{"id":"https://openalex.org/W2559820313","doi":"https://doi.org/10.1109/tfuzz.2016.2637369","title":"Analysis and Design of Functionally Weighted Single-Input-Rule-Modules Connected Fuzzy Inference Systems","display_name":"Analysis and Design of Functionally Weighted Single-Input-Rule-Modules Connected Fuzzy Inference Systems","publication_year":2016,"publication_date":"2016-12-08","ids":{"openalex":"https://openalex.org/W2559820313","doi":"https://doi.org/10.1109/tfuzz.2016.2637369","mag":"2559820313"},"language":"en","primary_location":{"id":"doi:10.1109/tfuzz.2016.2637369","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tfuzz.2016.2637369","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":false,"raw_author_name":"Chengdong Li","raw_affiliation_strings":["School of Information and Electrical Engineering, Shandong Jianzhu University, Jinan, China"],"raw_orcid":"https://orcid.org/0000-0002-9680-3523","affiliations":[{"raw_affiliation_string":"School of Information and Electrical Engineering, Shandong Jianzhu University, Jinan, China","institution_ids":["https://openalex.org/I44445938"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5102508721","display_name":"Junlong Gao","orcid":"https://orcid.org/0009-0008-6579-5330"},"institutions":[{"id":"https://openalex.org/I19820366","display_name":"Chinese Academy of Sciences","ror":"https://ror.org/034t30j35","country_code":"CN","type":"government","lineage":["https://openalex.org/I19820366"]},{"id":"https://openalex.org/I4210094879","display_name":"Shandong Institute of Automation","ror":"https://ror.org/00qdtba35","country_code":"CN","type":"facility","lineage":["https://openalex.org/I4210094879","https://openalex.org/I4210142748"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Junlong Gao","raw_affiliation_strings":["Institute of Automation, Chinese Academy of Sciences, Beijing, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute of Automation, Chinese Academy of Sciences, Beijing, China","institution_ids":["https://openalex.org/I19820366","https://openalex.org/I4210094879"]}]},{"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/I19820366","display_name":"Chinese Academy of Sciences","ror":"https://ror.org/034t30j35","country_code":"CN","type":"government","lineage":["https://openalex.org/I19820366"]},{"id":"https://openalex.org/I4210094879","display_name":"Shandong Institute of Automation","ror":"https://ror.org/00qdtba35","country_code":"CN","type":"facility","lineage":["https://openalex.org/I4210094879","https://openalex.org/I4210142748"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Jianqiang Yi","raw_affiliation_strings":["Institute of Automation, Chinese Academy of Sciences, Beijing, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute of Automation, Chinese Academy of Sciences, Beijing, China","institution_ids":["https://openalex.org/I19820366","https://openalex.org/I4210094879"]}]},{"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"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Information and Electrical Engineering, Shandong Jianzhu University, Jinan, China","institution_ids":["https://openalex.org/I44445938"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":26.8825,"has_fulltext":false,"cited_by_count":81,"citation_normalized_percentile":{"value":0.99487651,"is_in_top_1_percent":true,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":100},"biblio":{"volume":"26","issue":"1","first_page":"56","last_page":"71"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10820","display_name":"Fuzzy Logic and Control Systems","score":0.9998000264167786,"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":0.9998000264167786,"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":0.998199999332428,"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/T10876","display_name":"Fault Detection and Control Systems","score":0.9776999950408936,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/multivariable-calculus","display_name":"Multivariable calculus","score":0.5370136499404907},{"id":"https://openalex.org/keywords/fuzzy-inference","display_name":"Fuzzy inference","score":0.5209640264511108},{"id":"https://openalex.org/keywords/inference","display_name":"Inference","score":0.5112817287445068},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5071589946746826},{"id":"https://openalex.org/keywords/fuzzy-inference-system","display_name":"Fuzzy inference system","score":0.5055270195007324},{"id":"https://openalex.org/keywords/fuzzy-logic","display_name":"Fuzzy logic","score":0.49953651428222656},{"id":"https://openalex.org/keywords/partial-least-squares-regression","display_name":"Partial least squares regression","score":0.48208171129226685},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.4760962724685669},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4139039218425751},{"id":"https://openalex.org/keywords/data-mining","display_name":"Data