{"id":"https://openalex.org/W4391631316","doi":"https://doi.org/10.1080/11663081.2024.2336386","title":"Nelson algebras, residuated lattices and rough sets: A survey","display_name":"Nelson algebras, residuated lattices and rough sets: A survey","publication_year":2024,"publication_date":"2024-04-14","ids":{"openalex":"https://openalex.org/W4391631316","doi":"https://doi.org/10.1080/11663081.2024.2336386"},"language":"en","primary_location":{"id":"doi:10.1080/11663081.2024.2336386","is_oa":false,"landing_page_url":"https://doi.org/10.1080/11663081.2024.2336386","pdf_url":null,"source":{"id":"https://openalex.org/S93822064","display_name":"Journal of Applied Non-Classical Logics","issn_l":"1166-3081","issn":["1166-3081","1958-5780"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Applied Non-Classical Logics","raw_type":"journal-article"},"type":"preprint","indexed_in":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2402.02606","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5091139212","display_name":"Jouni J\u00e4rvinen","orcid":"https://orcid.org/0000-0002-8729-8633"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Jouni J\u00e4rvinen","raw_affiliation_strings":["Software Engineering, LUT School of Engineering Science, Lahti, Finland"],"raw_orcid":"https://orcid.org/0000-0002-8729-8633","affiliations":[{"raw_affiliation_string":"Software Engineering, LUT School of Engineering Science, Lahti, Finland","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5063053756","display_name":"S\u00e4ndor Radeleczki","orcid":"https://orcid.org/0000-0002-9719-4766"},"institutions":[{"id":"https://openalex.org/I20230540","display_name":"University of Miskolc","ror":"https://ror.org/038g7dk46","country_code":"HU","type":"education","lineage":["https://openalex.org/I20230540"]}],"countries":["HU"],"is_corresponding":false,"raw_author_name":"S\u00e1ndor Radeleczki","raw_affiliation_strings":["Institute of Mathematics, University of Miskolc, Miskolc-Egyetemv\u00e1ros, Hungary"],"raw_orcid":"https://orcid.org/0000-0002-9719-4766","affiliations":[{"raw_affiliation_string":"Institute of Mathematics, University of Miskolc, Miskolc-Egyetemv\u00e1ros, Hungary","institution_ids":["https://openalex.org/I20230540"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5008197317","display_name":"Umberto Rivieccio","orcid":"https://orcid.org/0000-0003-1364-5003"},"institutions":[{"id":"https://openalex.org/I178450904","display_name":"Universidad Nacional de Educaci\u00f3n a Distancia","ror":"https://ror.org/02msb5n36","country_code":"ES","type":"education","lineage":["https://openalex.org/I178450904"]}],"countries":["ES"],"is_corresponding":true,"raw_author_name":"Umberto Rivieccio","raw_affiliation_strings":["Departamento de L\u00f3gica e Historia y Filosof\u00eda de la Ciencia, UNED, Madrid, Spain"],"raw_orcid":"https://orcid.org/0000-0003-1364-5003","affiliations":[{"raw_affiliation_string":"Departamento de L\u00f3gica e Historia y Filosof\u00eda de la Ciencia, UNED, Madrid, Spain","institution_ids":["https://openalex.org/I178450904"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5008197317"],"corresponding_institution_ids":["https://openalex.org/I178450904"],"apc_list":null,"apc_paid":null,"fwci":0.6914,"has_fulltext":true,"cited_by_count":2,"citation_normalized_percentile":{"value":0.68979338,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":95,"max":96},"biblio":{"volume":"34","issue":"2-3","first_page":"368","last_page":"428"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11063","display_name":"Rough Sets and Fuzzy Logic","score":0.9861999750137329,"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":0.9861999750137329,"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":0.9207000136375427,"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/algebraic-logic","display_name":"Algebraic