{"id":"https://openalex.org/W2117501337","doi":"https://doi.org/10.1109/tfuzz.2011.2177272","title":"Enhanced Interval Approach for Encoding Words Into Interval Type-2 Fuzzy Sets and Its Convergence Analysis","display_name":"Enhanced Interval Approach for Encoding Words Into Interval Type-2 Fuzzy Sets and Its Convergence Analysis","publication_year":2011,"publication_date":"2011-11-23","ids":{"openalex":"https://openalex.org/W2117501337","doi":"https://doi.org/10.1109/tfuzz.2011.2177272","mag":"2117501337"},"language":"en","primary_location":{"id":"doi:10.1109/tfuzz.2011.2177272","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tfuzz.2011.2177272","pdf_url":null,"source":{"id":"https://openalex.org/S134177497","display_name":"IEEE Transactions on Fuzzy Systems","issn_l":"1063-6706","issn":["1063-6706","1941-0034"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on 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":"https://openalex.org/A5008740867","display_name":"Dongrui Wu","orcid":"https://orcid.org/0000-0002-7153-9703"},"institutions":[{"id":"https://openalex.org/I1332737386","display_name":"General Electric (United States)","ror":"https://ror.org/013msgt25","country_code":"US","type":"company","lineage":["https://openalex.org/I1332737386"]},{"id":"https://openalex.org/I4210134512","display_name":"GE Global Research (United States)","ror":"https://ror.org/03e06qt98","country_code":"US","type":"company","lineage":["https://openalex.org/I4210134512"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Dongrui Wu","raw_affiliation_strings":["Machine Learning Laboratory, GE Global Research Center, Niskayuna, NY, USA","Machine Learning Lab., GE Global Res., Niskayuna, NY, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Machine Learning Laboratory, GE Global Research Center, Niskayuna, NY, USA","institution_ids":["https://openalex.org/I4210134512"]},{"raw_affiliation_string":"Machine Learning Lab., GE Global Res., Niskayuna, NY, USA","institution_ids":["https://openalex.org/I1332737386"]}]},{"author_position":"middle","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":false,"raw_author_name":"J. M. Mendel","raw_affiliation_strings":["Signal and Image Processing Institute, Ming Hsieh Department of Electrical Engineering, University of Southern California, Los Angeles, CA, USA","Ming Hsieh Dept. of Electr. Eng., Univ. of Southern California, Los Angeles, CA, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Signal and Image Processing Institute, Ming Hsieh Department of Electrical Engineering, University of Southern California, Los Angeles, CA, USA","institution_ids":["https://openalex.org/I1174212"]},{"raw_affiliation_string":"Ming Hsieh Dept. of Electr. Eng., Univ. of Southern California, Los Angeles, CA, USA","institution_ids":["https://openalex.org/I1174212"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5039225823","display_name":"Simon Coupland","orcid":null},"institutions":[{"id":"https://openalex.org/I66943878","display_name":"De Montfort University","ror":"https://ror.org/0312pnr83","country_code":"GB","type":"education","lineage":["https://openalex.org/I66943878"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"S. Coupland","raw_affiliation_strings":["Center for Computational Intelligence, De Montfort University, Leicester, UK","Center for Comput. Intell., De Montfort Univ., Leicester, UK"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Center for Computational Intelligence, De Montfort University, Leicester, UK","institution_ids":["https://openalex.org/I66943878"]},{"raw_affiliation_string":"Center for Comput. Intell., De Montfort Univ., Leicester, UK","institution_ids":["https://openalex.org/I66943878"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":23.2943,"has_fulltext":false,"cited_by_count":201,"citation_normalized_percentile":{"value":0.99538126,"is_in_top_1_percent":true,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":94,"max":100},"biblio":{"volume":"20","issue":"3","first_page":"499","last_page":"513"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10320","display_name":"Neural Networks and Applications","score":0.996999979019165,"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/T10320","display_name":"Neural Networks and Applications","score":0.996999979019165,"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/T10820","display_name":"Fuzzy Logic and Control Systems","score":0.996999979019165,"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/T12135","display_name":"Fuzzy Systems and Optimization","score":0.9805999994277954,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/interval","display_name":"Interval (graph theory)","score":0.7276843190193176},{"id":"https://openalex.org/keywords/fuzzy-set","display_name":"Fuzzy