{"id":"https://openalex.org/W3032958609","doi":"https://doi.org/10.2478/forma-2020-0011","title":"On Fuzzy Negations Generated by Fuzzy Implications","display_name":"On Fuzzy Negations Generated by Fuzzy Implications","publication_year":2020,"publication_date":"2020-04-01","ids":{"openalex":"https://openalex.org/W3032958609","doi":"https://doi.org/10.2478/forma-2020-0011","mag":"3032958609"},"language":"en","primary_location":{"id":"doi:10.2478/forma-2020-0011","is_oa":true,"landing_page_url":"https://doi.org/10.2478/forma-2020-0011","pdf_url":"https://www.sciendo.com/pdf/10.2478/forma-2020-0011","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://www.sciendo.com/pdf/10.2478/forma-2020-0011","any_repository_has_fulltext":true},"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 , Poland"],"affiliations":[{"raw_affiliation_string":"Institute of Informatics , University of 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":0.4332,"has_fulltext":true,"cited_by_count":4,"citation_normalized_percentile":{"value":0.68288042,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":97},"biblio":{"volume":"28","issue":"1","first_page":"121","last_page":"128"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11063","display_name":"Rough Sets and Fuzzy Logic","score":0.9993000030517578,"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":0.9993000030517578,"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/T10050","display_name":"Multi-Criteria Decision Making","score":0.9979000091552734,"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/T10820","display_name":"Fuzzy Logic and Control Systems","score":0.9944000244140625,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/negation","display_name":"Negation","score":0.8067684769630432},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6838569641113281},{"id":"https://openalex.org/keywords/fuzzy-logic","display_name":"Fuzzy logic","score":0.6240232586860657},{"id":"https://openalex.org/keywords/pointwise","display_name":"Pointwise","score":0.5779792666435242},{"id":"https://openalex.org/keywords/fuzzy-classification","display_name":"Fuzzy classification","score":0.5301267504692078},{"id":"https://openalex.org/keywords/fuzzy-set-operations","display_name":"Fuzzy set operations","score":0.5227287411689758},{"id":"https://openalex.org/keywords/type-2-fuzzy-sets-and-systems","display_name":"Type-2 fuzzy sets and systems","score":0.48261675238609314},{"id":"https://openalex.org/keywords/fuzzy-set","display_name":"Fuzzy set","score":0.4664109945297241},{"id":"https://openalex.org/keywords/fuzzy-number","display_name":"Fuzzy number","score":0.46416738629341125},{"id":"https://openalex.org/keywords/defuzzification","display_name":"Defuzzification","score":0.4386034309864044},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.42879414558410645},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.38290393352508545},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.34556302428245544},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.3424392640590668},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.259040892124176},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.19257286190986633},{"id":"https://openalex.org/keywords/programming-language","display_name":"Programming language","score":0.13761085271835327}],"concepts":[{"id":"https://openalex.org/C2185349","wikidata":"https://www.wikidata.org/wiki/Q190558","display_name":"Negation","level":2,"score":0.8067684769630432},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6838569641113281},{"id":"https://openalex.org/C58166","wikidata":"https://www.wikidata.org/wiki/Q224821","display_name":"Fuzzy logic","level":2,"score":0.6240232586860657},{"id":"https://openalex.org/C2777984123","wikidata":"https://www.wikidata.org/wiki/Q9248237","display_name":"Pointwise","level":2,"score":0.5779792666435242},{"id":"https://openalex.org/C127385683","wikidata":"https://www.wikidata.org/wiki/Q1475696","display_name":"Fuzzy classification","level":4,"score":0.5301267504692078},{"id":"https://openalex.org/C148671577","wikidata":"https://www.wikidata.org/wiki/Q5511133","display_name":"Fuzzy set operations","level":4,"score":0.5227287411689758},{"id":"https://openalex.org/C17350324","wikidata":"https://www.wikidata.org/wiki/Q7860605","display_name":"Type-2 fuzzy sets and systems","level":5,"score":0.48261675238609314},{"id":"https://openalex.org/C42011625","wikidata":"https://www.wikidata.org/wiki/Q1055058","display_name":"Fuzzy set","level":3,"score":0.4664109945297241},{"id":"https://openalex.org/C1883856","wikidata":"https://www.wikidata.org/wiki/Q3407463","display_name":"Fuzzy