{"id":"https://openalex.org/W2026829949","doi":"https://doi.org/10.1016/s0019-9958(76)80011-3","title":"Some properties of fuzzy sets of type 2","display_name":"Some properties of fuzzy sets of type 2","publication_year":1976,"publication_date":"1976-08-01","ids":{"openalex":"https://openalex.org/W2026829949","doi":"https://doi.org/10.1016/s0019-9958(76)80011-3","mag":"2026829949"},"language":"en","primary_location":{"id":"doi:10.1016/s0019-9958(76)80011-3","is_oa":false,"landing_page_url":"https://doi.org/10.1016/s0019-9958(76)80011-3","pdf_url":null,"source":{"id":"https://openalex.org/S4210192454","display_name":"Information and Control","issn_l":"0019-9958","issn":["0019-9958","1878-2981"],"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/P4310319955","host_organization_name":"Academic Press","host_organization_lineage":["https://openalex.org/P4310319955","https://openalex.org/P4310320990"],"host_organization_lineage_names":["Academic Press","Elsevier BV"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Information and Control","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":"https://openalex.org/A5109877576","display_name":"M. Mizumoto","orcid":null},"institutions":[{"id":"https://openalex.org/I98285908","display_name":"The University of Osaka","ror":"https://ror.org/035t8zc32","country_code":"JP","type":"education","lineage":["https://openalex.org/I98285908"]}],"countries":["JP"],"is_corresponding":true,"raw_author_name":"Masaharu Mizumoto","raw_affiliation_strings":["Department of Information and Computer Sciences, Faculty of Engineering Science, Osaka University, Toyonaka, Osaka 560, Japan","Department of Information and Computer Sciences, Faculty of Engineering Science, Osaka University, Toyonaka, Osaka, 560, Japan.#TAB#"],"affiliations":[{"raw_affiliation_string":"Department of Information and Computer Sciences, Faculty of Engineering Science, Osaka University, Toyonaka, Osaka 560, Japan","institution_ids":["https://openalex.org/I98285908"]},{"raw_affiliation_string":"Department of Information and Computer Sciences, Faculty of Engineering Science, Osaka University, Toyonaka, Osaka, 560, Japan.#TAB#","institution_ids":["https://openalex.org/I98285908"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5111872812","display_name":"Kokichi Tanaka","orcid":null},"institutions":[{"id":"https://openalex.org/I98285908","display_name":"The University of Osaka","ror":"https://ror.org/035t8zc32","country_code":"JP","type":"education","lineage":["https://openalex.org/I98285908"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Kokichi Tanaka","raw_affiliation_strings":["Department of Information and Computer Sciences, Faculty of Engineering Science, Osaka University, Toyonaka, Osaka 560, Japan","Department of Information and Computer Sciences, Faculty of Engineering Science, Osaka University, Toyonaka, Osaka, 560, Japan.#TAB#"],"affiliations":[{"raw_affiliation_string":"Department of Information and Computer Sciences, Faculty of Engineering Science, Osaka University, Toyonaka, Osaka 560, Japan","institution_ids":["https://openalex.org/I98285908"]},{"raw_affiliation_string":"Department of Information and Computer Sciences, Faculty of Engineering Science, Osaka University, Toyonaka, Osaka, 560, Japan.#TAB#","institution_ids":["https://openalex.org/I98285908"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5109877576"],"corresponding_institution_ids":["https://openalex.org/I98285908"],"apc_list":null,"apc_paid":null,"fwci":7.335,"has_fulltext":false,"cited_by_count":769,"citation_normalized_percentile":{"value":0.97786211,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":97,"max":100},"biblio":{"volume":"31","issue":"4","first_page":"312","last_page":"340"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11671","display_name":"Fuzzy and Soft Set Theory","score":0.9990000128746033,"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"}},"topics":[{"id":"https://openalex.org/T11671","display_name":"Fuzzy and Soft Set Theory","score":0.9990000128746033,"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/T11063","display_name":"Rough Sets and Fuzzy Logic","score":0.998199999332428,"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":0.9976999759674072,"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/mathematics","display_name":"Mathematics","score":0.7397961616516113},{"id":"https://openalex.org/keywords/fuzzy-subalgebra","display_name":"Fuzzy subalgebra","score":0.6887792348861694},{"id":"https://openalex.org/keywords/fuzzy-set-operations","display_name":"Fuzzy set operations","score":0.6439627408981323},{"id":"https://openalex.org/keywords/type-2-fuzzy-sets-and-systems","display_name":"Type-2 fuzzy sets and systems","score":0.6413466930389404},{"id":"https://openalex.org/keywords/fuzzy-classification","display_name":"Fuzzy classification","score":0.6371448040008545},{"id":"https://openalex.org/keywords/defuzzification","display_name":"Defuzzification","score":0.6367537975311279},{"id":"https://openalex.org/keywords/membership-function","display_name":"Membership function","score":0.6222304701805115},{"id":"https://openalex.org/keywords/fuzzy-number","display_name":"Fuzzy number","score":0.6057639718055725},{"id":"https://openalex.org/keywords/fuzzy-mathematics","display_name":"Fuzzy mathematics","score":0.6056981086730957},{"id":"https://openalex.org/keywords/fuzzy-set","display_name":"Fuzzy set","score":0.5844485759735107},{"id":"https://openalex.org/keywords/fuzzy-logic","display_name":"Fuzzy logic","score":0.5246003866195679},{"id":"https://openalex.org/keywords/algebraic-operation","display_name":"Algebraic