{"id":"https://openalex.org/W4415687859","doi":"https://doi.org/10.1016/j.fss.2025.109663","title":"Uncertainty modelling of the nonlinear Black-Scholes equation and decision-making using fuzzy logic","display_name":"Uncertainty modelling of the nonlinear Black-Scholes equation and decision-making using fuzzy logic","publication_year":2025,"publication_date":"2025-10-30","ids":{"openalex":"https://openalex.org/W4415687859","doi":"https://doi.org/10.1016/j.fss.2025.109663"},"language":"en","primary_location":{"id":"doi:10.1016/j.fss.2025.109663","is_oa":false,"landing_page_url":"https://doi.org/10.1016/j.fss.2025.109663","pdf_url":null,"source":{"id":"https://openalex.org/S169411308","display_name":"Fuzzy Sets and Systems","issn_l":"0165-0114","issn":["0165-0114","1872-6801"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Fuzzy Sets and 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":null,"display_name":"Amal Aarab","orcid":"https://orcid.org/0009-0004-4656-3850"},"institutions":[{"id":"https://openalex.org/I4210145365","display_name":"Universit\u00e9 Hassan 1er","ror":"https://ror.org/03cdvht47","country_code":"MA","type":"education","lineage":["https://openalex.org/I4210145365"]}],"countries":["MA"],"is_corresponding":true,"raw_author_name":"Amal Aarab","raw_affiliation_strings":["Laboratory of Education, Sciences and Techniques, Higher School of Education and Training, Hassan First University, Avenue de l\u2019universit\u00e9, Berrechid, 26100, Morocco"],"raw_orcid":"https://orcid.org/0009-0004-4656-3850","affiliations":[{"raw_affiliation_string":"Laboratory of Education, Sciences and Techniques, Higher School of Education and Training, Hassan First University, Avenue de l\u2019universit\u00e9, Berrechid, 26100, Morocco","institution_ids":["https://openalex.org/I4210145365"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5006031418","display_name":"A\u00efcha Driouch","orcid":null},"institutions":[{"id":"https://openalex.org/I119856527","display_name":"Cadi Ayyad University","ror":"https://ror.org/04xf6nm78","country_code":"MA","type":"education","lineage":["https://openalex.org/I119856527"]}],"countries":["MA"],"is_corresponding":false,"raw_author_name":"Aicha Driouch","raw_affiliation_strings":["Laboratory of Applied Mathematics and Computer Science, Faculty of Science and Technologies, Cadi Ayyad University, 112 Bd Abdelkrim Al Khattabi, Marrakesh, 40000, Morocco"],"raw_orcid":"https://orcid.org/0000-0001-7532-9829","affiliations":[{"raw_affiliation_string":"Laboratory of Applied Mathematics and Computer Science, Faculty of Science and Technologies, Cadi Ayyad University, 112 Bd Abdelkrim Al Khattabi, Marrakesh, 40000, Morocco","institution_ids":["https://openalex.org/I119856527"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I4210145365"],"apc_list":{"value":2600,"currency":"USD","value_usd":2600},"apc_paid":null,"fwci":1.6042,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.86650143,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":95,"max":98},"biblio":{"volume":"525","issue":null,"first_page":"109663","last_page":"109663"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10067","display_name":"Stochastic processes and financial applications","score":0.5113000273704529,"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"}},"topics":[{"id":"https://openalex.org/T10067","display_name":"Stochastic processes and financial applications","score":0.5113000273704529,"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/T11976","display_name":"Capital Investment and Risk Analysis","score":0.2313999980688095,"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/T11413","display_name":"Risk and Portfolio Optimization","score":0.08229999989271164,"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-logic","display_name":"Fuzzy logic","score":0.6929000020027161},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.5547000169754028},{"id":"https://openalex.org/keywords/valuation-of-options","display_name":"Valuation of options","score":0.5396000146865845},{"id":"https://openalex.org/keywords/range","display_name":"Range (aeronautics)","score":0.499099999666214},{"id":"https://openalex.org/keywords/vagueness","display_name":"Vagueness","score":0.4496999979019165},{"id":"https://openalex.org/keywords/implied-volatility","display_name":"Implied volatility","score":0.446399986743927},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.43529999256134033},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.42080000042915344},{"id":"https://openalex.org/keywords/volatility","display_name":"Volatility (finance)","score":0.414000004529953}],"concepts":[{"id":"https://openalex.org/C58166","wikidata":"https://www.wikidata.org/wiki/Q224821","display_name":"Fuzzy