{"id":"https://openalex.org/W2052188750","doi":"https://doi.org/10.1109/tfuzz.2013.2286416","title":"On the Monotonicity of Interval Type-2 Fuzzy Logic Systems","display_name":"On the Monotonicity of Interval Type-2 Fuzzy Logic Systems","publication_year":2013,"publication_date":"2013-10-18","ids":{"openalex":"https://openalex.org/W2052188750","doi":"https://doi.org/10.1109/tfuzz.2013.2286416","mag":"2052188750"},"language":"en","primary_location":{"id":"doi:10.1109/tfuzz.2013.2286416","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tfuzz.2013.2286416","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/A5023987464","display_name":"Chengdong Li","orcid":"https://orcid.org/0000-0002-9680-3523"},"institutions":[{"id":"https://openalex.org/I44445938","display_name":"Shandong Jianzhu University","ror":"https://ror.org/01gbfax37","country_code":"CN","type":"education","lineage":["https://openalex.org/I44445938"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Chengdong Li","raw_affiliation_strings":["School of Information and Electrical Engineering, Shandong Jianzhu University, Jinan, China","School of Information and Electrical Engineering, Shandong Jianzhu University, Jinan, China#TAB#"],"affiliations":[{"raw_affiliation_string":"School of Information and Electrical Engineering, Shandong Jianzhu University, Jinan, China","institution_ids":["https://openalex.org/I44445938"]},{"raw_affiliation_string":"School of Information and Electrical Engineering, Shandong Jianzhu University, Jinan, China#TAB#","institution_ids":["https://openalex.org/I44445938"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5019541846","display_name":"Jianqiang Yi","orcid":"https://orcid.org/0000-0003-3268-9482"},"institutions":[{"id":"https://openalex.org/I4210112150","display_name":"Institute of Automation","ror":"https://ror.org/022c3hy66","country_code":"CN","type":"facility","lineage":["https://openalex.org/I19820366","https://openalex.org/I4210112150"]},{"id":"https://openalex.org/I19820366","display_name":"Chinese Academy of Sciences","ror":"https://ror.org/034t30j35","country_code":"CN","type":"funder","lineage":["https://openalex.org/I19820366"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Jianqiang Yi","raw_affiliation_strings":["Chinese Academy of Sciences, Institute of Automation, Beijing, China","Institute of Automation Chinese Academy of Sciences  Beijing China"],"affiliations":[{"raw_affiliation_string":"Chinese Academy of Sciences, Institute of Automation, Beijing, China","institution_ids":["https://openalex.org/I4210112150","https://openalex.org/I19820366"]},{"raw_affiliation_string":"Institute of Automation Chinese Academy of Sciences  Beijing China","institution_ids":["https://openalex.org/I4210112150","https://openalex.org/I19820366"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5050638709","display_name":"Guiqing Zhang","orcid":"https://orcid.org/0000-0001-6547-9049"},"institutions":[{"id":"https://openalex.org/I44445938","display_name":"Shandong Jianzhu University","ror":"https://ror.org/01gbfax37","country_code":"CN","type":"education","lineage":["https://openalex.org/I44445938"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Guiqing Zhang","raw_affiliation_strings":["School of Information and Electrical Engineering, Shandong Jianzhu University, Jinan, China","School of Information and Electrical Engineering, Shandong Jianzhu University, Jinan, China#TAB#"],"affiliations":[{"raw_affiliation_string":"School of Information and Electrical Engineering, Shandong Jianzhu University, Jinan, China","institution_ids":["https://openalex.org/I44445938"]},{"raw_affiliation_string":"School of Information and Electrical Engineering, Shandong Jianzhu University, Jinan, China#TAB#","institution_ids":["https://openalex.org/I44445938"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5023987464"],"corresponding_institution_ids":["https://openalex.org/I44445938"],"apc_list":null,"apc_paid":null,"fwci":10.4484,"has_fulltext":false,"cited_by_count":70,"citation_normalized_percentile":{"value":0.98127915,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":91,"max":99},"biblio":{"volume":"22","issue":"5","first_page":"1197","last_page":"1212"},"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":0.9945999979972839,"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":0.980400025844574,"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/monotonic-function","display_name":"Monotonic function","score":0.8512306213378906},{"id":"https://openalex.org/keywords/defuzzification","display_name":"Defuzzification","score":0.7006022334098816},{"id":"https://openalex.org/keywords/fuzzy-logic","display_name":"Fuzzy logic","score":0.6331382989883423},{"id":"https://openalex.org/keywords/fuzzy-set","display_name":"Fuzzy