operation","score":0.5039922595024109},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.48979663848876953},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.46243512630462646},{"id":"https://openalex.org/keywords/algebraic-structure","display_name":"Algebraic structure","score":0.4436832666397095},{"id":"https://openalex.org/keywords/fuzzy-measure-theory","display_name":"Fuzzy measure theory","score":0.4162876605987549},{"id":"https://openalex.org/keywords/algebraic-number","display_name":"Algebraic number","score":0.363718181848526},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3541996479034424},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.17087587714195251},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.16097834706306458},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.09037095308303833}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7397961616516113},{"id":"https://openalex.org/C115740575","wikidata":"https://www.wikidata.org/wiki/Q5511136","display_name":"Fuzzy subalgebra","level":5,"score":0.6887792348861694},{"id":"https://openalex.org/C148671577","wikidata":"https://www.wikidata.org/wiki/Q5511133","display_name":"Fuzzy set operations","level":4,"score":0.6439627408981323},{"id":"https://openalex.org/C17350324","wikidata":"https://www.wikidata.org/wiki/Q7860605","display_name":"Type-2 fuzzy sets and systems","level":5,"score":0.6413466930389404},{"id":"https://openalex.org/C127385683","wikidata":"https://www.wikidata.org/wiki/Q1475696","display_name":"Fuzzy classification","level":4,"score":0.6371448040008545},{"id":"https://openalex.org/C170260401","wikidata":"https://www.wikidata.org/wiki/Q5251735","display_name":"Defuzzification","level":5,"score":0.6367537975311279},{"id":"https://openalex.org/C5263885","wikidata":"https://www.wikidata.org/wiki/Q1967302","display_name":"Membership function","level":4,"score":0.6222304701805115},{"id":"https://openalex.org/C1883856","wikidata":"https://www.wikidata.org/wiki/Q3407463","display_name":"Fuzzy number","level":4,"score":0.6057639718055725},{"id":"https://openalex.org/C166586474","wikidata":"https://www.wikidata.org/wiki/Q5511129","display_name":"Fuzzy mathematics","level":5,"score":0.6056981086730957},{"id":"https://openalex.org/C42011625","wikidata":"https://www.wikidata.org/wiki/Q1055058","display_name":"Fuzzy set","level":3,"score":0.5844485759735107},{"id":"https://openalex.org/C58166","wikidata":"https://www.wikidata.org/wiki/Q224821","display_name":"Fuzzy logic","level":2,"score":0.5246003866195679},{"id":"https://openalex.org/C136003732","wikidata":"https://www.wikidata.org/wiki/Q3854337","display_name":"Algebraic operation","level":3,"score":0.5039922595024109},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.48979663848876953},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.46243512630462646},{"id":"https://openalex.org/C182419690","wikidata":"https://www.wikidata.org/wiki/Q205464","display_name":"Algebraic structure","level":2,"score":0.4436832666397095},{"id":"https://openalex.org/C100516043","wikidata":"https://www.wikidata.org/wiki/Q4455138","display_name":"Fuzzy measure theory","level":5,"score":0.4162876605987549},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.363718181848526},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3541996479034424},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.17087587714195251},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.16097834706306458},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.09037095308303833}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1016/s0019-9958(76)80011-3","is_oa":false,"landing_page_url":"https://doi.org/10.1016/s0019-9958(76)80011-3","pdf_url":null,"source":{"id":"https://openalex.org/S4210192454","display_name":"Information and Control","issn_l":"0019-9958","issn":["0019-9958","1878-2981"],"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/P4310319955","host_organization_name":"Academic Press","host_organization_lineage":["https://openalex.org/P4310319955","https://openalex.org/P4310320990"],"host_organization_lineage_names":["Academic Press","Elsevier BV"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Information and Control","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"score":0.41999998688697815,"id":"https://metadata.un.org/sdg/10","display_name":"Reduced inequalities"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":13,"referenced_works":["https://openalex.org/W145378302","https://openalex.org/W1982934077","https://openalex.org/W1990868719","https://openalex.org/W2017462139","https://openalex.org/W2045127810","https://openalex.org/W2054416947","https://openalex.org/W2157041604","https://openalex.org/W2598771954","https://openalex.org/W4211007335","https://openalex.org/W4254730433","https://openalex.org/W6605945896","https://openalex.org/W6647836167","https://openalex.org/W6836461034"],"related_works":["https://openalex.org/W2037428035","https://openalex.org/W2045460427","https://openalex.org/W2116819400","https://openalex.org/W1963942578","https://openalex.org/W4242545108","https://openalex.org/W1967467384","https://openalex.org/W2048452567","https://openalex.org/W2075305841","https://openalex.org/W2026829949","https://openalex.org/W2365416574"],"abstract_inverted_index":null,"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":13},{"year":2024,"cited_by_count":22},{"year":2023,"cited_by_count":18},{"year":2022,"cited_by_count":29},{"year":2021,"cited_by_count":30},{"year":2020,"cited_by_count":30},{"year":2019,"cited_by_count":43},{"year":2018,"cited_by_count":33},{"year":2017,"cited_by_count":37},{"year":2016,"cited_by_count":37},{"year":2015,"cited_by_count":47},{"year":2014,"cited_by_count":44},{"year":2013,"cited_by_count":36},{"year":2012,"cited_by_count":37}],"updated_date":"2026-03-20T23:20:44.827607","created_date":"2025-10-10T00:00:00"}