number","level":4,"score":0.46416738629341125},{"id":"https://openalex.org/C170260401","wikidata":"https://www.wikidata.org/wiki/Q5251735","display_name":"Defuzzification","level":5,"score":0.4386034309864044},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.42879414558410645},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.38290393352508545},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.34556302428245544},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.3424392640590668},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.259040892124176},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.19257286190986633},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.13761085271835327},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.2478/forma-2020-0011","is_oa":true,"landing_page_url":"https://doi.org/10.2478/forma-2020-0011","pdf_url":"https://www.sciendo.com/pdf/10.2478/forma-2020-0011","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:c61d9e35e1ab4c8fbd24cf956d1b3f04","is_oa":true,"landing_page_url":"https://doaj.org/article/c61d9e35e1ab4c8fbd24cf956d1b3f04","pdf_url":null,"source":{"id":"https://openalex.org/S112646816","display_name":"SHILAP Revista de lepidopterolog\u00eda","issn_l":"0300-5267","issn":["0300-5267","2340-4078"],"is_oa":true,"is_in_doaj":true,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Formalized Mathematics, Vol 28, Iss 1, Pp 121-128 (2020)","raw_type":"article"},{"id":"pmh:oai:repozytorium.uwb.edu.pl:11320/9229","is_oa":true,"landing_page_url":"http://hdl.handle.net/11320/9229","pdf_url":null,"source":{"id":"https://openalex.org/S4306400933","display_name":"The Repository of University in Bialystok (University in Bialystok)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210094198","host_organization_name":"University Clinical Hospital In Bialystok","host_organization_lineage":["https://openalex.org/I4210094198"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Article"}],"best_oa_location":{"id":"doi:10.2478/forma-2020-0011","is_oa":true,"landing_page_url":"https://doi.org/10.2478/forma-2020-0011","pdf_url":"https://www.sciendo.com/pdf/10.2478/forma-2020-0011","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":[{"display_name":"Reduced inequalities","score":0.49000000953674316,"id":"https://metadata.un.org/sdg/10"}],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3032958609.pdf","grobid_xml":"https://content.openalex.org/works/W3032958609.grobid-xml"},"referenced_works_count":10,"referenced_works":["https://openalex.org/W608087936","https://openalex.org/W1596666806","https://openalex.org/W2110182592","https://openalex.org/W2295728669","https://openalex.org/W2314125776","https://openalex.org/W2753614965","https://openalex.org/W2758703457","https://openalex.org/W2778928065","https://openalex.org/W2935510787","https://openalex.org/W4211007335"],"related_works":["https://openalex.org/W2184441312","https://openalex.org/W2674573885","https://openalex.org/W1485268022","https://openalex.org/W1975005191","https://openalex.org/W2331106272","https://openalex.org/W4361984403","https://openalex.org/W1542808721","https://openalex.org/W2960454922","https://openalex.org/W1487720066","https://openalex.org/W2253053392"],"abstract_inverted_index":{"Summary":[0],"We":[1,65],"continue":[2],"in":[3,93,97,102],"the":[4,8,15,86,128],"Mizar":[5,94,129],"system":[6],"[2]":[7],"formalization":[9],"of":[10,17,61,85,88,113,117],"fuzzy":[11,29,38,62,89,118],"implications":[12,39],"according":[13],"to":[14,122],"book":[16],"Baczy\u0144ski":[18],"and":[19,31,41,43,46,72,99,119],"Jayaram":[20],"\u201cFuzzy":[21],"Implications\u201d":[22],"[1].":[23],"In":[24],"this":[25],"article":[26],"we":[27],"define":[28],"negations":[30,71],"show":[32,73],"their":[33],"connections":[34],"with":[35],"previously":[36],"defined":[37],"[4]":[40],"[5]":[42],"triangular":[44],"norms":[45],"conorms":[47],"[6].":[48],"This":[49,80,104],"can":[50,106],"be":[51,107],"seen":[52],"as":[53,110],"a":[54,58,83,111,114],"step":[55],"towards":[56],"building":[57],"formal":[59,115],"framework":[60],"connectives":[63],"[10].":[64],"introduce":[66],"formally":[67],"Sugeno":[68],"negation,":[69],"boundary":[70],"how":[74],"these":[75],"operators":[76],"are":[77],"pointwise":[78],"ordered.":[79],"work":[81],"is":[82],"continuation":[84],"development":[87],"sets":[90],"[12],":[91],"[3]":[92],"[7]":[95],"started":[96],"[11]":[98],"partially":[100],"described":[101],"[8].":[103],"submission":[105],"treated":[108],"also":[109],"part":[112],"comparison":[116],"rough":[120],"approaches":[121],"incomplete":[123],"or":[124],"uncertain":[125],"information":[126],"within":[127],"Mathematical":[130],"Library":[131],"[9].":[132]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":3}],"updated_date":"2026-03-20T23:20:44.827607","created_date":"2025-10-10T00:00:00"}