{"id":"https://openalex.org/W4400197072","doi":"https://doi.org/10.3390/a17070289","title":"Fuzzy Fractional Brownian Motion: Review and Extension","display_name":"Fuzzy Fractional Brownian Motion: Review and Extension","publication_year":2024,"publication_date":"2024-07-01","ids":{"openalex":"https://openalex.org/W4400197072","doi":"https://doi.org/10.3390/a17070289"},"language":"en","primary_location":{"id":"doi:10.3390/a17070289","is_oa":true,"landing_page_url":"https://doi.org/10.3390/a17070289","pdf_url":"https://www.mdpi.com/1999-4893/17/7/289/pdf?version=1721037245","source":{"id":"https://openalex.org/S190629608","display_name":"Algorithms","issn_l":"1999-4893","issn":["1999-4893"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Algorithms","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/1999-4893/17/7/289/pdf?version=1721037245","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5022084998","display_name":"Georgy Urumov","orcid":null},"institutions":[{"id":"https://openalex.org/I94951947","display_name":"University of Westminster","ror":"https://ror.org/04ycpbx82","country_code":"GB","type":"education","lineage":["https://openalex.org/I94951947"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Georgy Urumov","raw_affiliation_strings":["School of Computer Science and Engineering, University of Westminster, 115 New Cavendish Street, London W1W 6UW, UK"],"raw_orcid":"https://orcid.org/0009-0002-0516-615X","affiliations":[{"raw_affiliation_string":"School of Computer Science and Engineering, University of Westminster, 115 New Cavendish Street, London W1W 6UW, UK","institution_ids":["https://openalex.org/I94951947"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5040925126","display_name":"Panagiotis Chountas","orcid":"https://orcid.org/0000-0003-3157-8887"},"institutions":[{"id":"https://openalex.org/I94951947","display_name":"University of Westminster","ror":"https://ror.org/04ycpbx82","country_code":"GB","type":"education","lineage":["https://openalex.org/I94951947"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Panagiotis Chountas","raw_affiliation_strings":["School of Computer Science and Engineering, University of Westminster, 115 New Cavendish Street, London W1W 6UW, UK"],"raw_orcid":"https://orcid.org/0000-0003-3157-8887","affiliations":[{"raw_affiliation_string":"School of Computer Science and Engineering, University of Westminster, 115 New Cavendish Street, London W1W 6UW, UK","institution_ids":["https://openalex.org/I94951947"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5075096076","display_name":"Thierry Chaussalet","orcid":"https://orcid.org/0000-0001-5507-6158"},"institutions":[{"id":"https://openalex.org/I94951947","display_name":"University of Westminster","ror":"https://ror.org/04ycpbx82","country_code":"GB","type":"education","lineage":["https://openalex.org/I94951947"]}],"countries":["GB"],"is_corresponding":true,"raw_author_name":"Thierry Chaussalet","raw_affiliation_strings":["School of Computer Science and Engineering, University of Westminster, 115 New Cavendish Street, London W1W 6UW, UK"],"raw_orcid":"https://orcid.org/0000-0001-5507-6158","affiliations":[{"raw_affiliation_string":"School of Computer Science and Engineering, University of Westminster, 115 New Cavendish Street, London W1W 6UW, UK","institution_ids":["https://openalex.org/I94951947"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5075096076"],"corresponding_institution_ids":["https://openalex.org/I94951947"],"apc_list":{"value":1400,"currency":"CHF","value_usd":1515},"apc_paid":{"value":1400,"currency":"CHF","value_usd":1515},"fwci":2.4974,"has_fulltext":true,"cited_by_count":4,"citation_normalized_percentile":{"value":0.89409449,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":95,"max":98},"biblio":{"volume":"17","issue":"7","first_page":"289","last_page":"289"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12135","display_name":"Fuzzy Systems and Optimization","score":0.9990000128746033,"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":0.9990000128746033,"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/T10282","display_name":"Financial Risk and Volatility