{"id":"https://openalex.org/W2025544956","doi":"https://doi.org/10.1109/fuzz-ieee.2012.6251286","title":"New closed-form solutions for Karnik-Mendel algorithm+defuzzification of an interval type-2 fuzzy set","display_name":"New closed-form solutions for Karnik-Mendel algorithm+defuzzification of an interval type-2 fuzzy set","publication_year":2012,"publication_date":"2012-06-01","ids":{"openalex":"https://openalex.org/W2025544956","doi":"https://doi.org/10.1109/fuzz-ieee.2012.6251286","mag":"2025544956"},"language":"en","primary_location":{"id":"doi:10.1109/fuzz-ieee.2012.6251286","is_oa":false,"landing_page_url":"https://doi.org/10.1109/fuzz-ieee.2012.6251286","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2012 IEEE International Conference on Fuzzy Systems","raw_type":"proceedings-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/A5028699912","display_name":"Jerry M. Mendel","orcid":"https://orcid.org/0000-0001-6377-2452"},"institutions":[{"id":"https://openalex.org/I1174212","display_name":"University of Southern California","ror":"https://ror.org/03taz7m60","country_code":"US","type":"education","lineage":["https://openalex.org/I1174212"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Jerry M. Mendel","raw_affiliation_strings":["Signal and Image Processing Institute, University of Southern California, Los Angeles, 90089-2564, USA","[Signal & Image Process. Inst., Univ. of Southern California, Los Angeles, CA, USA]"],"affiliations":[{"raw_affiliation_string":"Signal and Image Processing Institute, University of Southern California, Los Angeles, 90089-2564, USA","institution_ids":["https://openalex.org/I1174212"]},{"raw_affiliation_string":"[Signal & Image Process. Inst., Univ. of Southern California, Los Angeles, CA, USA]","institution_ids":["https://openalex.org/I1174212"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5048261783","display_name":"Xinwang Liu","orcid":"https://orcid.org/0000-0001-8230-8380"},"institutions":[{"id":"https://openalex.org/I76569877","display_name":"Southeast University","ror":"https://ror.org/04ct4d772","country_code":"CN","type":"education","lineage":["https://openalex.org/I76569877"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Xinwang Liu","raw_affiliation_strings":["School of Economics and Management, Southeast University, Nanjing, Jiangsu, 210096, China","Sch. of Econ. & Manage., Southeast Univ., NanJing, China"],"affiliations":[{"raw_affiliation_string":"School of Economics and Management, Southeast University, Nanjing, Jiangsu, 210096, China","institution_ids":["https://openalex.org/I76569877"]},{"raw_affiliation_string":"Sch. of Econ. & Manage., Southeast Univ., NanJing, China","institution_ids":["https://openalex.org/I76569877"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5028699912"],"corresponding_institution_ids":["https://openalex.org/I1174212"],"apc_list":null,"apc_paid":null,"fwci":4.4595,"has_fulltext":false,"cited_by_count":26,"citation_normalized_percentile":{"value":0.94332347,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":null,"issue":null,"first_page":"1","last_page":"8"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10820","display_name":"Fuzzy Logic and Control Systems","score":0.9998999834060669,"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"}},"topics":[{"id":"https://openalex.org/T10820","display_name":"Fuzzy Logic and Control Systems","score":0.9998999834060669,"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/T10320","display_name":"Neural Networks and Applications","score":0.9980000257492065,"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":0.9333000183105469,"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/defuzzification","display_name":"Defuzzification","score":0.833484411239624},{"id":"https://openalex.org/keywords/taylor-series","display_name":"Taylor series","score":0.754338264465332},{"id":"https://openalex.org/keywords/fuzzy-set","display_name":"Fuzzy set","score":0.6533753275871277},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6082066297531128},{"id":"https://openalex.org/keywords/fuzzy-logic","display_name":"Fuzzy logic","score":0.5705437660217285},{"id":"https://openalex.org/keywords/term","display_name":"Term (time)","score":0.5476239919662476},{"id":"https://openalex.org/keywords/series","display_name":"Series (stratigraphy)","score":0.5431804060935974},{"id":"https://openalex.org/keywords/interval","display_name":"Interval (graph theory)","score":0.5246427655220032},{"id":"https://openalex.org/keywords/approximation-theory","display_name":"Approximation theory","score":0.44011038541793823},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.4323571026325226},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.40864822268486023},{"id":"https://openalex.org/keywords/fuzzy-number","display_name":"Fuzzy number","score":0.3872697949409485},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.33440688252449036},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.2724311649799347},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.258469820022583},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.15700075030326843},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.11475422978401184}],"concepts":[{"id":"https://openalex.org/C170260401","wikidata":"https://www.wikidata.org/wiki/Q5251735","display_name":"Defuzzification","level":5,"score":0.833484411239624},{"id":"https://openalex.org/C158946198","wikidata":"https://www.wikidata.org/wiki/Q131187","display_name":"Taylor