{"id":"https://openalex.org/W3131793561","doi":"https://doi.org/10.3233/jifs-202523","title":"An efficient method to solve fuzzy Volterra integral equations using Fibonacci polynomials","display_name":"An efficient method to solve fuzzy Volterra integral equations using Fibonacci polynomials","publication_year":2021,"publication_date":"2021-02-13","ids":{"openalex":"https://openalex.org/W3131793561","doi":"https://doi.org/10.3233/jifs-202523","mag":"3131793561"},"language":"en","primary_location":{"id":"doi:10.3233/jifs-202523","is_oa":false,"landing_page_url":"https://doi.org/10.3233/jifs-202523","pdf_url":null,"source":{"id":"https://openalex.org/S179157397","display_name":"Journal of Intelligent & Fuzzy Systems","issn_l":"1064-1246","issn":["1064-1246","1875-8967"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310318577","host_organization_name":"IOS Press","host_organization_lineage":["https://openalex.org/P4310318577"],"host_organization_lineage_names":["IOS Press"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Intelligent &amp; 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/A5041682215","display_name":"M. Darabi","orcid":"https://orcid.org/0000-0001-5262-8500"},"institutions":[{"id":"https://openalex.org/I4210089026","display_name":"Islamic Azad University of Hamedan","ror":"https://ror.org/007zpd132","country_code":"IR","type":"education","lineage":["https://openalex.org/I110525433","https://openalex.org/I4210089026"]},{"id":"https://openalex.org/I4210107186","display_name":"Hamedan University of Technology","ror":"https://ror.org/01hgb6e08","country_code":"IR","type":"education","lineage":["https://openalex.org/I4210107186"]}],"countries":["IR"],"is_corresponding":false,"raw_author_name":"M. Darabi","raw_affiliation_strings":["Department of Mathematics, Hamedan Branch, Islamic Azad University, Hamedan, Iran"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Hamedan Branch, Islamic Azad University, Hamedan, Iran","institution_ids":["https://openalex.org/I4210107186","https://openalex.org/I4210089026"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5073095019","display_name":"Tofigh Allahviranloo","orcid":"https://orcid.org/0000-0002-6673-3560"},"institutions":[{"id":"https://openalex.org/I128277893","display_name":"Bah\u00e7e\u015fehir University","ror":"https://ror.org/00yze4d93","country_code":"TR","type":"education","lineage":["https://openalex.org/I128277893"]}],"countries":["TR"],"is_corresponding":true,"raw_author_name":"T. Allahviranloo","raw_affiliation_strings":["Faculty of Engineering and Natural Sciences, Bahcesehir University, Istanbul, Turkey"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Faculty of Engineering and Natural Sciences, Bahcesehir University, Istanbul, Turkey","institution_ids":["https://openalex.org/I128277893"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5073095019"],"corresponding_institution_ids":["https://openalex.org/I128277893"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.03790278,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"40","issue":"5","first_page":"9899","last_page":"9914"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12135","display_name":"Fuzzy Systems and Optimization","score":0.9997000098228455,"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":0.9997000098228455,"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/T12508","display_name":"Functional Equations Stability Results","score":0.9934999942779541,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"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/T10288","display_name":"Fractional Differential Equations Solutions","score":0.9911999702453613,"subfield":{"id":"https://openalex.org/subfields/2611","display_name":"Modeling and Simulation"},"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/mathematics","display_name":"Mathematics","score":0.6216447353363037},{"id":"https://openalex.org/keywords/volterra-integral-equation","display_name":"Volterra integral equation","score":0.5904992818832397},{"id":"https://openalex.org/keywords/uniqueness","display_name":"Uniqueness","score":0.5751285552978516},{"id":"https://openalex.org/keywords/collocation-method","display_name":"Collocation method","score":0.5730758309364319},{"id":"https://openalex.org/keywords/collocation","display_name":"Collocation (remote sensing)","score":0.5693602561950684},{"id":"https://openalex.org/keywords/integral-equation","display_name":"Integral equation","score":0.5533973574638367},{"id":"https://openalex.org/keywords/simple","display_name":"Simple (philosophy)","score":0.5440165400505066},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.5329457521438599},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5121424198150635},{"id":"https://openalex.org/keywords/fuzzy-logic","display_name":"Fuzzy logic","score":0.4899508059024811},{"id":"https://openalex.org/keywords/fibonacci-number","display_name":"Fibonacci number","score":0.4869609773159027},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3519994616508484},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.34584710001945496},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.2195969521999359},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.2026267945766449},{"id":"https://openalex.org/keywords/ordinary-differential-equation","display_name":"Ordinary differential equation","score":0.07880187034606934},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.0787232518196106}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6216447353363037},{"id":"https://openalex.org/C21965488","wikidata":"https://www.wikidata.org/wiki/Q2632613","display_name":"Volterra integral equation","level":3,"score":0.5904992818832397},{"id":"https://openalex.org/C2777021972","wikidata":"https://www.wikidata.org/wiki/Q22976830","display_name":"Uniqueness","level":2,"score":0.5751285552978516},{"id":"https://openalex.org/C2126413","wikidata":"https://www.wikidata.org/wiki/Q1779479","display_name":"Collocation method","level":4,"score":0.5730758309364319},{"id":"https://openalex.org/C80023036","wikidata":"https://www.wikidata.org/wiki/Q5147531","display_name":"Collocation (remote