Modeling","score":0.9933000206947327,"subfield":{"id":"https://openalex.org/subfields/2003","display_name":"Finance"},"field":{"id":"https://openalex.org/fields/20","display_name":"Economics, Econometrics and Finance"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T11270","display_name":"Complex Systems and Time Series Analysis","score":0.9926000237464905,"subfield":{"id":"https://openalex.org/subfields/2002","display_name":"Economics and Econometrics"},"field":{"id":"https://openalex.org/fields/20","display_name":"Economics, Econometrics and Finance"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/fractional-brownian-motion","display_name":"Fractional Brownian motion","score":0.7552798986434937},{"id":"https://openalex.org/keywords/fuzzy-logic","display_name":"Fuzzy logic","score":0.6206153035163879},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5470026135444641},{"id":"https://openalex.org/keywords/randomness","display_name":"Randomness","score":0.5236884355545044},{"id":"https://openalex.org/keywords/context","display_name":"Context (archaeology)","score":0.47292619943618774},{"id":"https://openalex.org/keywords/brownian-motion","display_name":"Brownian motion","score":0.45885613560676575},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.4579334557056427},{"id":"https://openalex.org/keywords/range","display_name":"Range (aeronautics)","score":0.4269120395183563},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3959575593471527},{"id":"https://openalex.org/keywords/econometrics","display_name":"Econometrics","score":0.33091360330581665},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.16261142492294312},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.1135992705821991}],"concepts":[{"id":"https://openalex.org/C108819105","wikidata":"https://www.wikidata.org/wiki/Q1143293","display_name":"Fractional Brownian motion","level":3,"score":0.7552798986434937},{"id":"https://openalex.org/C58166","wikidata":"https://www.wikidata.org/wiki/Q224821","display_name":"Fuzzy logic","level":2,"score":0.6206153035163879},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5470026135444641},{"id":"https://openalex.org/C125112378","wikidata":"https://www.wikidata.org/wiki/Q176640","display_name":"Randomness","level":2,"score":0.5236884355545044},{"id":"https://openalex.org/C2779343474","wikidata":"https://www.wikidata.org/wiki/Q3109175","display_name":"Context (archaeology)","level":2,"score":0.47292619943618774},{"id":"https://openalex.org/C112401455","wikidata":"https://www.wikidata.org/wiki/Q178036","display_name":"Brownian motion","level":2,"score":0.45885613560676575},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.4579334557056427},{"id":"https://openalex.org/C204323151","wikidata":"https://www.wikidata.org/wiki/Q905424","display_name":"Range (aeronautics)","level":2,"score":0.4269120395183563},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3959575593471527},{"id":"https://openalex.org/C149782125","wikidata":"https://www.wikidata.org/wiki/Q160039","display_name":"Econometrics","level":1,"score":0.33091360330581665},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.16261142492294312},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.1135992705821991},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.0},{"id":"https://openalex.org/C151730666","wikidata":"https://www.wikidata.org/wiki/Q7205","display_name":"Paleontology","level":1,"score":0.0},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","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}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.3390/a17070289","is_oa":true,"landing_page_url":"https://doi.org/10.3390/a17070289","pdf_url":"https://www.mdpi.com/1999-4893/17/7/289/pdf?version=1721037245","source":{"id":"https://openalex.org/S190629608","display_name":"Algorithms","issn_l":"1999-4893","issn":["1999-4893"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Algorithms","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:a683713876204f2996fab0f3448f23ca","is_oa":true,"landing_page_url":"https://doaj.org/article/a683713876204f2996fab0f3448f23ca","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Algorithms, Vol 17, Iss 7, p 289 (2024)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.3390/a17070289","is_oa":true,"landing_page_url":"https://doi.org/10.3390/a17070289","pdf_url":"https://www.mdpi.com/1999-4893/17/7/289/pdf?version=1721037245","source":{"id":"https://openalex.org/S190629608","display_name":"Algorithms","issn_l":"1999-4893","issn":["1999-4893"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Algorithms","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4400197072.pdf","grobid_xml":"https://content.openalex.org/works/W4400197072.grobid-xml"},"referenced_works_count":31,"referenced_works":["https://openalex.org/W1559441907","https://openalex.org/W1978436410","https://openalex.org/W1978989007","https://openalex.org/W1982790767","https://openalex.org/W2005322908","https://openalex.org/W2017545778","https://openalex.org/W2021244475","https://openalex.org/W2022020410","https://openalex.org/W2031753087","https://openalex.org/W2033972209","https://openalex.org/W2054804749","https://openalex.org/W2074366794","https://openalex.org/W2084731501","https://openalex.org/W2091178702","https://openalex.org/W2147576019","https://openalex.org/W2151065060","https://openalex.org/W2343910167","https://openalex.org/W2418281354","https://openalex.org/W2559969663","https://openalex.org/W2560032997","https://openalex.org/W2810460828","https://openalex.org/W2969647429","https://openalex.org/W3085654351","https://openalex.org/W3164475831","https://openalex.org/W4211007335","https://openalex.org/W4239308190","https://openalex.org/W4240177361","https://openalex.org/W6633550226","https://openalex.org/W6658278720","https://openalex.org/W6664105185","https://openalex.org/W6767514867"],"related_works":["https://openalex.org/W3034924094","https://openalex.org/W3094954546","https://openalex.org/W1488708774","https://openalex.org/W1982811510","https://openalex.org/W4391100477","https://openalex.org/W2402189625","https://openalex.org/W4327779705","https://openalex.org/W4310560702","https://openalex.org/W3034439966","https://openalex.org/W2960646972"],"abstract_inverted_index":{"In":[0,77],"traditional":[1],"finance,":[2],"option":[3,34,75],"prices":[4,35],"are":[5],"typically":[6],"calculated":[7],"using":[8],"crisp":[9],"sets":[10],"of":[11,25,46,58,73,110,136],"variables.":[12,141],"However,":[13],"as":[14,157],"reported":[15],"in":[16,70],"the":[17,50,71,108,133,175],"literature":[18],"novel,":[19],"these":[20],"parameters":[21],"possess":[22],"a":[23,44,55,82,93,163,181],"degree":[24],"fuzziness":[26],"or":[27],"uncertainty.":[28],"This":[29,52],"allows":[30,106],"participants":[31],"to":[32,124,187],"estimate":[33],"based":[36],"on":[37,61],"their":[38,189],"risk":[39,112],"preferences":[40,113],"and":[41,66,102,114,150,160,174],"beliefs,":[42],"considering":[43],"range":[45],"possible":[47],"values":[48],"for":[49,107,166,185],"parameters.":[51],"paper":[53,131],"presents":[54],"comprehensive":[56],"review":[57],"existing":[59],"work":[60],"fuzzy":[62,90,126,147,151,172],"fractional":[63,86,127],"Brownian":[64,87,128],"motion":[65,88],"proposes":[67],"an":[68],"extension":[69],"context":[72],"financial":[74,168],"pricing.":[76],"this":[78,130,178],"paper,":[79],"we":[80],"define":[81],"unified":[83],"framework":[84,184],"combining":[85],"with":[89,139],"processes,":[91],"creating":[92],"joint":[94],"product":[95],"measure":[96],"space":[97],"that":[98],"captures":[99],"both":[100],"randomness":[101],"fuzziness.":[103],"The":[104,142],"approach":[105,179],"consideration":[109],"individual":[111],"beliefs":[115],"about":[116],"parameter":[117],"uncertainties.":[118],"By":[119,170],"extending":[120],"Merton\u2019s":[121],"jump-diffusion":[122],"model":[123],"include":[125],"motion,":[129],"addresses":[132],"modelling":[134,167],"needs":[135],"hybrid":[137],"systems":[138],"uncertain":[140],"proposed":[143],"model,":[144],"which":[145],"includes":[146],"Poisson":[148],"processes":[149],"volatility,":[152],"demonstrates":[153],"advantageous":[154],"properties":[155],"such":[156],"long-range":[158],"dependence":[159],"self-similarity,":[161],"providing":[162],"robust":[164],"tool":[165],"markets.":[169],"incorporating":[171],"numbers":[173],"belief":[176],"degree,":[177],"provides":[180],"more":[182],"flexible":[183],"practitioners":[186],"make":[188],"investment":[190],"decisions.":[191]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":3}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}