{"id":"https://openalex.org/W2972483623","doi":"https://doi.org/10.1109/tfuzz.2019.2940919","title":"Neural Network Approach to Solving Fuzzy Nonlinear Equations using Z-Numbers","display_name":"Neural Network Approach to Solving Fuzzy Nonlinear Equations using Z-Numbers","publication_year":2019,"publication_date":"2019-01-01","ids":{"openalex":"https://openalex.org/W2972483623","doi":"https://doi.org/10.1109/tfuzz.2019.2940919","mag":"2972483623"},"language":"en","primary_location":{"id":"doi:10.1109/tfuzz.2019.2940919","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tfuzz.2019.2940919","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/A5083056452","display_name":"Raheleh Jafari","orcid":"https://orcid.org/0000-0001-7298-2363"},"institutions":[{"id":"https://openalex.org/I200650556","display_name":"University of Agder","ror":"https://ror.org/03x297z98","country_code":"NO","type":"education","lineage":["https://openalex.org/I200650556"]}],"countries":["NO"],"is_corresponding":false,"raw_author_name":"Raheleh Jafari","raw_affiliation_strings":["Centre for Artificial Intelligence Research, University of Agder, Grimstad, Norway"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Centre for Artificial Intelligence Research, University of Agder, Grimstad, Norway","institution_ids":["https://openalex.org/I200650556"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5047503590","display_name":"Sina Razvarz","orcid":"https://orcid.org/0000-0003-1549-7307"},"institutions":[{"id":"https://openalex.org/I59361560","display_name":"Instituto Polit\u00e9cnico Nacional","ror":"https://ror.org/059sp8j34","country_code":"MX","type":"education","lineage":["https://openalex.org/I59361560"]},{"id":"https://openalex.org/I68368234","display_name":"Centro de Investigaci\u00f3n y de Estudios Avanzados del Instituto Polit\u00e9cnico Nacional","ror":"https://ror.org/009eqmr18","country_code":"MX","type":"facility","lineage":["https://openalex.org/I59361560","https://openalex.org/I68368234"]}],"countries":["MX"],"is_corresponding":false,"raw_author_name":"Sina Razvarz","raw_affiliation_strings":["Department of Automatic Control, Centro de Investigaci\u00f3n y de Estudios Avanzados del Instituto Polit\u00e9cnico Nacional (CINVESTAV-IPN) (National Polytechnic Institute), Mexico City, Mexico"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Automatic Control, Centro de Investigaci\u00f3n y de Estudios Avanzados del Instituto Polit\u00e9cnico Nacional (CINVESTAV-IPN) (National Polytechnic Institute), Mexico City, Mexico","institution_ids":["https://openalex.org/I59361560","https://openalex.org/I68368234"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5016380950","display_name":"Alexander Gegov","orcid":"https://orcid.org/0000-0002-6166-296X"},"institutions":[{"id":"https://openalex.org/I63072094","display_name":"University of Portsmouth","ror":"https://ror.org/03ykbk197","country_code":"GB","type":"education","lineage":["https://openalex.org/I63072094"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Alexander Gegov","raw_affiliation_strings":["School of Computing, University of Portsmouth, Portsmouth, U.K"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Computing, University of Portsmouth, Portsmouth, U.K","institution_ids":["https://openalex.org/I63072094"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":6.2042,"has_fulltext":false,"cited_by_count":30,"citation_normalized_percentile":{"value":0.97364701,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":94,"max":100},"biblio":{"volume":null,"issue":null,"first_page":"1","last_page":"1"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12135","display_name":"Fuzzy Systems and Optimization","score":0.9998000264167786,"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"}},"topics":[{"id":"https://openalex.org/T12135","display_name":"Fuzzy Systems and Optimization","score":0.9998000264167786,"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"}},{"id":"https://openalex.org/T10820","display_name":"Fuzzy Logic and Control Systems","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/T10050","display_name":"Multi-Criteria Decision Making","score":0.9902999997138977,"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/fuzzy-number","display_name":"Fuzzy number","score":0.6685671806335449},{"id":"https://openalex.org/keywords/fuzzy-logic","display_name":"Fuzzy logic","score":0.6651625037193298},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6597199440002441},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.5802751779556274},{"id":"https://openalex.org/keywords/neuro-fuzzy","display_name":"Neuro-fuzzy","score":0.5470191240310669},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5017282962799072},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.457369863986969},{"id":"https://openalex.org/keywords/fuzzy-control-system","display_name":"Fuzzy control system","score":0.40934300422668457},{"id":"https://openalex.org/keywords/fuzzy-set","display_name":"Fuzzy set","score":0.3579082489013672},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.32065531611442566},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.2874506711959839},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.20484817028045654},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.055622607469558716}],"concepts":[{"id":"https://openalex.org/C1883856","wikidata":"https://www.wikidata.org/wiki/Q3407463","display_name":"Fuzzy number","level":4,"score":0.6685671806335449},{"id":"https://openalex.org/C58166","wikidata":"https://www.wikidata.org/wiki/Q224821","display_name":"Fuzzy