{"id":"https://openalex.org/W2567347677","doi":"https://doi.org/10.1515/forma-2016-0011","title":"Binary Relations-based Rough Sets \u2013 an Automated Approach","display_name":"Binary Relations-based Rough Sets \u2013 an Automated Approach","publication_year":2016,"publication_date":"2016-06-01","ids":{"openalex":"https://openalex.org/W2567347677","doi":"https://doi.org/10.1515/forma-2016-0011","mag":"2567347677"},"language":"en","primary_location":{"id":"doi:10.1515/forma-2016-0011","is_oa":true,"landing_page_url":"https://doi.org/10.1515/forma-2016-0011","pdf_url":"https://content.sciendo.com/downloadpdf/journals/forma/24/2/article-p143.pdf","source":{"id":"https://openalex.org/S179241345","display_name":"Formalized Mathematics","issn_l":"1426-2630","issn":["1426-2630","1898-9934"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320322","host_organization_name":"De Gruyter Open","host_organization_lineage":["https://openalex.org/P4310320322","https://openalex.org/P4310313990"],"host_organization_lineage_names":["De Gruyter Open","De Gruyter"],"type":"journal"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Formalized Mathematics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://content.sciendo.com/downloadpdf/journals/forma/24/2/article-p143.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5073856205","display_name":"Adam Grabowski","orcid":"https://orcid.org/0000-0001-5026-3990"},"institutions":[{"id":"https://openalex.org/I245364917","display_name":"University of Bia\u0142ystok","ror":"https://ror.org/01qaqcf60","country_code":"PL","type":"education","lineage":["https://openalex.org/I245364917"]}],"countries":["PL"],"is_corresponding":true,"raw_author_name":"Adam Grabowski","raw_affiliation_strings":["Institute of Informatics, University of Bia\u0142ystok, Cio\u0142kowskiego 1M, 15-245 Bia\u0142ystok, Poland"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute of Informatics, University of Bia\u0142ystok, Cio\u0142kowskiego 1M, 15-245 Bia\u0142ystok, Poland","institution_ids":["https://openalex.org/I245364917"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5073856205"],"corresponding_institution_ids":["https://openalex.org/I245364917"],"apc_list":null,"apc_paid":null,"fwci":2.1071,"has_fulltext":true,"cited_by_count":8,"citation_normalized_percentile":{"value":0.8891097,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"24","issue":"2","first_page":"143","last_page":"155"},"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/T10181","display_name":"Natural Language Processing Techniques","score":0.9179999828338623,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"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":0.9067000150680542,"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/binary-relation","display_name":"Binary relation","score":0.6370493173599243},{"id":"https://openalex.org/keywords/transitive-relation","display_name":"Transitive relation","score":0.633970320224762},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5954684019088745},{"id":"https://openalex.org/keywords/rough-set","display_name":"Rough set","score":0.5885709524154663},{"id":"https://openalex.org/keywords/equivalence-relation","display_name":"Equivalence relation","score":0.5371677875518799},{"id":"https://openalex.org/keywords/continuation","display_name":"Continuation","score":0.508441150188446},{"id":"https://openalex.org/keywords/proposition","display_name":"Proposition","score":0.43218111991882324},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3593391180038452},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.35218656063079834},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3451535701751709},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.2578311562538147},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.1804865002632141},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.16196975111961365},{"id":"https://openalex.org/keywords/epistemology","display_name":"Epistemology","score":0.11720719933509827},{"id":"https://openalex.org/keywords/programming-language","display_name":"Programming