{"id":"https://openalex.org/W2122401922","doi":"https://doi.org/10.1109/grc.2005.1547363","title":"Information quanta and approximation spaces. I. Non-classical approximation operators","display_name":"Information quanta and approximation spaces. I. Non-classical approximation operators","publication_year":2005,"publication_date":"2005-01-01","ids":{"openalex":"https://openalex.org/W2122401922","doi":"https://doi.org/10.1109/grc.2005.1547363","mag":"2122401922"},"language":"en","primary_location":{"id":"doi:10.1109/grc.2005.1547363","is_oa":false,"landing_page_url":"https://doi.org/10.1109/grc.2005.1547363","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2005 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/A5041395713","display_name":"Piero Pagliani","orcid":"https://orcid.org/0000-0002-7036-012X"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"P. Pagliani","raw_affiliation_strings":["Research Group on Knowledge and Communication Models, Roma, Italy","Res. Group on Knowledge & Commun. Models, Roma, Italy"],"affiliations":[{"raw_affiliation_string":"Research Group on Knowledge and Communication Models, Roma, Italy","institution_ids":[]},{"raw_affiliation_string":"Res. Group on Knowledge & Commun. Models, Roma, Italy","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5041395713"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":2.8108,"has_fulltext":false,"cited_by_count":24,"citation_normalized_percentile":{"value":0.90330189,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":97},"biblio":{"volume":null,"issue":null,"first_page":"605","last_page":"610 Vol. 2"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11063","display_name":"Rough Sets and Fuzzy Logic","score":0.9988999962806702,"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":0.9988999962806702,"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/T11727","display_name":"Advanced Algebra and Logic","score":0.9736999869346619,"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/class","display_name":"Class (philosophy)","score":0.5794461965560913},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5778222680091858},{"id":"https://openalex.org/keywords/discontinuity","display_name":"Discontinuity (linguistics)","score":0.5754927396774292},{"id":"https://openalex.org/keywords/property","display_name":"Property (philosophy)","score":0.5722071528434753},{"id":"https://openalex.org/keywords/operator-theory","display_name":"Operator theory","score":0.48718661069869995},{"id":"https://openalex.org/keywords/extensional-definition","display_name":"Extensional definition","score":0.4807598292827606},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.4688336253166199},{"id":"https://openalex.org/keywords/approximation-property","display_name":"Approximation property","score":0.44417813420295715},{"id":"https://openalex.org/keywords/quantum","display_name":"Quantum","score":0.44186609983444214},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.41161638498306274},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.39835456013679504},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.3623632490634918},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.34658491611480713},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3234128952026367},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.15245306491851807},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.09046226739883423},{"id":"https://openalex.org/keywords/banach-space","display_name":"Banach space","score":0.08624985814094543}],"concepts":[{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.5794461965560913},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5778222680091858},{"id":"https://openalex.org/C2777042112","wikidata":"https://www.wikidata.org/wiki/Q5281658","display_name":"Discontinuity (linguistics)","level":2,"score":0.5754927396774292},{"id":"https://openalex.org/C189950617","wikidata":"https://www.wikidata.org/wiki/Q937228","display_name":"Property (philosophy)","level":2,"score":0.5722071528434753},{"id":"https://openalex.org/C43929395","wikidata":"https://www.wikidata.org/wiki/Q1198874","display_name":"Operator theory","level":2,"score":0.48718661069869995},{"id":"https://openalex.org/C136137745","wikidata":"https://www.wikidata.org/wiki/Q19515659","display_name":"Extensional definition","level":3,"score":0.4807598292827606},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.4688336253166199},{"id":"https://openalex.org/C152306953","wikidata":"https://www.wikidata.org/wiki/Q621744","display_name":"Approximation property","level":3,"score":0.44417813420295715},{"id":"https://openalex.org/C84114770","wikidata":"https://www.wikidata.org/wiki/Q46344","display_name":"Quantum","level":2,"score":0.44186609983444214},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.41161638498306274},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.39835456013679504},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.3623632490634918},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.34658491611480713},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3234128952026367},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.15245306491851807},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.09046226739883423},{"id":"https://openalex.org/C132954091","wikidata":"https://www.wikidata.org/wiki/Q194397","display_name":"Banach space","level":2,"score":0.08624985814094543},{"id":"https://openalex.org/C151730666","wikidata":"https://www.wikidata.org/wiki/Q7205","display_name":"Paleontology","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","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},{"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/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0},{"id":"https://openalex.org/C77928131","wikidata":"https://www.wikidata.org/wiki/Q193343","display_name":"Tectonics","level":2,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/grc.2005.1547363","is_oa":false,"landing_page_url":"https://doi.org/10.1109/grc.2005.1547363","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2005 IEEE International Conference on Granular Computing","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[{"score":0.4000000059604645,"display_name":"Reduced inequalities","id":"https://metadata.un.org/sdg/10"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":13,"referenced_works":["https://openalex.org/W1493616114","https://openalex.org/W1505150927","https://openalex.org/W1559868033","https://openalex.org/W1559879410","https://openalex.org/W1623621557","https://openalex.org/W1996323836","https://openalex.org/W2002097778","https://openalex.org/W2130579983","https://openalex.org/W2141175249","https://openalex.org/W2148443116","https://openalex.org/W2170714435","https://openalex.org/W4239097602","https://openalex.org/W4285719527"],"related_works":["https://openalex.org/W1983139231","https://openalex.org/W1983326582","https://openalex.org/W1486407994","https://openalex.org/W2196757011","https://openalex.org/W2888814539","https://openalex.org/W4297411373","https://openalex.org/W2377228065","https://openalex.org/W4211150010","https://openalex.org/W4282964373","https://openalex.org/W2968953010"],"abstract_inverted_index":{"In":[0],"the":[1,59,62],"first":[2],"part":[3],"of":[4,27,41,43,53,66,109],"this":[5,23],"paper":[6],"property":[7,81],"systems":[8,77,82],"are":[9,29,32],"investigated":[10],"in":[11,48,58,94],"order":[12,49,64],"to":[13,34,50,105],"define":[14,106],"intensional":[15],"and":[16,38,101],"extensional":[17],"operators":[18,28,55,98],"fulfilling":[19],"adjointness":[20,96],"properties.":[21,46],"On":[22],"basis":[24],"a":[25,107],"set":[26],"defined":[30],"which":[31,95],"able":[33],"determine":[35],"non-classical":[36],"upper":[37],"lower":[39],"approximations":[40],"subsets":[42],"objects":[44],"or":[45],"But":[47],"bypass":[51],"\"discontinuity\"":[52],"such":[54],"we":[56,72],"introduce,":[57],"second":[60],"part,":[61],"higher":[63],"notion":[65],"an":[67],"\"information":[68,90],"quantum\".":[69],"This":[70],"way":[71],"can":[73],"account":[74],"for":[75],"attribute":[76],"as":[78,80],"well":[79],"by":[83],"transforming":[84],"them":[85],"into":[86],"new":[87],"structures":[88],"called":[89],"quantum":[91],"relational":[92],"systems\"":[93],"makes":[97,102],"fulfil":[99],"continuity":[100],"it":[103],"possible":[104],"class":[108],"generalised":[110],"approximation":[111],"spaces.":[112]},"counts_by_year":[{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":2},{"year":2014,"cited_by_count":2},{"year":2012,"cited_by_count":3}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}