{"id":"https://openalex.org/W2995094519","doi":"https://doi.org/10.1155/2019/8348603","title":"The Measure of Fuzzy Filters on <i>BL</i>-Algebras","display_name":"The Measure of Fuzzy Filters on <i>BL</i>-Algebras","publication_year":2019,"publication_date":"2019-12-12","ids":{"openalex":"https://openalex.org/W2995094519","doi":"https://doi.org/10.1155/2019/8348603","mag":"2995094519"},"language":"en","primary_location":{"id":"doi:10.1155/2019/8348603","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2019/8348603","pdf_url":"https://downloads.hindawi.com/journals/afs/2019/8348603.pdf","source":{"id":"https://openalex.org/S117816480","display_name":"Advances in Fuzzy Systems","issn_l":"1687-7101","issn":["1687-7101","1687-711X"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Advances in Fuzzy Systems","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://downloads.hindawi.com/journals/afs/2019/8348603.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5072360042","display_name":"Zhu Xiang","orcid":"https://orcid.org/0000-0001-5721-9642"},"institutions":[{"id":"https://openalex.org/I1336834208","display_name":"Management and Science University","ror":"https://ror.org/027zr9y17","country_code":"MY","type":"education","lineage":["https://openalex.org/I1336834208"]},{"id":"https://openalex.org/I77631543","display_name":"Wuxi Institute of Technology","ror":"https://ror.org/00ab95029","country_code":"CN","type":"education","lineage":["https://openalex.org/I77631543"]}],"countries":["CN","MY"],"is_corresponding":false,"raw_author_name":"Xiang Zhu","raw_affiliation_strings":["Division of General Courses, Wuxi Institute of Technology, Wuxi 214121, China","Information Science & Engineering, Management & Science University, Shah Alam 40100, Malaysia"],"affiliations":[{"raw_affiliation_string":"Division of General Courses, Wuxi Institute of Technology, Wuxi 214121, China","institution_ids":["https://openalex.org/I77631543"]},{"raw_affiliation_string":"Information Science & Engineering, Management & Science University, Shah Alam 40100, Malaysia","institution_ids":["https://openalex.org/I1336834208"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5023950394","display_name":"Md Gapar Md Johar","orcid":"https://orcid.org/0000-0001-7986-3834"},"institutions":[{"id":"https://openalex.org/I1336834208","display_name":"Management and Science University","ror":"https://ror.org/027zr9y17","country_code":"MY","type":"education","lineage":["https://openalex.org/I1336834208"]}],"countries":["MY"],"is_corresponding":true,"raw_author_name":"Md Gapar Md Johar","raw_affiliation_strings":["Information Science & Engineering, Management & Science University, Shah Alam 40100, Malaysia"],"affiliations":[{"raw_affiliation_string":"Information Science & Engineering, Management & Science University, Shah Alam 40100, Malaysia","institution_ids":["https://openalex.org/I1336834208"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5051499834","display_name":"Lilysuriazna Raya","orcid":"https://orcid.org/0000-0002-3189-2078"},"institutions":[{"id":"https://openalex.org/I1336834208","display_name":"Management and Science University","ror":"https://ror.org/027zr9y17","country_code":"MY","type":"education","lineage":["https://openalex.org/I1336834208"]}],"countries":["MY"],"is_corresponding":false,"raw_author_name":"Lilysuriazna Binti Raya","raw_affiliation_strings":["Information Science & Engineering, Management & Science University, Shah Alam 40100, Malaysia"],"affiliations":[{"raw_affiliation_string":"Information Science & Engineering, Management & Science University, Shah Alam 40100, Malaysia","institution_ids":["https://openalex.org/I1336834208"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5049191270","display_name":"Zuhua Liao","orcid":null},"institutions":[{"id":"https://openalex.org/I111599522","display_name":"Jiangnan University","ror":"https://ror.org/04mkzax54","country_code":"CN","type":"education","lineage":["https://openalex.org/I111599522"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Zu-hua Liao","raw_affiliation_strings":["School of Science, Jiangnan University, Wuxi 214122, China"],"affiliations":[{"raw_affiliation_string":"School of Science, Jiangnan University, Wuxi 214122, China","institution_ids":["https://openalex.org/I111599522"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5023950394"],"corresponding_institution_ids":["https://openalex.org/I1336834208"],"apc_list":{"value":900,"currency":"USD","value_usd":900},"apc_paid":{"value":900,"currency":"USD","value_usd":900},"fwci":0.0,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":{"value":0.2,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"2019","issue":null,"first_page":"1","last_page":"8"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11727","display_name":"Advanced Algebra and Logic","score":0.9976000189781189,"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":0.9976000189781189,"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/T10820","display_name":"Fuzzy