{"id":"https://openalex.org/W2002109251","doi":"https://doi.org/10.1109/grc.2011.6122560","title":"Granular mathematics foundation and current state","display_name":"Granular mathematics foundation and current state","publication_year":2011,"publication_date":"2011-11-01","ids":{"openalex":"https://openalex.org/W2002109251","doi":"https://doi.org/10.1109/grc.2011.6122560","mag":"2002109251"},"language":"en","primary_location":{"id":"doi:10.1109/grc.2011.6122560","doi":"https://doi.org/10.1109/grc.2011.6122560","is_oa":false,"landing_page_url":"https://doi.org/10.1109/grc.2011.6122560","pdf_url":null,"source":{"id":"https://openalex.org/S4363608172","display_name":"IEEE International Conference on Granular Computing (GrC)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"conference"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2011 IEEE International Conference on Granular Computing","raw_type":"proceedings-article"},"parent_works":[],"lineage":["https://openalex.org/W2002109251"],"child_works_count":0,"type":"conference-paper","is_traditional":true,"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/A5105340327","display_name":"Tsau Young Lin","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I51504820","display_name":"San Jose State University","ror":"https://ror.org/04qyvz380","country_code":"US","type":"education","lineage":["https://openalex.org/I51504820"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Tsau Young Lin","raw_affiliation_strings":["Department of Computer Science, San Jose State University Foundation, San Jose, CA, USA","Department of Computer Science, San Jose State University, San Jose, CA#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computer Science, San Jose State University Foundation, San Jose, CA, USA","institution_ids":["https://openalex.org/I51504820"]},{"raw_affiliation_string":"Department of Computer Science, San Jose State University, San Jose, CA#TAB#","institution_ids":["https://openalex.org/I51504820"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5069937323","display_name":"Yu-Ru Syau","orcid":"https://orcid.org/0000-0002-1307-9876","observed_orcids":["https://orcid.org/0000-0002-1307-9876"]},"institutions":[{"id":"https://openalex.org/I40689657","display_name":"National Formosa University","ror":"https://ror.org/00q523p52","country_code":"TW","type":"education","lineage":["https://openalex.org/I40689657"]}],"countries":["TW"],"is_corresponding":false,"raw_author_name":"Yu Ru Syau","raw_affiliation_strings":["Department of Information Management, National Formosa University, Huwei, Yunlin, Taiwan","Department of Information Management, National Formosa University, Huwei 63201, Yunlin, Taiwan#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Information Management, National Formosa University, Huwei, Yunlin, Taiwan","institution_ids":["https://openalex.org/I40689657"]},{"raw_affiliation_string":"Department of Information Management, National Formosa University, Huwei 63201, Yunlin, Taiwan#TAB#","institution_ids":["https://openalex.org/I40689657"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":2.1793,"has_fulltext":false,"cited_by_count":14,"citation_normalized_percentile":{"value":0.87562019,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":88,"max":97},"biblio":{"volume":null,"issue":null,"first_page":"4","last_page":"12"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11063","display_name":"Rough Sets and Fuzzy Logic","score":0.9916999936103821,"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":0.9916999936103821,"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/T11671","display_name":"Fuzzy and Soft Set Theory","score":0.004900000058114529,"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":0.0024999999441206455,"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/neighborhood-systems","display_name":"neighborhood systems","score":0.8040000200271606},{"id":"https://openalex.org/keywords/axiomatization","display_name":"axiomatization","score":0.746999979019165},{"id":"https://openalex.org/keywords/fuzzification","display_name":"fuzzification","score":0.7400000095367432},{"id":"https://openalex.org/keywords/pretopological-spaces","display_name":"pretopological spaces","score":0.878000020980835},{"id":"https://openalex.org/keywords/topological-space","display_name":"topological spaces","score":0.8679999709129333},{"id":"https://openalex.org/keywords/generalized-rough-sets","display_name":"generalized rough sets","score":0.9639999866485596},{"id":"https://openalex.org/keywords/variable-precision-rough-sets","display_name":"variable precision rough sets","score":0.972000002861023},{"id":"https://openalex.org/keywords/zadeh","display_name":"Zadeh","score":0.7409999966621399}],"concepts":[{"id":"https://openalex.org/C167729594","wikidata":"https://www.wikidata.org/wiki/Q17736","display_name":"Axiom","level":2,"score":0.7416847944259644},{"id":"https://openalex.org/C111012933","wikidata":"https://www.wikidata.org/wiki/Q3137210","display_name":"Rough set","level":2,"score":0.6908750534057617},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5808266997337341},{"id":"https://openalex.org/C27176706","wikidata":"https://www.wikidata.org/wiki/Q663365","display_name":"Sierpinski triangle","level":3,"score":0.576680064201355},{"id":"https://openalex.org/C153046414","wikidata":"https://www.wikidata.org/wiki/Q12482","display_name":"Set