series","level":2,"score":0.754338264465332},{"id":"https://openalex.org/C42011625","wikidata":"https://www.wikidata.org/wiki/Q1055058","display_name":"Fuzzy set","level":3,"score":0.6533753275871277},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6082066297531128},{"id":"https://openalex.org/C58166","wikidata":"https://www.wikidata.org/wiki/Q224821","display_name":"Fuzzy logic","level":2,"score":0.5705437660217285},{"id":"https://openalex.org/C61797465","wikidata":"https://www.wikidata.org/wiki/Q1188986","display_name":"Term (time)","level":2,"score":0.5476239919662476},{"id":"https://openalex.org/C143724316","wikidata":"https://www.wikidata.org/wiki/Q312468","display_name":"Series (stratigraphy)","level":2,"score":0.5431804060935974},{"id":"https://openalex.org/C2778067643","wikidata":"https://www.wikidata.org/wiki/Q166507","display_name":"Interval (graph theory)","level":2,"score":0.5246427655220032},{"id":"https://openalex.org/C145242015","wikidata":"https://www.wikidata.org/wiki/Q774123","display_name":"Approximation theory","level":2,"score":0.44011038541793823},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4323571026325226},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.40864822268486023},{"id":"https://openalex.org/C1883856","wikidata":"https://www.wikidata.org/wiki/Q3407463","display_name":"Fuzzy number","level":4,"score":0.3872697949409485},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.33440688252449036},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2724311649799347},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.258469820022583},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.15700075030326843},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.11475422978401184},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C151730666","wikidata":"https://www.wikidata.org/wiki/Q7205","display_name":"Paleontology","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/fuzz-ieee.2012.6251286","is_oa":false,"landing_page_url":"https://doi.org/10.1109/fuzz-ieee.2012.6251286","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2012 IEEE International Conference on Fuzzy Systems","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":38,"referenced_works":["https://openalex.org/W1977425756","https://openalex.org/W1983658296","https://openalex.org/W2000976145","https://openalex.org/W2021429464","https://openalex.org/W2039037639","https://openalex.org/W2059901265","https://openalex.org/W2101560809","https://openalex.org/W2103232511","https://openalex.org/W2105234323","https://openalex.org/W2108225531","https://openalex.org/W2116046819","https://openalex.org/W2116579452","https://openalex.org/W2120165455","https://openalex.org/W2128251760","https://openalex.org/W2130135344","https://openalex.org/W2132885717","https://openalex.org/W2141218840","https://openalex.org/W2147708960","https://openalex.org/W2149604064","https://openalex.org/W2151614844","https://openalex.org/W2152329090","https://openalex.org/W2153406165","https://openalex.org/W2153744349","https://openalex.org/W2154186319","https://openalex.org/W2155263265","https://openalex.org/W2158759539","https://openalex.org/W2161771180","https://openalex.org/W2162315444","https://openalex.org/W2162706466","https://openalex.org/W2164879989","https://openalex.org/W2165064705","https://openalex.org/W2165846406","https://openalex.org/W2913642042","https://openalex.org/W4206636130","https://openalex.org/W4247749894","https://openalex.org/W6655743869","https://openalex.org/W6682133608","https://openalex.org/W6682291467"],"related_works":["https://openalex.org/W2773005380","https://openalex.org/W4388451300","https://openalex.org/W2060361571","https://openalex.org/W1879432897","https://openalex.org/W2256857057","https://openalex.org/W3167814444","https://openalex.org/W3176863924","https://openalex.org/W2023513928","https://openalex.org/W2182392910","https://openalex.org/W4361984403"],"abstract_inverted_index":{"Karnik-Mendel":[0],"(KM)":[1],"algorithms":[2],"used":[3,13],"for":[4,30,35],"type":[5],"reduction":[6],"(TR)":[7],"followed":[8],"by":[9],"defuzzification":[10],"are":[11],"commonly":[12],"in":[14,47,64,91],"interval":[15],"type-2":[16],"fuzzy":[17],"logic":[18],"systems":[19],"(IT2":[20],"FLSs).":[21],"Up":[22],"until":[23],"now":[24],"no":[25],"closed-form":[26],"solution":[27],"has":[28],"existed":[29],"KM+defuzzification.":[31,43,113],"Our":[32],"paper":[33],"gives,":[34],"the":[36,48,51,56,61,65,79,88,93,98,104],"first":[37,45,99,105],"time,":[38],"a":[39,69,108],"Taylor-series":[40],"approximation":[41,49,82,111],"to":[42,71,112],"The":[44],"term":[46,63,95,106],"is":[50,59,68,77,83,87,107],"Nie-Tan":[52],"(NT)":[53],"formula,":[54],"and":[55],"second-term":[57],"(which":[58],"actually":[60],"third-order":[62],"Taylor":[66,80],"series)":[67],"correction":[70],"it.":[72],"One":[73],"very":[74,109],"interesting":[75],"fact":[76],"that":[78,92,103],"series":[81],"itself":[84],"iterative":[85],"(as":[86],"KM":[89],"Algorithm)":[90],"second":[94],"depends":[96],"on":[97],"term.":[100],"Simulations":[101],"show":[102],"good":[110]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2024,"cited_by_count":2},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":2},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":4},{"year":2016,"cited_by_count":4},{"year":2015,"cited_by_count":2},{"year":2014,"cited_by_count":3},{"year":2013,"cited_by_count":4},{"year":2012,"cited_by_count":1}],"updated_date":"2026-03-31T07:56:22.981413","created_date":"2025-10-10T00:00:00"}