set","score":0.703631579875946},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.556765079498291},{"id":"https://openalex.org/keywords/fuzzy-logic","display_name":"Fuzzy logic","score":0.5062360167503357},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4909527599811554},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.47436580061912537},{"id":"https://openalex.org/keywords/data-mining","display_name":"Data mining","score":0.46170809864997864},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4581938683986664},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.45652642846107483},{"id":"https://openalex.org/keywords/interval-arithmetic","display_name":"Interval arithmetic","score":0.4372140169143677},{"id":"https://openalex.org/keywords/term","display_name":"Term (time)","score":0.4200911819934845},{"id":"https://openalex.org/keywords/data-set","display_name":"Data set","score":0.4136800169944763},{"id":"https://openalex.org/keywords/membership-function","display_name":"Membership function","score":0.4118083417415619},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.33306989073753357},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.24830323457717896}],"concepts":[{"id":"https://openalex.org/C2778067643","wikidata":"https://www.wikidata.org/wiki/Q166507","display_name":"Interval (graph theory)","level":2,"score":0.7276843190193176},{"id":"https://openalex.org/C42011625","wikidata":"https://www.wikidata.org/wiki/Q1055058","display_name":"Fuzzy set","level":3,"score":0.703631579875946},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.556765079498291},{"id":"https://openalex.org/C58166","wikidata":"https://www.wikidata.org/wiki/Q224821","display_name":"Fuzzy logic","level":2,"score":0.5062360167503357},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4909527599811554},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.47436580061912537},{"id":"https://openalex.org/C124101348","wikidata":"https://www.wikidata.org/wiki/Q172491","display_name":"Data mining","level":1,"score":0.46170809864997864},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4581938683986664},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.45652642846107483},{"id":"https://openalex.org/C191252586","wikidata":"https://www.wikidata.org/wiki/Q1671453","display_name":"Interval arithmetic","level":3,"score":0.4372140169143677},{"id":"https://openalex.org/C61797465","wikidata":"https://www.wikidata.org/wiki/Q1188986","display_name":"Term (time)","level":2,"score":0.4200911819934845},{"id":"https://openalex.org/C58489278","wikidata":"https://www.wikidata.org/wiki/Q1172284","display_name":"Data set","level":2,"score":0.4136800169944763},{"id":"https://openalex.org/C5263885","wikidata":"https://www.wikidata.org/wiki/Q1967302","display_name":"Membership function","level":4,"score":0.4118083417415619},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.33306989073753357},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.24830323457717896},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.0},{"id":"https://openalex.org/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","level":1,"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/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"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/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/tfuzz.2011.2177272","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tfuzz.2011.2177272","pdf_url":null,"source":{"id":"https://openalex.org/S134177497","display_name":"IEEE Transactions on Fuzzy Systems","issn_l":"1063-6706","issn":["1063-6706","1941-0034"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Fuzzy Systems","raw_type":"journal-article"},{"id":"pmh:oai:dora.dmu.ac.uk:2086/6823","is_oa":false,"landing_page_url":"http://hdl.handle.net/2086/6823","pdf_url":null,"source":{"id":"https://openalex.org/S4306400394","display_name":"DMU Open Research Archive (De Montfort University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I66943878","host_organization_name":"De Montfort