mining","score":0.40973320603370667},{"id":"https://openalex.org/keywords/fuzzy-control-system","display_name":"Fuzzy control system","score":0.3726333975791931},{"id":"https://openalex.org/keywords/adaptive-neuro-fuzzy-inference-system","display_name":"Adaptive neuro fuzzy inference system","score":0.3424961566925049},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.3293367624282837},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.31811827421188354},{"id":"https://openalex.org/keywords/machine-learning","display_name":"Machine learning","score":0.2422793209552765},{"id":"https://openalex.org/keywords/control","display_name":"Control (management)","score":0.18488845229148865},{"id":"https://openalex.org/keywords/engineering","display_name":"Engineering","score":0.10713657736778259}],"concepts":[{"id":"https://openalex.org/C117312493","wikidata":"https://www.wikidata.org/wiki/Q2035437","display_name":"Multivariable calculus","level":2,"score":0.5370136499404907},{"id":"https://openalex.org/C2986395286","wikidata":"https://www.wikidata.org/wiki/Q224821","display_name":"Fuzzy inference","level":5,"score":0.5209640264511108},{"id":"https://openalex.org/C2776214188","wikidata":"https://www.wikidata.org/wiki/Q408386","display_name":"Inference","level":2,"score":0.5112817287445068},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5071589946746826},{"id":"https://openalex.org/C2987376176","wikidata":"https://www.wikidata.org/wiki/Q224821","display_name":"Fuzzy inference system","level":5,"score":0.5055270195007324},{"id":"https://openalex.org/C58166","wikidata":"https://www.wikidata.org/wiki/Q224821","display_name":"Fuzzy logic","level":2,"score":0.49953651428222656},{"id":"https://openalex.org/C22354355","wikidata":"https://www.wikidata.org/wiki/Q422009","display_name":"Partial least squares regression","level":2,"score":0.48208171129226685},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4760962724685669},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4139039218425751},{"id":"https://openalex.org/C124101348","wikidata":"https://www.wikidata.org/wiki/Q172491","display_name":"Data mining","level":1,"score":0.40973320603370667},{"id":"https://openalex.org/C195975749","wikidata":"https://www.wikidata.org/wiki/Q1475705","display_name":"Fuzzy control system","level":3,"score":0.3726333975791931},{"id":"https://openalex.org/C186108316","wikidata":"https://www.wikidata.org/wiki/Q352530","display_name":"Adaptive neuro fuzzy inference system","level":4,"score":0.3424961566925049},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.3293367624282837},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.31811827421188354},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.2422793209552765},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.18488845229148865},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.10713657736778259},{"id":"https://openalex.org/C133731056","wikidata":"https://www.wikidata.org/wiki/Q4917288","display_name":"Control engineering","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tfuzz.2016.2637369","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tfuzz.2016.2637369","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/G2640375836","display_name":null,"funder_award_id":"61473176","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"},{"id":"https://openalex.org/G8008034493","display_name":null,"funder_award_id":"61573225","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G8732479604","display_name":null,"funder_award_id":"61374187","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G8969041995","display_name":null,"funder_award_id":"61421004","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":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":70,"referenced_works":["https://openalex.org/W92965938","https://openalex.org/W333500581","https://openalex.org/W987746478","https://openalex.org/W1588359778","https://openalex.org/W1884347414","https://openalex.org/W1964400613","https://openalex.org/W1967734360","https://openalex.org/W1969885422","https://openalex.org/W1971598426","https://openalex.org/W1976623372","https://openalex.org/W1982957836","https://openalex.org/W1983457957","https://openalex.org/W1991444795","https://openalex.org/W2000825868","https://openalex.org/W2003756933","https://openalex.org/W2009389984","https://openalex.org/W2019207321","https://openalex.org/W2037568427","https://openalex.org/W2043283914","https://openalex.org/W2047966982","https://openalex.org/W2049999705","https://openalex.org/W2052188750","https://openalex.org/W2054371071","https://openalex.org/W2056646884","https://openalex.org/W2057683924","https://openalex.org/W2060488658","https://openalex.org/W2064692019","https://openalex.org/W2068059066","https://openalex.org/W2068660934","https://openalex.org/W2070865291","https://openalex.org/W2078094465","https://openalex.org/W2083844667","https://openalex.org/W2084072817","https://openalex.org/W2089530466","https://openalex.org/W2093684572","https://openalex.org/W2097146256","https://openalex.org/W2097930197","https://openalex.org/W2104051623","https://openalex.org/W2104727184","https://openalex.org/W2108913366","https://openalex.org/W2109816400","https://openalex.org/W2111833132","https://openalex.org/W2116046819","https://openalex.org/W2128313554","https://openalex.org/W2129013743","https://openalex.org/W2133267871","https://openalex.org/W2134961275","https://openalex.org/W2135849563","https://openalex.org/W2136340804","https://openalex.org/W2136384734","https://openalex.org/W2149363668","https://openalex.org/W2153649435","https://openalex.org/W2160447507","https://openalex.org/W2166681263","https://openalex.org/W2168389101","https://openalex.org/W2168448725","https://openalex.org/W2170104456","https://openalex.org/W2271358270","https://openalex.org/W2322432043","https://openalex.org/W2460900022","https://openalex.org/W2912565176","https://openalex.org/W3119126960","https://openalex.org/W4211007335","https://openalex.org/W4238586295","https://openalex.org/W4300203081","https://openalex.org/W6682637218","https://openalex.org/W6700444536","https://openalex.org/W6718331588","https://openalex.org/W6996755349","https://openalex.org/W7068123407"],"related_works":["https://openalex.org/W1668308244","https://openalex.org/W2562311745","https://openalex.org/W1643768816","https://openalex.org/W2091885912","https://openalex.org/W1778843519","https://openalex.org/W2113763900","https://openalex.org/W2208855561","https://openalex.org/W2391286742","https://openalex.org/W2918889792","https://openalex.org/W2364476030"],"abstract_inverted_index":{"The":[0],"single-input-rule-modules":[1],"(SIRMs)":[2],"connected":[3,31],"fuzzy":[4,11,32],"inference":[5,33],"method":[6,152],"can":[7,137,162,189,234,250],"efficiently":[8],"solve":[9],"the":[10,19,26,29,50,66,70,79,83,88,91,95,99,115,126,145,156,168,178,181,184,191,194,211,218,239],"rule":[12],"explosion":[13],"phenomenon,":[14],"which":[15,59],"usually":[16],"occurs":[17],"in":[18,75],"multivariable":[20,61],"modeling":[21],"and/or":[22],"control":[23],"applications.":[24],"However,":[25],"performance":[27,51,136,237,255],"of":[28,52,69,82,87,159,170,180,193,215],"SIRMs":[30,84,100,128,241],"system":[34],"(SIRM-FIS)":[35],"is":[36,72,153],"limited":[37],"due":[38],"to":[39,47,64,77,166,177,209],"its":[40],"simple":[41],"input-output":[42,123],"mapping.":[43],"In":[44],"this":[45],"paper,":[46],"further":[48],"enhance":[49],"SIRM-FIS,":[53,90,171],"a":[54,148],"functionally":[55],"weighted":[56],"SIRM-FIS":[57,93,97],"(FWSIRM-FIS),":[58],"adopts":[60],"functional":[62,96,104],"weights":[63,105],"measure":[65],"important":[67],"degrees":[68],"SIRMs,":[71],"presented.":[73],"Then,":[74],"order":[76],"show":[78,210,231],"fundamental":[80],"differences":[81],"methods,":[85,242,248],"properties":[86,112,131,179],"traditional":[89],"type-2":[92],"(T2SIRM-FIS),":[94],"(FSIRM-FIS),":[98],"model":[101],"with":[102,245],"single-variable":[103],"(SIRM-FW),":[106],"and":[107,121,174,199,205,213,217,224,261],"FWSIRM-FIS":[108,117,216,233,249],"are":[109,227],"explored.":[110],"These":[111],"demonstrate":[113],"that":[114,134,232],"proposed":[116,185,219],"has":[118,257],"more":[119],"general":[120],"complex":[122],"mapping":[124],"than":[125,238],"existing":[127],"methods.":[129],"Such":[130],"theoretically":[132],"guarantee":[133],"better":[135,236,254],"be":[138,164],"achieved":[139],"by":[140],"FWSIRM-FIS.":[141,160],"Furthermore,":[142],"based":[143],"on":[144],"least-squares":[146,182],"method,":[147,183,221],"novel":[149],"data-driven":[150],"optimization":[151,220],"presented":[154],"for":[155],"parameter":[157,186,196],"learning":[158,187,197],"It":[161],"also":[163],"used":[165],"optimize":[167],"parameters":[169,260],"T2SIRM-FIS,":[172],"FSIRM-FIS,":[173],"SIRM-FW.":[175],"Due":[176],"algorithm":[188],"overcome":[190],"drawbacks":[192],"gradients-based":[195],"methods":[198],"obtain":[200,235],"both":[201],"smallest":[202,206],"training":[203,263],"errors":[204],"parameters.":[207],"Finally,":[208],"effectiveness":[212],"superiority":[214],"six":[222],"examples":[223],"detailed":[225],"comparisons":[226],"given.":[228],"Simulation":[229],"results":[230],"other":[240],"and,":[243],"compared":[244],"some":[246],"well-known":[247],"achieve":[251],"similar":[252],"or":[253],"but":[256],"much":[258],"less":[259],"faster":[262],"speed.":[264]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":5},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":4},{"year":2020,"cited_by_count":14},{"year":2019,"cited_by_count":18},{"year":2018,"cited_by_count":26},{"year":2017,"cited_by_count":5}],"updated_date":"2026-07-22T07:51:19.307946","created_date":"2025-10-10T00:00:00"}