logic","level":2,"score":0.6929000020027161},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.5601999759674072},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.5547000169754028},{"id":"https://openalex.org/C194483076","wikidata":"https://www.wikidata.org/wiki/Q380382","display_name":"Valuation of options","level":2,"score":0.5396000146865845},{"id":"https://openalex.org/C204323151","wikidata":"https://www.wikidata.org/wiki/Q905424","display_name":"Range (aeronautics)","level":2,"score":0.499099999666214},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4925000071525574},{"id":"https://openalex.org/C2776825360","wikidata":"https://www.wikidata.org/wiki/Q1411921","display_name":"Vagueness","level":3,"score":0.4496999979019165},{"id":"https://openalex.org/C24189920","wikidata":"https://www.wikidata.org/wiki/Q1660345","display_name":"Implied volatility","level":3,"score":0.446399986743927},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.43529999256134033},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.42080000042915344},{"id":"https://openalex.org/C91602232","wikidata":"https://www.wikidata.org/wiki/Q756115","display_name":"Volatility (finance)","level":2,"score":0.414000004529953},{"id":"https://openalex.org/C149782125","wikidata":"https://www.wikidata.org/wiki/Q160039","display_name":"Econometrics","level":1,"score":0.41179999709129333},{"id":"https://openalex.org/C1883856","wikidata":"https://www.wikidata.org/wiki/Q3407463","display_name":"Fuzzy number","level":4,"score":0.3734000027179718},{"id":"https://openalex.org/C19244329","wikidata":"https://www.wikidata.org/wiki/Q208697","display_name":"Financial market","level":2,"score":0.35989999771118164},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3573000133037567},{"id":"https://openalex.org/C163128081","wikidata":"https://www.wikidata.org/wiki/Q1338307","display_name":"Black\u2013Scholes model","level":3,"score":0.34470000863075256},{"id":"https://openalex.org/C42011625","wikidata":"https://www.wikidata.org/wiki/Q1055058","display_name":"Fuzzy set","level":3,"score":0.3328000009059906},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.31619998812675476},{"id":"https://openalex.org/C104859751","wikidata":"https://www.wikidata.org/wiki/Q5450390","display_name":"Finite difference methods for option pricing","level":4,"score":0.31520000100135803},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3043999969959259},{"id":"https://openalex.org/C195975749","wikidata":"https://www.wikidata.org/wiki/Q1475705","display_name":"Fuzzy control system","level":3,"score":0.2741999924182892},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.26739999651908875},{"id":"https://openalex.org/C51544822","wikidata":"https://www.wikidata.org/wiki/Q465274","display_name":"Ordinary differential equation","level":3,"score":0.2623000144958496},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.2621999979019165},{"id":"https://openalex.org/C101710237","wikidata":"https://www.wikidata.org/wiki/Q6904701","display_name":"Monte Carlo methods for option pricing","level":3,"score":0.25589999556541443},{"id":"https://openalex.org/C159694833","wikidata":"https://www.wikidata.org/wiki/Q2321565","display_name":"Iterative method","level":2,"score":0.25589999556541443}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1016/j.fss.2025.109663","is_oa":false,"landing_page_url":"https://doi.org/10.1016/j.fss.2025.109663","pdf_url":null,"source":{"id":"https://openalex.org/S169411308","display_name":"Fuzzy Sets and Systems","issn_l":"0165-0114","issn":["0165-0114","1872-6801"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Fuzzy Sets and 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":27,"referenced_works":["https://openalex.org/W1828415971","https://openalex.org/W1967056914","https://openalex.org/W1968509795","https://openalex.org/W1984157987","https://openalex.org/W2005451925","https://openalex.org/W2015726575","https://openalex.org/W2024284069","https://openalex.org/W2027282331","https://openalex.org/W2027654260","https://openalex.org/W2033972209","https://openalex.org/W2035305968","https://openalex.org/W2040394324","https://openalex.org/W2054804749","https://openalex.org/W2055898480","https://openalex.org/W2077791698","https://openalex.org/W2094835159","https://openalex.org/W2100526065","https://openalex.org/W2115163964","https://openalex.org/W2418281354","https://openalex.org/W2559969663","https://openalex.org/W2963188763","https://openalex.org/W3009966143","https://openalex.org/W3031698536","https://openalex.org/W4210441151","https://openalex.org/W4211007335","https://openalex.org/W4240177361","https://openalex.org/W4401096838"],"related_works":[],"abstract_inverted_index":null,"counts_by_year":[{"year":2026,"cited_by_count":1}],"updated_date":"2026-06-15T08:34:33.830935","created_date":"2025-10-30T00:00:00"}