logic","score":0.7034977674484253},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5865297913551331},{"id":"https://openalex.org/keywords/representation-theorem","display_name":"Representation theorem","score":0.5820916295051575},{"id":"https://openalex.org/keywords/subalgebra","display_name":"Subalgebra","score":0.5803418159484863},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.5540428161621094},{"id":"https://openalex.org/keywords/residuated-lattice","display_name":"Residuated lattice","score":0.5375522971153259},{"id":"https://openalex.org/keywords/negation","display_name":"Negation","score":0.5087152123451233},{"id":"https://openalex.org/keywords/field","display_name":"Field (mathematics)","score":0.4946739375591278},{"id":"https://openalex.org/keywords/distributive-lattice","display_name":"Distributive lattice","score":0.4893495440483093},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.48391419649124146},{"id":"https://openalex.org/keywords/duality","display_name":"Duality (order theory)","score":0.4702621400356293},{"id":"https://openalex.org/keywords/representation-theory","display_name":"Representation theory","score":0.4586884677410126},{"id":"https://openalex.org/keywords/algebraic-number","display_name":"Algebraic number","score":0.43365585803985596},{"id":"https://openalex.org/keywords/rough-set","display_name":"Rough set","score":0.4286131262779236},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.42514553666114807},{"id":"https://openalex.org/keywords/distributive-property","display_name":"Distributive property","score":0.3039904236793518},{"id":"https://openalex.org/keywords/fuzzy-logic","display_name":"Fuzzy logic","score":0.22876739501953125},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.15390411019325256}],"concepts":[{"id":"https://openalex.org/C86523455","wikidata":"https://www.wikidata.org/wiki/Q1005222","display_name":"Algebraic logic","level":3,"score":0.7034977674484253},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5865297913551331},{"id":"https://openalex.org/C2776230367","wikidata":"https://www.wikidata.org/wiki/Q7314222","display_name":"Representation theorem","level":2,"score":0.5820916295051575},{"id":"https://openalex.org/C67996461","wikidata":"https://www.wikidata.org/wiki/Q629933","display_name":"Subalgebra","level":3,"score":0.5803418159484863},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.5540428161621094},{"id":"https://openalex.org/C2781278839","wikidata":"https://www.wikidata.org/wiki/Q9462417","display_name":"Residuated lattice","level":3,"score":0.5375522971153259},{"id":"https://openalex.org/C2185349","wikidata":"https://www.wikidata.org/wiki/Q190558","display_name":"Negation","level":2,"score":0.5087152123451233},{"id":"https://openalex.org/C9652623","wikidata":"https://www.wikidata.org/wiki/Q190109","display_name":"Field (mathematics)","level":2,"score":0.4946739375591278},{"id":"https://openalex.org/C192606457","wikidata":"https://www.wikidata.org/wiki/Q2363730","display_name":"Distributive lattice","level":3,"score":0.4893495440483093},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.48391419649124146},{"id":"https://openalex.org/C2778023678","wikidata":"https://www.wikidata.org/wiki/Q554403","display_name":"Duality (order theory)","level":2,"score":0.4702621400356293},{"id":"https://openalex.org/C197273675","wikidata":"https://www.wikidata.org/wiki/Q13220368","display_name":"Representation theory","level":2,"score":0.4586884677410126},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.43365585803985596},{"id":"https://openalex.org/C111012933","wikidata":"https://www.wikidata.org/wiki/Q3137210","display_name":"Rough set","level":2,"score":0.4286131262779236},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.42514553666114807},{"id":"https://openalex.org/C11821877","wikidata":"https://www.wikidata.org/wiki/Q187959","display_name":"Distributive property","level":2,"score":0.3039904236793518},{"id":"https://openalex.org/C58166","wikidata":"https://www.wikidata.org/wiki/Q224821","display_name":"Fuzzy