theory","level":3,"score":0.5675384998321533},{"id":"https://openalex.org/C48103436","wikidata":"https://www.wikidata.org/wiki/Q599031","display_name":"State (computer science)","level":2,"score":0.5237812399864197},{"id":"https://openalex.org/C148043351","wikidata":"https://www.wikidata.org/wiki/Q4456944","display_name":"Current (fluid)","level":2,"score":0.500349760055542},{"id":"https://openalex.org/C42011625","wikidata":"https://www.wikidata.org/wiki/Q1055058","display_name":"Fuzzy set","level":3,"score":0.47983643412590027},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.4657156467437744},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4414992332458496},{"id":"https://openalex.org/C17209119","wikidata":"https://www.wikidata.org/wiki/Q5596712","display_name":"Granular computing","level":3,"score":0.42834314703941345},{"id":"https://openalex.org/C182365436","wikidata":"https://www.wikidata.org/wiki/Q50701","display_name":"Variable (mathematics)","level":2,"score":0.4178622364997864},{"id":"https://openalex.org/C81332173","wikidata":"https://www.wikidata.org/wiki/Q179899","display_name":"Topological space","level":2,"score":0.4119141101837158},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.3612494468688965},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.33018261194229126},{"id":"https://openalex.org/C58166","wikidata":"https://www.wikidata.org/wiki/Q224821","display_name":"Fuzzy logic","level":2,"score":0.2689821124076843},{"id":"https://openalex.org/C40636538","wikidata":"https://www.wikidata.org/wiki/Q81392","display_name":"Fractal","level":2,"score":0.2577056288719177},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.23775115609169006},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.22014948725700378},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.1937689483165741},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.08175739645957947},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C119599485","wikidata":"https://www.wikidata.org/wiki/Q43035","display_name":"Electrical engineering","level":1,"score":0.0},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/grc.2011.6122560","doi":"https://doi.org/10.1109/grc.2011.6122560","is_oa":false,"landing_page_url":"https://doi.org/10.1109/grc.2011.6122560","pdf_url":null,"source":{"id":"https://openalex.org/S4363608172","display_name":"IEEE International Conference on Granular Computing (GrC)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"conference"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2011 IEEE International Conference on Granular Computing","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":12,"referenced_works":["https://openalex.org/W53283552","https://openalex.org/W1514968118","https://openalex.org/W1519304330","https://openalex.org/W1557923305","https://openalex.org/W1635651613","https://openalex.org/W1997362234","https://openalex.org/W2030827420","https://openalex.org/W2052608046","https://openalex.org/W2170544171","https://openalex.org/W4255034261","https://openalex.org/W4299886749","https://openalex.org/W4301971136"],"related_works":["https://openalex.org/W1492213309","https://openalex.org/W2184310151","https://openalex.org/W1997422793","https://openalex.org/W1969998140","https://openalex.org/W7100570914","https://openalex.org/W179603222","https://openalex.org/W1978266471","https://openalex.org/W2234239303","https://openalex.org/W1486623813","https://openalex.org/W7096032703"],"abstract_inverted_index":{"The":[0,55],"keynote":[1],"contains":[2,25],"two":[3],"parts,":[4],"one":[5],"is":[6,12,72,88],"the":[7,10,13,20,27,39,93,103,121],"formal":[8,28],"theory,":[9],"other":[11],"current":[14],"state.":[15],"Though":[16],"we":[17,46],"have":[18],"used":[19],"full":[21],"title,":[22],"this":[23,44],"paper":[24],"only":[26],"theory.":[29],"Neighborhood":[30],"system":[31,35],"generalizes":[32],"topological":[33],"neighborhood":[34],"by":[36,67],"simply":[37],"dropping":[38],"axioms":[40],"of":[41,98],"topology.":[42],"In":[43],"paper,":[45],"use":[47],"it":[48,74],"to":[49,102],"define":[50],"Zadeh's":[51],"Granular":[52],"Mathematics":[53],"(GrM).":[54],"main":[56],"results":[57],"are:":[58],"1)":[59],"GrM,":[60],"though":[61],"defined":[62],"locally,":[63],"can":[64],"be":[65],"axiomatized":[66],"global":[68],"concepts.":[69],"This":[70],"axiomatization":[71],"significant,":[73],"has":[75],"completed":[76],"what":[77],"Sierpinski":[78],"had":[79],"done":[80],"partially":[81],"in":[82,92],"his":[83],"book":[84],"(1952).":[85],"2)":[86],"GrM":[87,99,110],"a":[89,96],"stable":[90],"concept":[91],"sense":[94],"that":[95],"fuzzification":[97],"is,":[100],"up":[101],"labels":[104],"\u03b1,":[105],"just":[106],"another":[107],"GrM.":[108],"3)":[109],"unifies":[111],"rather":[112],"trivially":[113],"pre-/topological":[114],"spaces":[115],"and":[116],"generalized":[117],"rough":[118,124],"sets,":[119],"even":[120],"variable":[122],"precision":[123],"sets":[125],"(though":[126],"not":[127],"so":[128],"obviously).":[129]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2017,"cited_by_count":2},{"year":2014,"cited_by_count":3},{"year":2013,"cited_by_count":4},{"year":2012,"cited_by_count":2}],"updated_date":"2026-11-14T11:04:58.165337","created_date":"2016-06-24T00:00:00"}