language","score":0.10901772975921631}],"concepts":[{"id":"https://openalex.org/C65180967","wikidata":"https://www.wikidata.org/wiki/Q130901","display_name":"Binary relation","level":2,"score":0.6370493173599243},{"id":"https://openalex.org/C191399111","wikidata":"https://www.wikidata.org/wiki/Q64861","display_name":"Transitive relation","level":2,"score":0.633970320224762},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5954684019088745},{"id":"https://openalex.org/C111012933","wikidata":"https://www.wikidata.org/wiki/Q3137210","display_name":"Rough set","level":2,"score":0.5885709524154663},{"id":"https://openalex.org/C156103551","wikidata":"https://www.wikidata.org/wiki/Q130998","display_name":"Equivalence relation","level":2,"score":0.5371677875518799},{"id":"https://openalex.org/C88626702","wikidata":"https://www.wikidata.org/wiki/Q1128903","display_name":"Continuation","level":2,"score":0.508441150188446},{"id":"https://openalex.org/C2777152325","wikidata":"https://www.wikidata.org/wiki/Q108163","display_name":"Proposition","level":2,"score":0.43218111991882324},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3593391180038452},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.35218656063079834},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3451535701751709},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.2578311562538147},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.1804865002632141},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.16196975111961365},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.11720719933509827},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.10901772975921631},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1515/forma-2016-0011","is_oa":true,"landing_page_url":"https://doi.org/10.1515/forma-2016-0011","pdf_url":"https://content.sciendo.com/downloadpdf/journals/forma/24/2/article-p143.pdf","source":{"id":"https://openalex.org/S179241345","display_name":"Formalized Mathematics","issn_l":"1426-2630","issn":["1426-2630","1898-9934"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320322","host_organization_name":"De Gruyter Open","host_organization_lineage":["https://openalex.org/P4310320322","https://openalex.org/P4310313990"],"host_organization_lineage_names":["De Gruyter Open","De Gruyter"],"type":"journal"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Formalized Mathematics","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:027d324b458a4cb1a60527d51da6bd8a","is_oa":false,"landing_page_url":"https://doaj.org/article/027d324b458a4cb1a60527d51da6bd8a","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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Formalized Mathematics, Vol 24, Iss 2, Pp 143-155 (2016)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.1515/forma-2016-0011","is_oa":true,"landing_page_url":"https://doi.org/10.1515/forma-2016-0011","pdf_url":"https://content.sciendo.com/downloadpdf/journals/forma/24/2/article-p143.pdf","source":{"id":"https://openalex.org/S179241345","display_name":"Formalized Mathematics","issn_l":"1426-2630","issn":["1426-2630","1898-9934"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320322","host_organization_name":"De Gruyter Open","host_organization_lineage":["https://openalex.org/P4310320322","https://openalex.org/P4310313990"],"host_organization_lineage_names":["De Gruyter Open","De Gruyter"],"type":"journal"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Formalized Mathematics","raw_type":"journal-article"},"sustainable_development_goals":[{"score":0.5699999928474426,"id":"https://metadata.un.org/sdg/16","display_name":"Peace, Justice and strong