set","score":0.5882053375244141},{"id":"https://openalex.org/keywords/interval","display_name":"Interval (graph theory)","score":0.5520393252372742},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5358648896217346},{"id":"https://openalex.org/keywords/fuzzy-number","display_name":"Fuzzy number","score":0.49045225977897644},{"id":"https://openalex.org/keywords/fuzzy-control-system","display_name":"Fuzzy control system","score":0.48957380652427673},{"id":"https://openalex.org/keywords/antecedent","display_name":"Antecedent (behavioral psychology)","score":0.4357272982597351},{"id":"https://openalex.org/keywords/type","display_name":"Type (biology)","score":0.43002021312713623},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.4276273250579834},{"id":"https://openalex.org/keywords/fuzzy-set-operations","display_name":"Fuzzy set operations","score":0.4237705171108246},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3696812391281128},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.32542866468429565},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.32331398129463196},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.08582544326782227}],"concepts":[{"id":"https://openalex.org/C72169020","wikidata":"https://www.wikidata.org/wiki/Q194404","display_name":"Monotonic function","level":2,"score":0.8512306213378906},{"id":"https://openalex.org/C170260401","wikidata":"https://www.wikidata.org/wiki/Q5251735","display_name":"Defuzzification","level":5,"score":0.7006022334098816},{"id":"https://openalex.org/C58166","wikidata":"https://www.wikidata.org/wiki/Q224821","display_name":"Fuzzy logic","level":2,"score":0.6331382989883423},{"id":"https://openalex.org/C42011625","wikidata":"https://www.wikidata.org/wiki/Q1055058","display_name":"Fuzzy set","level":3,"score":0.5882053375244141},{"id":"https://openalex.org/C2778067643","wikidata":"https://www.wikidata.org/wiki/Q166507","display_name":"Interval (graph theory)","level":2,"score":0.5520393252372742},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5358648896217346},{"id":"https://openalex.org/C1883856","wikidata":"https://www.wikidata.org/wiki/Q3407463","display_name":"Fuzzy number","level":4,"score":0.49045225977897644},{"id":"https://openalex.org/C195975749","wikidata":"https://www.wikidata.org/wiki/Q1475705","display_name":"Fuzzy control system","level":3,"score":0.48957380652427673},{"id":"https://openalex.org/C2781256819","wikidata":"https://www.wikidata.org/wiki/Q16828835","display_name":"Antecedent (behavioral psychology)","level":2,"score":0.4357272982597351},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.43002021312713623},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.4276273250579834},{"id":"https://openalex.org/C148671577","wikidata":"https://www.wikidata.org/wiki/Q5511133","display_name":"Fuzzy set operations","level":4,"score":0.4237705171108246},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3696812391281128},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.32542866468429565},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.32331398129463196},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.08582544326782227},{"id":"https://openalex.org/C15744967","wikidata":"https://www.wikidata.org/wiki/Q9418","display_name":"Psychology","level":0,"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/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C138496976","wikidata":"https://www.wikidata.org/wiki/Q175002","display_name":"Developmental psychology","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tfuzz.2013.2286416","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tfuzz.2013.2286416","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"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G2665641960","display_name":null,"funder_award_id":"61273149","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G5479127128","display_name":null,"funder_award_id":"61074149","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G7912547315","display_name":null,"funder_award_id":"61105077","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"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":74,"referenced_works":["https://openalex.org/W564030374","https://openalex.org/W647481897","https://openalex.org/W1528458083","https://openalex.org/W1964569793","https://openalex.org/W1972413910","https://openalex.org/W1977425756","https://openalex.org/W1981119555","https://openalex.org/W1983561707","https://openalex.org/W1983601602","https://openalex.org/W1984643425","https://openalex.org/W1987976143","https://openalex.org/W1988053196","https://openalex.org/W1992625160","https://openalex.org/W1993810822","https://openalex.org/W1996786