","display_name":null,"funder_award_id":"2012H0043","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G3991528498","display_name":null,"funder_award_id":"2012H0043","funder_id":"https://openalex.org/F4320321878","funder_display_name":"Natural Science Foundation of Fujian Province"},{"id":"https://openalex.org/G434788163","display_name":null,"funder_award_id":"61170128","funder_id":"https://openalex.org/F4320321878","funder_display_name":"Natural Science Foundation of Fujian Province"},{"id":"https://openalex.org/G4450483943","display_name":null,"funder_award_id":"2012J01294","funder_id":"https://openalex.org/F4320321878","funder_display_name":"Natural Science Foundation of Fujian Province"},{"id":"https://openalex.org/G7908117107","display_name":null,"funder_award_id":"61379049","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G8971423281","display_name":null,"funder_award_id":"2012J01294","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320321878","display_name":"Natural Science Foundation of Fujian Province","ror":null}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W1963536179.pdf","grobid_xml":"https://content.openalex.org/works/W1963536179.grobid-xml"},"referenced_works_count":33,"referenced_works":["https://openalex.org/W74588876","https://openalex.org/W1506662207","https://openalex.org/W1662123485","https://openalex.org/W1851672339","https://openalex.org/W1964508465","https://openalex.org/W1970331042","https://openalex.org/W1980605059","https://openalex.org/W1990961529","https://openalex.org/W1991528957","https://openalex.org/W1994425726","https://openalex.org/W1996202983","https://openalex.org/W2020699441","https://openalex.org/W2024638676","https://openalex.org/W2041182276","https://openalex.org/W2041596646","https://openalex.org/W2043931780","https://openalex.org/W2053749030","https://openalex.org/W2055428278","https://openalex.org/W2064664059","https://openalex.org/W2076265335","https://openalex.org/W2079229074","https://openalex.org/W2081148452","https://openalex.org/W2082266564","https://openalex.org/W2093397547","https://openalex.org/W2097287674","https://openalex.org/W2121772728","https://openalex.org/W2122937613","https://openalex.org/W2137405087","https://openalex.org/W2137576710","https://openalex.org/W2143985241","https://openalex.org/W2165267798","https://openalex.org/W2179643736","https://openalex.org/W4255833381"],"related_works":["https://openalex.org/W4387497383","https://openalex.org/W3183948672","https://openalex.org/W3173606202","https://openalex.org/W3110381201","https://openalex.org/W2948807893","https://openalex.org/W2778153218","https://openalex.org/W2758277628","https://openalex.org/W1531601525","https://openalex.org/W2352672974","https://openalex.org/W2328104713"],"abstract_inverted_index":{"The":[0],"reduction":[1,46,134,182],"of":[2,81,89,115,136,143,153,184],"covering":[3,91],"decision":[4],"systems":[5],"is":[6,50,92,156],"an":[7,19,41,159,172],"important":[8,42],"problem":[9],"in":[10,32,44],"data":[11],"mining,":[12],"and":[13,74,102,130],"covering-based":[14],"rough":[15],"sets":[16,114],"serve":[17],"as":[18,158],"efficient":[20],"technique":[21],"to":[22,52,58,78,104,146,161,178],"process":[23],"the":[24,45,60,79,106,112,132,137,141,163,180],"problem.":[25],"Geometric":[26],"lattices":[27,57,69,145],"have":[28],"been":[29],"widely":[30],"used":[31,103],"many":[33],"fields,":[34],"especially":[35],"greedy":[36],"algorithm":[37],"design":[38],"which":[39,139],"plays":[40],"role":[43],"problems.":[47,62],"Therefore,":[48],"it":[49],"meaningful":[51],"combine":[53],"coverings":[54,71],"with":[55],"geometric":[56,68,86,121,144,176],"solve":[59],"optimization":[61],"In":[63,165],"this":[64,168],"paper,":[65],"we":[66,123],"obtain":[67],"from":[70],"through":[72,94,128],"matroids":[73,129],"then":[75],"apply":[76],"them":[77],"issue":[80],"attribute":[82,133,147,181],"reduction.":[83,148],"First,":[84],"a":[85,90,116,120,125,150,166],"lattice":[87],"structure":[88],"constructed":[93],"transversal":[95],"matroids.":[96],"Then":[97],"its":[98],"atoms":[99],"are":[100],"studied":[101],"describe":[105],"lattice.":[107],"Second,":[108],"considering":[109],"that":[110],"all":[111],"closed":[113],"finite":[117],"matroid":[118],"form":[119],"lattice,":[122,177],"propose":[124],"dependence":[126],"space":[127],"study":[131,179],"issues":[135,183],"space,":[138],"realizes":[140],"application":[142],"Furthermore,":[149],"special":[151],"type":[152],"information":[154,185],"system":[155],"taken":[157],"example":[160],"illustrate":[162],"application.":[164],"word,":[167],"work":[169],"points":[170],"out":[171],"interesting":[173],"view,":[174],"namely,":[175],"systems.":[186]},"counts_by_year":[{"year":2017,"cited_by_count":1},{"year":2015,"cited_by_count":2}],"updated_date":"2026-07-23T08:03:31.855105","created_date":"2019-06-27T00:00:00"}