logic","level":2,"score":0.6651625037193298},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6597199440002441},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.5802751779556274},{"id":"https://openalex.org/C29470771","wikidata":"https://www.wikidata.org/wiki/Q4165150","display_name":"Neuro-fuzzy","level":4,"score":0.5470191240310669},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5017282962799072},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.457369863986969},{"id":"https://openalex.org/C195975749","wikidata":"https://www.wikidata.org/wiki/Q1475705","display_name":"Fuzzy control system","level":3,"score":0.40934300422668457},{"id":"https://openalex.org/C42011625","wikidata":"https://www.wikidata.org/wiki/Q1055058","display_name":"Fuzzy set","level":3,"score":0.3579082489013672},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.32065531611442566},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2874506711959839},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.20484817028045654},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.055622607469558716},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1109/tfuzz.2019.2940919","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tfuzz.2019.2940919","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:eprints.whiterose.ac.uk:156074","is_oa":false,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S4306400854","display_name":"White Rose Research Online (University of Leeds, The University of Sheffield, University of York)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I2800616092","host_organization_name":"White Rose University Consortium","host_organization_lineage":["https://openalex.org/I2800616092"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":"","raw_type":"Article"},{"id":"pmh:oai:researchportal.port.ac.uk:publications/ffd8b3c0-4a85-4a70-8d19-955641590b91","is_oa":false,"landing_page_url":"https://ieeexplore.ieee.org/document/8831412","pdf_url":null,"source":{"id":"https://openalex.org/S4306401774","display_name":"Portsmouth Research Portal (University of Portsmouth)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I63072094","host_organization_name":"University of Portsmouth","host_organization_lineage":["https://openalex.org/I63072094"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":""}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":48,"referenced_works":["https://openalex.org/W157855642","https://openalex.org/W568759720","https://openalex.org/W611415252","https://openalex.org/W1890072956","https://openalex.org/W1964997874","https://openalex.org/W1965744721","https://openalex.org/W1978996791","https://openalex.org/W1992747194","https://openalex.org/W1995667902","https://openalex.org/W1997952930","https://openalex.org/W2004719426","https://openalex.org/W2009062909","https://openalex.org/W2019878538","https://openalex.org/W2036102558","https://openalex.org/W2038354216","https://openalex.org/W2039022442","https://openalex.org/W2042774699","https://openalex.org/W2065388376","https://openalex.org/W2065466432","https://openalex.org/W2065804254","https://openalex.org/W2066391914","https://openalex.org/W2073237559","https://openalex.org/W2075572001","https://openalex.org/W2103496339","https://openalex.org/W2103730177","https://openalex.org/W2106459532","https://openalex.org/W2122361993","https://openalex.org/W2142863015","https://openalex.org/W2143591652","https://openalex.org/W2163982943","https://openalex.org/W2216971780","https://openalex.org/W2238703984","https://openalex.org/W2317916567","https://openalex.org/W2508963551","https://openalex.org/W2520993935","https://openalex.org/W2521399310","https://openalex.org/W2734990489","https://openalex.org/W2744102091","https://openalex.org/W2756420755","https://openalex.org/W2805850040","https://openalex.org/W2917281601","https://openalex.org/W3021509614","https://openalex.org/W4245290017","https://openalex.org/W4285719527","https://openalex.org/W4361808948","https://openalex.org/W6639515500","https://openalex.org/W6699821906","https://openalex.org/W6744654902"],"related_works":["https://openalex.org/W1508347401","https://openalex.org/W2135891541","https://openalex.org/W2061828243","https://openalex.org/W2112778063","https://openalex.org/W2104217550","https://openalex.org/W2164589519","https://openalex.org/W2134826631","https://openalex.org/W2154097169","https://openalex.org/W1975773326","https://openalex.org/W4380083368"],"abstract_inverted_index":{"In":[0,36,93],"this":[1,37,94],"article,":[2,38,95],"the":[3,11,14,19,25,39,53,56,64,70,76,86,90,100,108,124,128],"fuzzy":[4,20,26,40,77,91,129],"property":[5],"is":[6,28,47,67,81,112,120,134],"described":[7],"by":[8,136],"means":[9],"of":[10,18,75,89,107,127],"Z-number":[12,34,43,71,87,125],"as":[13,52],"coefficients":[15,44,72,88,126],"and":[16,45,73],"variables":[17,46,74],"equations.":[21,92],"This":[22],"alteration":[23],"for":[24,30,55],"equation":[27,41],"appropriate":[29],"system":[31,66],"modeling":[32,60],"with":[33,42,139],"parameters.":[35],"tended":[48],"to":[49,63,68,84,98,122],"be":[50],"used":[51],"models":[54],"uncertain":[57,65,101],"systems.":[58],"The":[59,131],"issue":[61],"related":[62],"obtain":[69,123],"equation.":[78,130],"Nevertheless,":[79],"it":[80,119],"extremely":[82],"hard":[83],"get":[85],"in":[96,114],"order":[97],"model":[99],"nonlinear":[102],"systems,":[103],"a":[104,116],"novel":[105],"structure":[106],"multilayer":[109],"neural":[110],"network":[111],"utilized":[113],"such":[115],"manner":[117],"that":[118],"able":[121],"suggested":[132],"technique":[133],"validated":[135],"some":[137],"examples":[138],"applications.":[140]},"counts_by_year":[{"year":2023,"cited_by_count":4},{"year":2022,"cited_by_count":4},{"year":2021,"cited_by_count":4},{"year":2020,"cited_by_count":16},{"year":2019,"cited_by_count":2}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}