357","https://openalex.org/W2000976145","https://openalex.org/W2001220060","https://openalex.org/W2027623192","https://openalex.org/W2028249667","https://openalex.org/W2043897597","https://openalex.org/W2044062812","https://openalex.org/W2054416947","https://openalex.org/W2058778638","https://openalex.org/W2063928388","https://openalex.org/W2072506331","https://openalex.org/W2074537354","https://openalex.org/W2085386836","https://openalex.org/W2092144116","https://openalex.org/W2094585062","https://openalex.org/W2094760805","https://openalex.org/W2101877421","https://openalex.org/W2105234323","https://openalex.org/W2105985709","https://openalex.org/W2108225531","https://openalex.org/W2108913366","https://openalex.org/W2109816400","https://openalex.org/W2110574362","https://openalex.org/W2116046819","https://openalex.org/W2117501337","https://openalex.org/W2121463530","https://openalex.org/W2122827945","https://openalex.org/W2123964448","https://openalex.org/W2124041779","https://openalex.org/W2125223024","https://openalex.org/W2130501771","https://openalex.org/W2132685025","https://openalex.org/W2133141734","https://openalex.org/W2134005254","https://openalex.org/W2136384734","https://openalex.org/W2141178894","https://openalex.org/W2143760316","https://openalex.org/W2145416734","https://openalex.org/W2147708960","https://openalex.org/W2148925928","https://openalex.org/W2149363668","https://openalex.org/W2149483754","https://openalex.org/W2149604064","https://openalex.org/W2150263198","https://openalex.org/W2150879558","https://openalex.org/W2151614844","https://openalex.org/W2153744349","https://openalex.org/W2154186319","https://openalex.org/W2158091284","https://openalex.org/W2162706466","https://openalex.org/W2163166525","https://openalex.org/W2189303575","https://openalex.org/W2434888247","https://openalex.org/W2913642042","https://openalex.org/W3147710177","https://openalex.org/W4247749894","https://openalex.org/W4292295629","https://openalex.org/W6682133608","https://openalex.org/W6682291467","https://openalex.org/W6718194012"],"related_works":["https://openalex.org/W647390320","https://openalex.org/W2184441312","https://openalex.org/W4242970302","https://openalex.org/W4388451300","https://openalex.org/W2571050636","https://openalex.org/W2060361571","https://openalex.org/W1975005191","https://openalex.org/W3176863924","https://openalex.org/W4361984403","https://openalex.org/W1485268022"],"abstract_inverted_index":{"Qualitative":[0],"knowledge":[1,16],"is":[2,17,26,183],"very":[3],"useful":[4,168],"for":[5,123,145,151,176],"system":[6],"modeling":[7,157],"and":[8,19,51,65,73,88,102,139,143,158],"control":[9,159],"problems,":[10],"especially":[11],"when":[12,179],"specific":[13],"physical":[14],"structure":[15],"unavailable":[18],"the":[20,31,49,61,79,82,85,89,100,113,124,153,170,180],"number":[21],"of":[22,33,54,105,130,172],"training":[23],"data":[24],"points":[25],"small.":[27],"This":[28],"paper":[29],"studies":[30],"incorporation":[32],"one":[34],"common":[35],"qualitative":[36],"knowledge-monotonicity":[37],"into":[38,69],"interval":[39],"type-2":[40],"(IT2)":[41],"fuzzy":[42,55,107,132],"logic":[43],"systems":[44],"(FLSs).":[45],"Sufficient":[46],"conditions":[47,120,155],"on":[48],"antecedent":[50,101],"consequent":[52],"parts":[53,104],"rules":[56,108],"are":[57,97,109,121,161],"derived":[58,118],"to":[59,112,156],"guarantee":[60],"monotonicity":[62,115,119,181],"between":[63],"inputs":[64],"outputs.":[66],"We":[67,92],"take":[68],"account":[70],"five":[71],"type-reduction":[72],"defuzzification":[74],"methods":[75],"(the":[76],"Karnik-Mendel":[77],"method,":[78,81,84,87],"Du-Ying":[80],"Begian-Melek-Mendel":[83],"Wu-Tan":[86],"Nie-Tan":[90],"method).":[91],"show":[93],"that":[94],"IT2":[95,125,131,137,141,174],"FLSs":[96,126,147,175],"monotonic":[98,173],"if":[99],"consequents":[103],"their":[106],"arranged":[110],"according":[111],"proposed":[114,154],"conditions.":[116],"The":[117],"valid":[122],"using":[127],"any":[128],"kind":[129],"sets":[133],"(FSs)":[134],"(e.g.,":[135],"Trapezoidal":[136],"FSs":[138],"Gaussian":[140],"FSs)":[142],"stand":[144],"type-1":[146],"as":[148],"well.":[149],"Guidelines":[150],"applying":[152],"problems":[160],"also":[162],"given.":[163],"Our":[164],"results":[165],"will":[166],"be":[167],"in":[169],"design":[171],"engineering":[177],"applications":[178],"property":[182],"desired.":[184]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":4},{"year":2020,"cited_by_count":7},{"year":2019,"cited_by_count":10},{"year":2018,"cited_by_count":12},{"year":2017,"cited_by_count":8},{"year":2016,"cited_by_count":12},{"year":2015,"cited_by_count":6},{"year":2014,"cited_by_count":4}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}