logic","level":2,"score":0.22876739501953125},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.15390411019325256},{"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/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1080/11663081.2024.2336386","is_oa":false,"landing_page_url":"https://doi.org/10.1080/11663081.2024.2336386","pdf_url":null,"source":{"id":"https://openalex.org/S93822064","display_name":"Journal of Applied Non-Classical Logics","issn_l":"1166-3081","issn":["1166-3081","1958-5780"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Applied Non-Classical Logics","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:2402.02606","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2402.02606","pdf_url":"https://arxiv.org/pdf/2402.02606","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2402.02606","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2402.02606","pdf_url":"https://arxiv.org/pdf/2402.02606","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320310209","display_name":"Fundaci\u00f3n Banco Santander","ror":"https://ror.org/01wy67m98"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4391631316.pdf","grobid_xml":"https://content.openalex.org/works/W4391631316.grobid-xml"},"referenced_works_count":125,"referenced_works":["https://openalex.org/W61972725","https://openalex.org/W87187940","https://openalex.org/W163554217","https://openalex.org/W179988417","https://openalex.org/W279306447","https://openalex.org/W289988227","https://openalex.org/W565780523","https://openalex.org/W956848902","https://openalex.org/W1487409515","https://openalex.org/W1498937593","https://openalex.org/W1525647423","https://openalex.org/W1581532077","https://openalex.org/W1582314147","https://openalex.org/W1589307624","https://openalex.org/W1602202955","https://openalex.org/W1618431959","https://openalex.org/W1692538989","https://openalex.org/W1777300595","https://openalex.org/W1964591144","https://openalex.org/W1968663039","https://openalex.org/W1971226702","https://openalex.org/W1978201126","https://openalex.org/W1994633855","https://openalex.org/W2000140686","https://openalex.org/W2002177677","https://openalex.org/W2003571395","https://openalex.org/W2004776947","https://openalex.org/W2005027389","https://openalex.org/W2006242427","https://openalex.org/W2007838222","https://openalex.org/W2009243753","https://openalex.org/W2017295143","https://openalex.org/W2029455106","https://openalex.org/W2031598858","https://openalex.org/W2034510531","https://openalex.org/W2036183559","https://openalex.org/W2036321418","https://openalex.org/W2038185098","https://openalex.org/W2039232530","https://openalex.org/W2041418362","https://openalex.org/W2043835012","https://openalex.org/W2045084061","https://openalex.org/W2053168571","https://openalex.org/W2054776590","https://openalex.org/W2055054170","https://openalex.org/W2055266411","https://openalex.org/W2056669561","https://openalex.org/W2057901465","https://openalex.org/W2065181693","https://openalex.org/W2070411061","https://openalex.org/W2075033708","https://openalex.org/W2077242255","https://openalex.org/W2077585551","https://openalex.org/W2080173448","https://openalex.org/W2080462204","https://openalex.org/W2084571374","https://openalex.org/W2089047827","https://openalex.org/W2090633591","https://openalex.org/W2091158126","https://openalex.org/W2091295886","https://openalex.org/W2093397547","https://openalex.org/W2102134079","https://openalex.org/W2104974367","https://openalex.org/W2106306813","https://openalex.org/W2115548617","https://openalex.org/W2117459082","https://openalex.org/W2120854078","https://openalex.org/W2138601456","https://openalex.org/W2139264389","https://openalex.org/W2140351059","https://openalex.org/W2142616542","https://openalex.org/W2144447804","https://openalex.org/W2150425213","https://openalex.org/W2153536416","https