{"id":"https://openalex.org/W2018236896","doi":"https://doi.org/10.1109/grc.2012.6468593","title":"Pre-closedness in L-topological spaces","display_name":"Pre-closedness in L-topological spaces","publication_year":2012,"publication_date":"2012-08-01","ids":{"openalex":"https://openalex.org/W2018236896","doi":"https://doi.org/10.1109/grc.2012.6468593","mag":"2018236896"},"language":"en","primary_location":{"id":"doi:10.1109/grc.2012.6468593","is_oa":false,"landing_page_url":"https://doi.org/10.1109/grc.2012.6468593","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/A5040178189","display_name":"Shi-Zhong Bai","orcid":null},"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":true,"raw_author_name":"Shizhong Bai","raw_affiliation_strings":["School of Mathematics and computational science, Wuyi University, Guangdong, China","School of Mathematics and Computational Science, Wuyi University, Guangdong, China"],"affiliations":[{"raw_affiliation_string":"School of Mathematics and computational science, Wuyi University, Guangdong, China","institution_ids":["https://openalex.org/I98834328"]},{"raw_affiliation_string":"School of Mathematics and Computational Science, Wuyi University, Guangdong, China","institution_ids":["https://openalex.org/I98834328"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5101794241","display_name":"Xixi Chen","orcid":"https://orcid.org/0000-0003-3415-0800"},"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":"Xixi Chen","raw_affiliation_strings":["School of Mathematics and computational science, Wuyi University, Guangdong, China","School of Mathematics and Computational Science, Wuyi University, Guangdong, China"],"affiliations":[{"raw_affiliation_string":"School of Mathematics and computational science, Wuyi University, Guangdong, China","institution_ids":["https://openalex.org/I98834328"]},{"raw_affiliation_string":"School of Mathematics and Computational Science, Wuyi University, Guangdong, China","institution_ids":["https://openalex.org/I98834328"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100783073","display_name":"Peng Yu","orcid":"https://orcid.org/0000-0002-0402-5390"},"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":"Yu Peng","raw_affiliation_strings":["School of Mathematics and computational science, Wuyi University, Guangdong, China","School of Mathematics and Computational Science, Wuyi University, Guangdong, China"],"affiliations":[{"raw_affiliation_string":"School of Mathematics and computational science, Wuyi University, Guangdong, China","institution_ids":["https://openalex.org/I98834328"]},{"raw_affiliation_string":"School of Mathematics and Computational Science, Wuyi University, Guangdong, China","institution_ids":["https://openalex.org/I98834328"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5040178189"],"corresponding_institution_ids":["https://openalex.org/I98834328"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.13864348,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"2","issue":null,"first_page":"695","last_page":"698"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11671","display_name":"Fuzzy and Soft Set Theory","score":0.9994999766349792,"subfield":{"id":"https://openalex.org/subfields/1803","display_name":"Management Science and Operations Research"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},"topics":[{"id":"https://openalex.org/T11671","display_name":"Fuzzy and Soft Set Theory","score":0.9994999766349792,"subfield":{"id":"https://openalex.org/subfields/1803","display_name":"Management Science and Operations Research"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T11727","display_name":"Advanced Algebra and Logic","score":0.996999979019165,"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/T11063","display_name":"Rough Sets and Fuzzy Logic","score":0.9840999841690063,"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/distributivity","display_name":"Distributivity","score":0.8375735282897949},{"id":"https://openalex.org/keywords/topological-space","display_name":"Topological space","score":0.6106511950492859},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6069287657737732},{"id":"https://openalex.org/keywords/lattice","display_name":"Lattice (music)","score":0.5301486253738403},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.5290668606758118},{"id":"https://openalex.org/keywords/basis","display_name":"Basis (linear algebra)","score":0.41214561462402344},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.3869195282459259},{"id":"https://openalex.org/keywords/topology","display_name":"Topology (electrical circuits)","score":0.3696296811103821},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.34517186880111694},{"id":"https://openalex.org/keywords/distributive-property","display_name":"Distributive property","score":0.2349628210067749},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.22645807266235352},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.11054888367652893},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.06605711579322815}],"concepts":[{"id":"https://openalex.org/C138390121","wikidata":"https://www.wikidata.org/wiki/Q5283219","display_name":"Distributivity","level":3,"score":0.8375735282897949},{"id":"https://openalex.org/C81332173","wikidata":"https://www.wikidata.org/wiki/Q179899","display_name":"Topological space","level":2,"score":0.6106511950492859},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6069287657737732},{"id":"https://openalex.org/C2781204021","wikidata":"https://www.wikidata.org/wiki/Q6497091","display_name":"Lattice (music)","level":2,"score":0.5301486253738403},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.5290668606758118},{"id":"https://openalex.org/C12426560","wikidata":"https://www.wikidata.org/wiki/Q189569","display_name":"Basis (linear algebra)","level":2,"score":0.41214561462402344},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.3869195282459259},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.3696296811103821},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.34517186880111694},{"id":"https://openalex.org/C11821877","wikidata":"https://www.wikidata.org/wiki/Q187959","display_name":"Distributive property","level":2,"score":0.2349628210067749},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.22645807266235352},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.11054888367652893},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.06605711579322815},{"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:10.1109/grc.2012.6468593","is_oa":false,"landing_page_url":"https://doi.org/10.1109/grc.2012.6468593","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":[{"display_name":"Reduced inequalities","id":"https://metadata.un.org/sdg/10","score":0.5899999737739563}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":27,"referenced_works":["https://openalex.org/W1523276351","https://openalex.org/W1582269801","https://openalex.org/W1985992189","https://openalex.org/W1991241698","https://openalex.org/W1999782862","https://openalex.org/W2001263138","https://openalex.org/W2002541167","https://openalex.org/W2016371370","https://openalex.org/W2023743353","https://openalex.org/W2027900260","https://openalex.org/W2038429746","https://openalex.org/W2042102499","https://openalex.org/W2057647469","https://openalex.org/W2060463975","https://openalex.org/W2061931954","https://openalex.org/W2067432234","https://openalex.org/W2068787715","https://openalex.org/W2077709279","https://openalex.org/W2092266125","https://openalex.org/W2094972943","https://openalex.org/W2259640660","https://openalex.org/W2304956378","https://openalex.org/W2381852738","https://openalex.org/W2992559086","https://openalex.org/W3217008510","https://openalex.org/W4246118734","https://openalex.org/W4249939961"],"related_works":["https://openalex.org/W3017062904","https://openalex.org/W2535873559","https://openalex.org/W2018390992","https://openalex.org/W578326175","https://openalex.org/W2883359489","https://openalex.org/W2593170496","https://openalex.org/W2561764048","https://openalex.org/W4306177072","https://openalex.org/W4206672782","https://openalex.org/W59101178"],"abstract_inverted_index":{"The":[0,26],"new":[1,27],"notion":[2,28],"of":[3,12,35],"pre-cIosedness":[4],"is":[5,20],"introduced":[6],"in":[7],"L-topological":[8],"spaces":[9],"by":[10],"means":[11],"pre-open":[13],"L-sets":[14],"and":[15],"their":[16],"inequality,":[17],"where":[18],"L":[19,38],"a":[21],"complete":[22],"De":[23],"Morgan":[24],"algebra.":[25],"does":[29,40],"not":[30,41],"depend":[31],"on":[32],"the":[33],"structure":[34],"basis":[36],"lattice":[37],"which":[39],"require":[42],"any":[43],"distributivity.":[44]},"counts_by_year":[],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