University","host_organization_lineage":["https://openalex.org/I66943878"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":65,"referenced_works":["https://openalex.org/W68393453","https://openalex.org/W78832896","https://openalex.org/W118522944","https://openalex.org/W128658818","https://openalex.org/W189183223","https://openalex.org/W261062478","https://openalex.org/W564030374","https://openalex.org/W647481897","https://openalex.org/W1524157153","https://openalex.org/W1536630500","https://openalex.org/W1545605939","https://openalex.org/W1787190784","https://openalex.org/W1972012616","https://openalex.org/W1987937723","https://openalex.org/W1995903245","https://openalex.org/W2000976145","https://openalex.org/W2002797931","https://openalex.org/W2020694587","https://openalex.org/W2026754475","https://openalex.org/W2037940305","https://openalex.org/W2042157954","https://openalex.org/W2043792182","https://openalex.org/W2053142133","https://openalex.org/W2057794837","https://openalex.org/W2068882433","https://openalex.org/W2085777574","https://openalex.org/W2087471614","https://openalex.org/W2101560809","https://openalex.org/W2103299443","https://openalex.org/W2113181660","https://openalex.org/W2116044789","https://openalex.org/W2116818985","https://openalex.org/W2117827905","https://openalex.org/W2124041779","https://openalex.org/W2125077478","https://openalex.org/W2125631815","https://openalex.org/W2130902850","https://openalex.org/W2131379830","https://openalex.org/W2132885717","https://openalex.org/W2141178894","https://openalex.org/W2142181942","https://openalex.org/W2143630575","https://openalex.org/W2144451432","https://openalex.org/W2145224695","https://openalex.org/W2146792988","https://openalex.org/W2149483754","https://openalex.org/W2149816138","https://openalex.org/W2150879558","https://openalex.org/W2152329090","https://openalex.org/W2157041604","https://openalex.org/W2157389400","https://openalex.org/W2157423656","https://openalex.org/W2165094119","https://openalex.org/W2283007371","https://openalex.org/W2496376991","https://openalex.org/W2500472211","https://openalex.org/W2796556654","https://openalex.org/W2912565176","https://openalex.org/W2949173247","https://openalex.org/W4211007335","https://openalex.org/W4245152641","https://openalex.org/W4247749894","https://openalex.org/W6605253631","https://openalex.org/W6607707727","https://openalex.org/W6683094445"],"related_works":["https://openalex.org/W2520934858","https://openalex.org/W2990487117","https://openalex.org/W2012882356","https://openalex.org/W2098412892","https://openalex.org/W109635080","https://openalex.org/W4213384165","https://openalex.org/W2377262226","https://openalex.org/W2531534085","https://openalex.org/W4285295794","https://openalex.org/W2387705642"],"abstract_inverted_index":{"Construction":[0],"of":[1,19,90,107],"interval":[2,24,71,135,169],"type-2":[3,136,170],"fuzzy":[4,104,137,171],"set":[5,105,138,172],"models":[6,38],"is":[7,16,173],"the":[8,12,31,91,100,103,108,116,133,140,167,177,188],"first":[9],"step":[10],"in":[11,52,191],"perceptual":[13],"computer,":[14],"which":[15],"an":[17,69,111],"implementation":[18],"computing":[20],"with":[21],"words.":[22],"The":[23,87],"approach":[25,72],"(IA)":[26],"has,":[27],"so":[28],"far,":[29],"been":[30],"only":[32],"systematic":[33],"method":[34],"to":[35,114,126,143,176,201],"construct":[36],"such":[37],"from":[39,45,83,139,180],"data":[40,79,88,150,162,183,198],"intervals":[41,151,163,199],"that":[42,80,187],"are":[43,81,152,164],"collected":[44,82],"a":[46,84,123,144,192,203],"survey.":[47,86],"However,":[48],"as":[49,147],"pointed":[50],"out":[51],"this":[53],"paper,":[54],"it":[55,157],"has":[56,93,110],"some":[57],"limitations,":[58],"and":[59,74,96,102,154,195,208],"its":[60,76],"performance":[61,77],"can":[62],"be":[63,202],"further":[64],"improved.":[65],"This":[66],"paper":[67],"proposes":[68],"enhanced":[70],"(EIA)":[73],"demonstrates":[75],"on":[78],"web":[85],"part":[89,106],"EIA":[92,109,141,189],"more":[94,149],"strict":[95],"reasonable":[97],"tests":[98],"than":[99],"IA,":[101],"improved":[112],"procedure":[113],"compute":[115],"lower":[117],"membership":[118],"function.":[119],"We":[120,185],"also":[121],"perform":[122],"convergence":[124],"analysis":[125],"answer":[127],"two":[128],"important":[129],"questions:":[130],"1)":[131],"Does":[132],"output":[134],"converge":[142],"stable":[145],"model":[146,178],"increasingly":[148],"collected,":[153],"2)":[155],"if":[156],"converges,":[158],"then":[159],"how":[160],"many":[161,182],"needed":[165],"before":[166],"resulting":[168],"sufficiently":[174],"similar":[175],"obtained":[179],"infinitely":[181],"intervals?":[184],"show":[186],"converges":[190],"mean-square":[193],"sense,":[194],"generally,":[196],"30":[197],"seem":[200],"good":[204],"compromise":[205],"between":[206],"cost":[207],"accuracy.":[209]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":4},{"year":2024,"cited_by_count":13},{"year":2023,"cited_by_count":7},{"year":2022,"cited_by_count":13},{"year":2021,"cited_by_count":18},{"year":2020,"cited_by_count":19},{"year":2019,"cited_by_count":18},{"year":2018,"cited_by_count":18},{"year":2017,"cited_by_count":13},{"year":2016,"cited_by_count":9},{"year":2015,"cited_by_count":14},{"year":2014,"cited_by_count":24},{"year":2013,"cited_by_count":20},{"year":2012,"cited_by_count":10}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}