Logic and Control Systems","score":0.9948999881744385,"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/T11063","display_name":"Rough Sets and Fuzzy Logic","score":0.9948999881744385,"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/fuzzy-logic","display_name":"Fuzzy logic","score":0.7462827563285828},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6667790412902832},{"id":"https://openalex.org/keywords/filter","display_name":"Filter (signal processing)","score":0.6029552817344666},{"id":"https://openalex.org/keywords/measure","display_name":"Measure (data warehouse)","score":0.5841578841209412},{"id":"https://openalex.org/keywords/homomorphism","display_name":"Homomorphism","score":0.5552117228507996},{"id":"https://openalex.org/keywords/intersection","display_name":"Intersection (aeronautics)","score":0.5298022627830505},{"id":"https://openalex.org/keywords/fuzzy-number","display_name":"Fuzzy number","score":0.5057640075683594},{"id":"https://openalex.org/keywords/degree","display_name":"Degree (music)","score":0.5030891299247742},{"id":"https://openalex.org/keywords/defuzzification","display_name":"Defuzzification","score":0.4922751486301422},{"id":"https://openalex.org/keywords/fuzzy-classification","display_name":"Fuzzy classification","score":0.4736132323741913},{"id":"https://openalex.org/keywords/fuzzy-subalgebra","display_name":"Fuzzy subalgebra","score":0.45415133237838745},{"id":"https://openalex.org/keywords/fuzzy-measure-theory","display_name":"Fuzzy measure theory","score":0.4450325071811676},{"id":"https://openalex.org/keywords/image","display_name":"Image (mathematics)","score":0.42686140537261963},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.41303038597106934},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.39773669838905334},{"id":"https://openalex.org/keywords/fuzzy-set","display_name":"Fuzzy set","score":0.37643352150917053},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.37166786193847656},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.27452552318573},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.27033406496047974},{"id":"https://openalex.org/keywords/data-mining","display_name":"Data mining","score":0.17357710003852844},{"id":"https://openalex.org/keywords/computer-vision","display_name":"Computer vision","score":0.14497321844100952},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.07735207676887512}],"concepts":[{"id":"https://openalex.org/C58166","wikidata":"https://www.wikidata.org/wiki/Q224821","display_name":"Fuzzy logic","level":2,"score":0.7462827563285828},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6667790412902832},{"id":"https://openalex.org/C106131492","wikidata":"https://www.wikidata.org/wiki/Q3072260","display_name":"Filter (signal processing)","level":2,"score":0.6029552817344666},{"id":"https://openalex.org/C2780009758","wikidata":"https://www.wikidata.org/wiki/Q6804172","display_name":"Measure (data warehouse)","level":2,"score":0.5841578841209412},{"id":"https://openalex.org/C4042151","wikidata":"https://www.wikidata.org/wiki/Q215111","display_name":"Homomorphism","level":2,"score":0.5552117228507996},{"id":"https://openalex.org/C64543145","wikidata":"https://www.wikidata.org/wiki/Q162942","display_name":"Intersection (aeronautics)","level":2,"score":0.5298022627830505},{"id":"https://openalex.org/C1883856","wikidata":"https://www.wikidata.org/wiki/Q3407463","display_name":"Fuzzy number","level":4,"score":0.5057640075683594},{"id":"https://openalex.org/C2775997480","wikidata":"https://www.wikidata.org/wiki/Q586277","display_name":"Degree (music)","level":2,"score":0.5030891299247742},{"id":"https://openalex.org/C170260401","wikidata":"https://www.wikidata.org/wiki/Q5251735","display_name":"Defuzzification","level":5,"score":0.4922751486301422},{"id":"https://openalex.org/C127385683","wikidata":"https://www.wikidata.org/wiki/Q1475696","display_name":"Fuzzy classification","level":4,"score":0.4736132323741913},{"id":"https://openalex.org/C115740575","wikidata":"https://www.wikidata.org/wiki/Q5511136","display_name":"Fuzzy subalgebra","level":5,"score":0.45415133237838745},{"id":"https://openalex.org/C100516043","wikidata":"https://www.wikidata.org/wiki/Q4455138","display_name":"Fuzzy measure theory","level":5,"score":0.4450325071811676},{"id":"https://openalex.org/C115961682","wikidata":"https://www.wikidata.org/wiki/Q860623","display_name":"Image (mathematics)","level":2,"score":0.42686140537261963},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.41303038597106934},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.39773669838905334},{"id":"https://openalex.org/C42011625","wikidata":"https://www.wikidata.org/wiki/Q1055058","display_name":"Fuzzy set","level":3,"score":0.37643352150917053},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.37166786193847656},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.27452552318573},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.27033406496047974},{"id":"https://openalex.org/C124101348","wikidata":"https://www.wikidata.org/wiki/Q172491","display_name":"Data