institutions"}],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2567347677.pdf","grobid_xml":"https://content.openalex.org/works/W2567347677.grobid-xml"},"referenced_works_count":11,"referenced_works":["https://openalex.org/W139714950","https://openalex.org/W1535984574","https://openalex.org/W1855754411","https://openalex.org/W1938825438","https://openalex.org/W1983426508","https://openalex.org/W1987251161","https://openalex.org/W2006653307","https://openalex.org/W2128085487","https://openalex.org/W2158360838","https://openalex.org/W2184838578","https://openalex.org/W4255833381"],"related_works":["https://openalex.org/W2056040336","https://openalex.org/W2295438979","https://openalex.org/W2383282217","https://openalex.org/W2388867275","https://openalex.org/W2354976030","https://openalex.org/W3121877141","https://openalex.org/W1968318401","https://openalex.org/W2349212754","https://openalex.org/W4247436880","https://openalex.org/W2064989302"],"abstract_inverted_index":{"Summary":[0],"Rough":[1],"sets,":[2],"developed":[3],"by":[4],"Zdzis\u0142aw":[5],"Pawlak":[6],"[12],":[7],"are":[8,273],"an":[9,247,252],"important":[10],"tool":[11],"to":[12,34,79,93,110,203,302],"describe":[13],"the":[14,28,36,61,69,99,102,158,179,244,249,260,279],"state":[15],"of":[16,30,38,43,46,50,75,83,88,101,104,126,160,171,178,209,235,238,246,251,281],"incomplete":[17],"or":[18],"partially":[19],"unknown":[20],"information.":[21],"In":[22,108],"this":[23,89],"article,":[24],"which":[25,272],"is":[26,92,133,223],"essentially":[27,240],"continuation":[29],"[8],":[31],"we":[32,67,113,138,164,201,228,266],"try":[33],"give":[35],"characterization":[37],"approximation":[39,214],"operators":[40],"in":[41,60,135,169,216,259,278,292],"terms":[42,170],"ordinary":[44],"properties":[45,271],"underlying":[47],"relations":[48],"(some":[49],"them,":[51],"as":[52,197,200],"serial":[53],"and":[54,72,155,183,188,265,294],"mediate":[55],"relations,":[56],"were":[57,194,256],"not":[58,195,241,257],"available":[59],"Mizar":[62,90,217,261],"Mathematical":[63,262],"Library":[64,263],"[11]).":[65],"Here":[66],"drop":[68],"classical":[70],"equivalence-":[71],"tolerance-based":[73],"models":[74,212],"rough":[76,282],"sets":[77],"trying":[78],"formalize":[80],"some":[81,231,236],"parts":[82],"[18].":[84,107,145],"The":[85,123],"main":[86],"aim":[87],"article":[91],"provide":[94],"a":[95,198,205],"formal":[96],"counterpart":[97],"for":[98,213],"rest":[100],"paper":[103,121],"William":[105],"Zhu":[106],"order":[109],"do":[111],"this,":[112],"recall":[114],"also":[115,191,274],"Theorem":[116],"3":[117],"from":[118,140],"Y.Y.":[119],"Yao\u2019s":[120],"[17].":[122],"first":[124,130],"part":[125],"our":[127,166],"formalization":[128],"(covering":[129],"seven":[131],"pages)":[132],"contained":[134],"[8].":[136],"Now":[137],"start":[139],"page":[141],"5003,":[142],"sec.":[143],"3.4.":[144],"We":[146,173],"formalized":[147],"almost":[148],"all":[149],"numbered":[150],"items":[151],"(definitions,":[152],"propositions,":[153],"theorems,":[154],"corollaries),":[156],"with":[157,186,243],"exception":[159],"Proposition":[161],"7,":[162],"where":[163],"stated":[165],"theorem":[167],"only":[168],"singletons.":[172],"provided":[174],"more":[175,206,219,232],"thorough":[176],"discussion":[177],"property":[180],"positive":[181],"alliance":[182,253],"its":[184],"connection":[185],"seriality":[187],"reflexivity":[189],"(and":[190],"transitivity).":[192],"Examples":[193],"covered":[196],"rule":[199],"tried":[202],"construct":[204],"general":[207,233],"mechanism":[208],"finding":[210],"appropriate":[211],"spaces":[215],"providing":[218],"automatization":[220],"than":[221],"it":[222],"now":[224],"[10].":[225],"Of":[226],"course,":[227],"can":[229,299],"see":[230],"applications":[234],"registrations":[237],"clusters,":[239],"dealing":[242],"notion":[245],"approximation:":[248],"notions":[250],"binary":[254],"relation":[255],"defined":[258],"before,":[264],"should":[267],"think":[268],"about":[269],"other":[270,303],"absent":[275],"but":[276],"needed":[277],"context":[280],"approximations":[283],"[9],":[284],"[5].":[285],"Via":[286],"theory":[287],"merging,":[288],"using":[289],"mechanisms":[290],"described":[291],"[6]":[293],"[7],":[295],"such":[296],"elementary":[297],"constructions":[298],"be":[300],"extended":[301],"frameworks.":[304]},"counts_by_year":[{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":3},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":2}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}