{"id":"https://openalex.org/W2883490761","doi":"https://doi.org/10.3233/jifs-172169","title":"On A-subsets in lattice implication algebras","display_name":"On A-subsets in lattice implication algebras","publication_year":2018,"publication_date":"2018-07-26","ids":{"openalex":"https://openalex.org/W2883490761","doi":"https://doi.org/10.3233/jifs-172169","mag":"2883490761"},"language":"en","primary_location":{"id":"doi:10.3233/jifs-172169","is_oa":false,"landing_page_url":"https://doi.org/10.3233/jifs-172169","pdf_url":null,"source":{"id":"https://openalex.org/S179157397","display_name":"Journal of Intelligent & Fuzzy Systems","issn_l":"1064-1246","issn":["1064-1246","1875-8967"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310318577","host_organization_name":"IOS Press","host_organization_lineage":["https://openalex.org/P4310318577"],"host_organization_lineage_names":["IOS Press"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Intelligent & Fuzzy Systems","raw_type":"journal-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":null,"display_name":"Xiqing Long","orcid":null},"institutions":[{"id":"https://openalex.org/I4210131342","display_name":"Yibin University","ror":"https://ror.org/03w8m2977","country_code":"CN","type":"education","lineage":["https://openalex.org/I4210131342"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Xiqing Long","raw_affiliation_strings":["School of Mathematics, YiBin University, YiBin, P.R. China"],"affiliations":[{"raw_affiliation_string":"School of Mathematics, YiBin University, YiBin, P.R. China","institution_ids":["https://openalex.org/I4210131342"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100330428","display_name":"Yi Liu","orcid":"https://orcid.org/0000-0001-5304-235X"},"institutions":[{"id":"https://openalex.org/I4210117337","display_name":"Neijiang Normal University","ror":"https://ror.org/02bc8tz70","country_code":"CN","type":"education","lineage":["https://openalex.org/I4210117337"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yi Liu","raw_affiliation_strings":["Data Recovery Key Laboratory of Sichuan Province, Neijiang Normal University, Neijiang, P.R. China"],"affiliations":[{"raw_affiliation_string":"Data Recovery Key Laboratory of Sichuan Province, Neijiang Normal University, Neijiang, P.R. China","institution_ids":["https://openalex.org/I4210117337"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100462090","display_name":"Yang Xu","orcid":"https://orcid.org/0000-0002-9151-8555"},"institutions":[{"id":"https://openalex.org/I4800084","display_name":"Southwest Jiaotong University","ror":"https://ror.org/00hn7w693","country_code":"CN","type":"education","lineage":["https://openalex.org/I4800084"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yang Xu","raw_affiliation_strings":["Department of Mathematics, Southwest Jiaotong University, Chengdu, P.R. China","E-mail:"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Southwest Jiaotong University, Chengdu, P.R. China","institution_ids":["https://openalex.org/I4800084"]},{"raw_affiliation_string":"E-mail:","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I4210131342"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.11747315,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"35","issue":"2","first_page":"2189","last_page":"2198"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11727","display_name":"Advanced Algebra and Logic","score":0.9997000098228455,"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":0.9997000098228455,"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/T11063","display_name":"Rough Sets and Fuzzy Logic","score":0.9969000220298767,"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/T11671","display_name":"Fuzzy and Soft Set Theory","score":0.9902999997138977,"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/homomorphism","display_name":"Homomorphism","score":0.7635228633880615},{"id":"https://openalex.org/keywords/lattice","display_name":"Lattice (music)","score":0.7110328674316406},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6461894512176514},{"id":"https://openalex.org/keywords/boolean-algebra","display_name":"Boolean algebra","score":0.4665719270706177},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.4079321324825287},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.39442121982574463},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3848859667778015},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.33238404989242554},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.09087318181991577}],"concepts":[{"id":"https://openalex.org/C4042151","wikidata":"https://www.wikidata.org/wiki/Q215111","display_name":"Homomorphism","level":2,"score":0.7635228633880615},{"id":"https://openalex.org/C2781204021","wikidata":"https://www.wikidata.org/wiki/Q6497091","display_name":"Lattice (music)","level":2,"score":0.7110328674316406},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6461894512176514},{"id":"https://openalex.org/C39685927","wikidata":"https://www.wikidata.org/wiki/Q173183","display_name":"Boolean algebra","level":2,"score":0.4665719270706177},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.4079321324825287},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.39442121982574463},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3848859667778015},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.33238404989242554},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.09087318181991577},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.3233/jifs-172169","is_oa":false,"landing_page_url":"https://doi.org/10.3233/jifs-172169","pdf_url":null,"source":{"id":"https://openalex.org/S179157397","display_name":"Journal of Intelligent & Fuzzy Systems","issn_l":"1064-1246","issn":["1064-1246","1875-8967"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310318577","host_organization_name":"IOS Press","host_organization_lineage":["https://openalex.org/P4310318577"],"host_organization_lineage_names":["IOS Press"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Intelligent & Fuzzy Systems","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":19,"referenced_works":["https://openalex.org/W1570073479","https://openalex.org/W1966289666","https://openalex.org/W1966321785","https://openalex.org/W1981472242","https://openalex.org/W1988384023","https://openalex.org/W2017999234","https://openalex.org/W2034876376","https://openalex.org/W2053399223","https://openalex.org/W2079159346","https://openalex.org/W2087796831","https://openalex.org/W2092180595","https://openalex.org/W2283886275","https://openalex.org/W2296256030","https://openalex.org/W2312744322","https://openalex.org/W2337369158","https://openalex.org/W2475038724","https://openalex.org/W2498912203","https://openalex.org/W2774046574","https://openalex.org/W4206828130"],"related_works":["https://openalex.org/W4308159138","https://openalex.org/W1979798674","https://openalex.org/W3169947911","https://openalex.org/W1965803518","https://openalex.org/W2052359815","https://openalex.org/W2020491689","https://openalex.org/W2000364634","https://openalex.org/W3105028440","https://openalex.org/W4244612409","https://openalex.org/W2074361790"],"abstract_inverted_index":{"In":[0,33],"this":[1],"paper,":[2],"we":[3,17,54],"further":[4],"study":[5],"the":[6,19,35,56,69,103],"theory":[7],"of":[8,21,27,37,44,58,71,73],"A-subsets":[9,28],"in":[10,29,49],"lattice":[11,30,50,94,97],"implication":[12,31,51,98],"algebras.":[13,32,52],"To":[14],"begin":[15],"with,":[16],"introduce":[18,55],"propositions":[20],"homomorphism":[22],"image":[23,26],"and":[24,41,67,95],"original":[25],"addition,":[34],"notion":[36,57],"A*-subsets":[38,45],"is":[39],"introduced":[40],"some":[42],"properties":[43],"are":[46],"also":[47],"investigated":[48],"Finally,":[53],"involutory":[59],"LI-ideals":[60],"with":[61,100],"respect":[62,101],"to":[63,102],"an":[64],"LI-ideal":[65],"A":[66,77,83],"denote":[68],"set":[70],"all":[72],"them":[74],"by":[75],"S":[76,82],"(":[78,84],"L":[79,85],").":[80],"Then":[81],")":[86],"can":[87],"be":[88],"made":[89],"into":[90],"a":[91,96],"complete":[92],"Boolean":[93],"algebra":[99],"suit":[104],"operations,":[105],"respectively.":[106]},"counts_by_year":[],"updated_date":"2026-04-16T08:26:57.006410","created_date":"2025-10-10T00:00:00"}