://openalex.org/W2189295089","https://openalex.org/W2229542852","https://openalex.org/W2269068137","https://openalex.org/W2276796001","https://openalex.org/W2322956382","https://openalex.org/W2340110558","https://openalex.org/W2406211624","https://openalex.org/W2527773187","https://openalex.org/W2558470815","https://openalex.org/W2772038619","https://openalex.org/W2790159133","https://openalex.org/W2811391427","https://openalex.org/W2898664970","https://openalex.org/W2914384061","https://openalex.org/W2945663150","https://openalex.org/W2948358921","https://openalex.org/W2969981807","https://openalex.org/W3014113905","https://openalex.org/W3081703353","https://openalex.org/W3105252723","https://openalex.org/W3120557254","https://openalex.org/W3160119527","https://openalex.org/W3161785549","https://openalex.org/W3185436550","https://openalex.org/W3196497357","https://openalex.org/W3196604676","https://openalex.org/W4205529794","https://openalex.org/W4232798335","https://openalex.org/W4234099711","https://openalex.org/W4234865680","https://openalex.org/W4235299755","https://openalex.org/W4239011127","https://openalex.org/W4245674526","https://openalex.org/W4246761341","https://openalex.org/W4246797202","https://openalex.org/W4252113473","https://openalex.org/W4255833381","https://openalex.org/W4293176479","https://openalex.org/W4385302370","https://openalex.org/W4400535622","https://openalex.org/W6614721590","https://openalex.org/W6616805996","https://openalex.org/W6631133014","https://openalex.org/W6679680674","https://openalex.org/W6680519539","https://openalex.org/W6695889459","https://openalex.org/W6750163850","https://openalex.org/W6789891232","https://openalex.org/W6797632140","https://openalex.org/W6999973451","https://openalex.org/W7027370833"],"related_works":["https://openalex.org/W2907458896","https://openalex.org/W2973382780","https://openalex.org/W2348318278","https://openalex.org/W3148291609","https://openalex.org/W3089038997","https://openalex.org/W4288281056","https://openalex.org/W2014718701","https://openalex.org/W2962310823","https://openalex.org/W1965995586","https://openalex.org/W4394793006"],"abstract_inverted_index":{"Over":[0],"the":[1,15,32,38,59,63,66,83],"past":[2,67],"50":[3],"years,":[4],"Nelson":[5,41,75,115,126,139,151],"algebras":[6,42],"have":[7],"been":[8],"extensively":[9],"studied":[10],"by":[11,56,129,154],"distinguished":[12],"scholars":[13],"as":[14,78,89,91,102],"algebraic":[16],"counterpart":[17],"of":[18,31,40,74,86,97,122,138],"Nelson's":[19,87],"constructive":[20],"logic":[21,140],"with":[22],"strong":[23],"negation.":[24],"Despite":[25],"these":[26],"studies,":[27],"a":[28,120,123,130,133,136,155],"comprehensive":[29],"survey":[30],"topic":[33],"is":[34,117,135,146],"currently":[35],"lacking,":[36],"and":[37,104,142],"theory":[39],"remains":[43],"largely":[44],"unknown":[45],"to":[46,52,82,94,99,119],"most":[47],"logicians.":[48],"This":[49],"paper":[50],"aims":[51],"fill":[53],"this":[54],"gap":[55],"focussing":[57],"on":[58],"essential":[60],"developments":[61],"in":[62,148],"field":[64],"over":[65],"two":[68],"decades.":[69],"Additionally,":[70],"we":[71],"explore":[72],"generalisations":[73],"algebras,":[76],"such":[77,101],"N4-lattices":[79],"which":[80],"correspond":[81],"paraconsistent":[84],"version":[85],"logic,":[88],"well":[90],"their":[92],"applications":[93],"other":[95],"areas":[96],"interest":[98],"logicians,":[100],"duality":[103],"rough":[105,124],"set":[106],"theory.":[107],"A":[108],"general":[109],"representation":[110],"theorem":[111,137],"states":[112],"that":[113],"each":[114],"algebra":[116,127,152],"isomorphic":[118],"subalgebra":[121],"set-based":[125],"induced":[128,153],"quasiorder.":[131,156],"Furthermore,":[132],"formula":[134],"if":[141,144],"only":[143],"it":[145],"valid":[147],"every":[149],"finite":[150]},"counts_by_year":[{"year":2025,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}