{"id":"https://openalex.org/W2036468166","doi":"https://doi.org/10.1016/j.fss.2014.01.010","title":"On distributivity equations of implications and contrapositive symmetry equations of implications","display_name":"On distributivity equations of implications and contrapositive symmetry equations of implications","publication_year":2014,"publication_date":"2014-01-29","ids":{"openalex":"https://openalex.org/W2036468166","doi":"https://doi.org/10.1016/j.fss.2014.01.010","mag":"2036468166"},"language":"en","primary_location":{"id":"doi:10.1016/j.fss.2014.01.010","doi":"https://doi.org/10.1016/j.fss.2014.01.010","is_oa":false,"landing_page_url":"https://doi.org/10.1016/j.fss.2014.01.010","pdf_url":null,"source":{"id":"https://openalex.org/S169411308","display_name":"Fuzzy Sets and Systems","issn_l":"0165-0114","issn":["0165-0114","1872-6801"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["cwts-core","jufo-1","norway-1"],"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Fuzzy Sets and Systems","raw_type":"journal-article"},"volume":null,"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/A5101452765","display_name":"Feng Qin","orcid":"https://orcid.org/0000-0001-9163-0021","observed_orcids":["https://orcid.org/0000-0001-9163-0021"]},"institutions":[{"id":"https://openalex.org/I53592917","display_name":"Jiangxi Normal University","ror":"https://ror.org/05nkgk822","country_code":"CN","type":"education","lineage":["https://openalex.org/I53592917"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Feng Qin","raw_affiliation_strings":["College of Mathematics and Information Science, Jiangxi Normal University, 330022 Nanchang, PR China","College of Mathematics and Information Science, Jiangxi Normal University, 330022, Nanchang, PR China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"College of Mathematics and Information Science, Jiangxi Normal University, 330022 Nanchang, PR China","institution_ids":["https://openalex.org/I53592917"]},{"raw_affiliation_string":"College of Mathematics and Information Science, Jiangxi Normal University, 330022, Nanchang, PR China","institution_ids":["https://openalex.org/I53592917"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5003579916","display_name":"Micha\u0142 Baczy\u0144ski","orcid":"https://orcid.org/0000-0002-4442-2112","observed_orcids":["https://orcid.org/0000-0002-4442-2112"]},"institutions":[{"id":"https://openalex.org/I864159182","display_name":"University of Silesia in Katowice","ror":"https://ror.org/0104rcc94","country_code":"PL","type":"education","lineage":["https://openalex.org/I864159182"]}],"countries":["PL"],"is_corresponding":false,"raw_author_name":"Micha\u0142 Baczy\u0144ski","raw_affiliation_strings":["Institute of Mathematics, University of Silesia, ul. Bankowa 14, 40-007 Katowice, Poland","Institute of Mathematics University of Silesia ul. Bankowa 14 40-007 Katowice, Poland"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute of Mathematics, University of Silesia, ul. Bankowa 14, 40-007 Katowice, Poland","institution_ids":["https://openalex.org/I864159182"]},{"raw_affiliation_string":"Institute of Mathematics University of Silesia ul. Bankowa 14 40-007 Katowice, Poland","institution_ids":["https://openalex.org/I864159182"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5101452765"],"corresponding_institution_ids":["https://openalex.org/I53592917"],"apc_list":{"value":2550,"currency":"USD","value_usd":2550},"apc_paid":null,"fwci":0.3336,"has_fulltext":false,"cited_by_count":7,"citation_normalized_percentile":{"value":0.62273653,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":88,"max":96},"biblio":{"volume":"247","issue":null,"first_page":"81","last_page":"91"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11727","display_name":"Advanced Algebra and Logic","score":1.0,"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/T11727","display_name":"Advanced Algebra and Logic","score":1.0,"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/T12508","display_name":"Functional Equations Stability Results","score":0.0,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11671","display_name":"Fuzzy and Soft Set Theory","score":0.0,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/fuzzy-implications","display_name":"fuzzy