sensing)","level":2,"score":0.5693602561950684},{"id":"https://openalex.org/C27016315","wikidata":"https://www.wikidata.org/wiki/Q580101","display_name":"Integral equation","level":2,"score":0.5533973574638367},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.5440165400505066},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.5329457521438599},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5121424198150635},{"id":"https://openalex.org/C58166","wikidata":"https://www.wikidata.org/wiki/Q224821","display_name":"Fuzzy logic","level":2,"score":0.4899508059024811},{"id":"https://openalex.org/C173734053","wikidata":"https://www.wikidata.org/wiki/Q47577","display_name":"Fibonacci number","level":2,"score":0.4869609773159027},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3519994616508484},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.34584710001945496},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.2195969521999359},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.2026267945766449},{"id":"https://openalex.org/C51544822","wikidata":"https://www.wikidata.org/wiki/Q465274","display_name":"Ordinary differential equation","level":3,"score":0.07880187034606934},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.0787232518196106},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"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/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.0},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","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}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.3233/jifs-202523","is_oa":false,"landing_page_url":"https://doi.org/10.3233/jifs-202523","pdf_url":null,"source":{"id":"https://openalex.org/S179157397","display_name":"Journal of Intelligent & Fuzzy Systems","issn_l":"1064-1246","issn":["1064-1246","1875-8967"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310318577","host_organization_name":"IOS Press","host_organization_lineage":["https://openalex.org/P4310318577"],"host_organization_lineage_names":["IOS Press"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Intelligent &amp; Fuzzy Systems","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":51,"referenced_works":["https://openalex.org/W18221980","https://openalex.org/W139326556","https://openalex.org/W272933953","https://openalex.org/W369901564","https://openalex.org/W1657177910","https://openalex.org/W1963660290","https://openalex.org/W1965349501","https://openalex.org/W1965955764","https://openalex.org/W1991476326","https://openalex.org/W1994178762","https://openalex.org/W2001600751","https://openalex.org/W2003042428","https://openalex.org/W2004610033","https://openalex.org/W2006017042","https://openalex.org/W2018154656","https://openalex.org/W2022135193","https://openalex.org/W2023295713","https://openalex.org/W2023328727","https://openalex.org/W2027316781","https://openalex.org/W2036102558","https://openalex.org/W2036331868","https://openalex.org/W2063047919","https://openalex.org/W2070545443","https://openalex.org/W2077884988","https://openalex.org/W2082200510","https://openalex.org/W2083466213","https://openalex.org/W2094194195","https://openalex.org/W2094632804","https://openalex.org/W2108625605","https://openalex.org/W2109704832","https://openalex.org/W2162836710","https://openalex.org/W2180113582","https://openalex.org/W2216275375","https://openalex.org/W2255430481","https://openalex.org/W2276710745","https://openalex.org/W2323958254","https://openalex.org/W2324195862","https://openalex.org/W2336178288","https://openalex.org/W2476507202","https://openalex.org/W2922036988","https://openalex.org/W2946167914","https://openalex.org/W2971430195","https://openalex.org/W2998996055","https://openalex.org/W3018099102","https://openalex.org/W4403297475","https://openalex.org/W6605659364","https://openalex.org/W6636885608","https://openalex.org/W6685646043","https://openalex.org/W6688557887","https://openalex.org/W6691712646","https://openalex.org/W6873006859"],"related_works":["https://openalex.org/W2517687681","https://openalex.org/W2118560105","https://openalex.org/W2358959122","https://openalex.org/W2078318892","https://openalex.org/W4225984655","https://openalex.org/W2031624200","https://openalex.org/W2791210196","https://openalex.org/W1987365920","https://openalex.org/W1826865795","https://openalex.org/W2754932876"],"abstract_inverted_index":{"According":[0],"to":[1,21,51,62,69,103,155],"a":[2,42,133],"huge":[3],"interest":[4],"in":[5,64,99,132,153],"implementation":[6],"of":[7,57,73,77,87,95,109,127,143,162],"the":[8,14,65,71,74,84,88,92,96,105,110,123,128,137,141,144,163],"fuzzy":[9,78],"Volterra":[10,79],"integral":[11,80],"equations,":[12],"especially":[13],"second":[15,75],"kind,":[16],"researchers":[17],"have":[18],"been":[19],"investigating":[20],"solve":[22,53],"such":[23,58],"equations":[24],"using":[25],"numerical":[26,119],"methods":[27,157],"since":[28],"analytical":[29],"ones":[30],"might":[31],"not":[32],"be":[33],"accessible":[34],"usually.":[35],"In":[36,101],"this":[37],"research":[38],"paper,":[39],"we":[40,113],"introduce":[41],"new":[43],"approach":[44],"based":[45],"on":[46],"Fibonacci":[47],"polynomials":[48,59],"collocation":[49,66],"method":[50,67,98,130,146],"numerically":[52],"them.":[54],"Several":[55],"properties":[56],"were":[60,131],"considered":[61],"implement":[63],"due":[68],"approximate":[70],"solution":[72],"kind":[76],"equations.":[81],"We":[82],"approved":[83],"existence,":[85],"uniqueness":[86],"solution,":[89],"convergence":[90,124],"and":[91,107,125,149],"error":[93],"analysis":[94],"proposed":[97,111],"detail.":[100],"order":[102],"show":[104,121],"authenticity":[106],"applicability":[108],"method,":[112],"employed":[114],"several":[115],"illustrative":[116],"examples.":[117],"The":[118],"results":[120],"that":[122],"precision":[126],"recent":[129],"good":[134],"settlement":[135],"with":[136],"exact":[138],"solution.":[139],"Also,":[140],"calculations":[142],"suggested":[145],"are":[147],"simple":[148],"low":[150],"computational":[151],"complexity":[152],"respect":[154],"other":[156],"as":[158],"an":[159],"advantage":[160],"feature":[161],"presented":[164],"approach.":[165]},"counts_by_year":[],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}