mining","level":1,"score":0.17357710003852844},{"id":"https://openalex.org/C31972630","wikidata":"https://www.wikidata.org/wiki/Q844240","display_name":"Computer vision","level":1,"score":0.14497321844100952},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.07735207676887512},{"id":"https://openalex.org/C146978453","wikidata":"https://www.wikidata.org/wiki/Q3798668","display_name":"Aerospace engineering","level":1,"score":0.0},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1155/2019/8348603","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2019/8348603","pdf_url":"https://downloads.hindawi.com/journals/afs/2019/8348603.pdf","source":{"id":"https://openalex.org/S117816480","display_name":"Advances in Fuzzy Systems","issn_l":"1687-7101","issn":["1687-7101","1687-711X"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Advances in Fuzzy Systems","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:7e55ff27d14f472ba6f765fa23db05f8","is_oa":true,"landing_page_url":"https://doaj.org/article/7e55ff27d14f472ba6f765fa23db05f8","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":"Advances in Fuzzy Systems, Vol 2019 (2019)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.1155/2019/8348603","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2019/8348603","pdf_url":"https://downloads.hindawi.com/journals/afs/2019/8348603.pdf","source":{"id":"https://openalex.org/S117816480","display_name":"Advances in Fuzzy Systems","issn_l":"1687-7101","issn":["1687-7101","1687-711X"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Advances in Fuzzy Systems","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1085732412","display_name":null,"funder_award_id":"11401259","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G3248934085","display_name":null,"funder_award_id":"61170121","funder_id":"https://openalex.org/F4320322769","funder_display_name":"Natural Science Foundation of Jiangsu Province"},{"id":"https://openalex.org/G4794401583","display_name":null,"funder_award_id":"BK20151117","funder_id":"https://openalex.org/F4320322769","funder_display_name":"Natural Science Foundation of Jiangsu Province"},{"id":"https://openalex.org/G6951918679","display_name":null,"funder_award_id":"11401259","funder_id":"https://openalex.org/F4320322769","funder_display_name":"Natural Science Foundation of Jiangsu Province"},{"id":"https://openalex.org/G7207672108","display_name":null,"funder_award_id":"61673193","funder_id":"https://openalex.org/F4320322769","funder_display_name":"Natural Science Foundation of Jiangsu Province"},{"id":"https://openalex.org/G7440332813","display_name":null,"funder_award_id":"61673193","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G7816615122","display_name":null,"funder_award_id":"BK20151117","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G891265210","display_name":null,"funder_award_id":"61170121","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320321605","display_name":"Government of Jiangsu Province","ror":"https://ror.org/004svx814"},{"id":"https://openalex.org/F4320322769","display_name":"Natural Science Foundation of Jiangsu Province","ror":"https://ror.org/01h0zpd94"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2995094519.pdf","grobid_xml":"https://content.openalex.org/works/W2995094519.grobid-xml"},"referenced_works_count":6,"referenced_works":["https://openalex.org/W2014932432","https://openalex.org/W2050951782","https://openalex.org/W2082180911","https://openalex.org/W2149020820","https://openalex.org/W2912856609","https://openalex.org/W4211007335"],"related_works":["https://openalex.org/W2184441312","https://openalex.org/W4242970302","https://openalex.org/W2571050636","https://openalex.org/W1485268022","https://openalex.org/W2037428035","https://openalex.org/W1489009679","https://openalex.org/W2048452567","https://openalex.org/W4242545108","https://openalex.org/W2092290989","https://openalex.org/W2088978098"],"abstract_inverted_index":{"The":[0],"new":[1],"concept":[2],"of":[3,12,27,44,67,74,83,89],"the":[4,13,45,54,63,68,79,84,87],"fuzzy":[5,25,33,46,64,71,75,80,91],"filter":[6,47,65,81],"degree":[7,21,48],"was":[8],"given":[9],"by":[10,49],"means":[11],"implication":[14],"operator,":[15],"which":[16,23],"enables":[17],"to":[18,22],"measure":[19],"a":[20,24,28,32,90,94],"subset":[26,92],"BL":[29],"-algebra":[30],"is":[31],"filter.":[34],"In":[35],"this":[36],"paper,":[37],"we":[38,61],"put":[39],"forward":[40],"several":[41],"equivalent":[42],"characterizations":[43],"studying":[50],"its":[51],"properties":[52],"and":[53,70,77,86],"relationship":[55],"with":[56],"level":[57],"cut":[58],"sets.":[59],"Furthermore,":[60],"study":[62],"degrees":[66,82],"intersection":[69],"direct":[72],"products":[73],"subsets":[76],"investigate":[78],"image":[85],"preimage":[88],"under":[93],"homomorphism.":[95]},"counts_by_year":[{"year":2024,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