implications","score":0.8080000281333923},{"id":"https://openalex.org/keywords/t-norms","display_name":"t-norms","score":0.9100000262260437},{"id":"https://openalex.org/keywords/strong-negation","display_name":"strong negation","score":0.8289999961853027},{"id":"https://openalex.org/keywords/fuzzy-inference","display_name":"fuzzy inference","score":0.6850000023841858},{"id":"https://openalex.org/keywords/functional-equations","display_name":"functional equations","score":0.5389999747276306}],"concepts":[{"id":"https://openalex.org/C138390121","wikidata":"https://www.wikidata.org/wiki/Q5283219","display_name":"Distributivity","level":3,"score":0.8804396390914917},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.800470769405365},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.48470616340637207},{"id":"https://openalex.org/C191795146","wikidata":"https://www.wikidata.org/wiki/Q3878446","display_name":"Norm (philosophy)","level":2,"score":0.4802289605140686},{"id":"https://openalex.org/C58166","wikidata":"https://www.wikidata.org/wiki/Q224821","display_name":"Fuzzy logic","level":2,"score":0.47614526748657227},{"id":"https://openalex.org/C2185349","wikidata":"https://www.wikidata.org/wiki/Q190558","display_name":"Negation","level":2,"score":0.45022010803222656},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.4177659749984741},{"id":"https://openalex.org/C2779886137","wikidata":"https://www.wikidata.org/wiki/Q21030012","display_name":"Symmetry (geometry)","level":2,"score":0.41301512718200684},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3327345848083496},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3266669511795044},{"id":"https://openalex.org/C11821877","wikidata":"https://www.wikidata.org/wiki/Q187959","display_name":"Distributive property","level":2,"score":0.16372302174568176},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.11958804726600647},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.09576502442359924},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.0},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","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/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","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/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1016/j.fss.2014.01.010","doi":"https://doi.org/10.1016/j.fss.2014.01.010","is_oa":false,"landing_page_url":"https://doi.org/10.1016/j.fss.2014.01.010","pdf_url":null,"source":{"id":"https://openalex.org/S169411308","display_name":"Fuzzy Sets and Systems","issn_l":"0165-0114","issn":["0165-0114","1872-6801"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["cwts-core","jufo-1","norway-1"],"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Fuzzy Sets and Systems","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"sustainable_development_goals_aurora":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":23,"referenced_works":["https://openalex.org/W92944258","https://openalex.org/W1535673504","https://openalex.org/W1606108510","https://openalex.org/W1986391289","https://openalex.org/W1987918021","https://openalex.org/W2000022321","https://openalex.org/W2015620414","https://openalex.org/W2019142394","https://openalex.org/W2065986912","https://openalex.org/W2078962071","https://openalex.org/W2082291671","https://openalex.org/W2101292580","https://openalex.org/W2112660043","https://openalex.org/W2127221526","https://openalex.org/W2155096631","https://openalex.org/W2163737009","https://openalex.org/W2909580269","https://openalex.org/W2915061287","https://openalex.org/W2985787168","https://openalex.org/W3213572188","https://openalex.org/W4242775544","https://openalex.org/W4255264342","https://openalex.org/W6603775708"],"related_works":["https://openalex.org/W3017062904","https://openalex.org/W2535873559","https://openalex.org/W578326175","https://openalex.org/W2883359489","https://openalex.org/W2593170496","https://openalex.org/W2561764048","https://openalex.org/W4306177072","https://openalex.org/W4206672782","https://openalex.org/W2245124313","https://openalex.org/W2007532429"],"abstract_inverted_index":null,"counts_by_year":[{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":2},{"year":2016,"cited_by_count":1},{"year":2013,"cited_by_count":1}],"updated_date":"2026-08-21T09:56:20.448147","created_date":"2025-10-10T00:00:00"}
