An application of decision theory on the approximation of a generalized Apollonius-type quadratic functional equation

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dc.authoridAllahviranloo, Tofigh/0000-0002-6673-3560
dc.authoridSaadati, Reza/0000-0002-6770-6951
dc.authorwosidAllahviranloo, Tofigh/V-4843-2019
dc.authorwosidSaadati, Reza/C-6330-2018
dc.contributor.authorAhadi, Azam
dc.contributor.authorSaadati, Reza
dc.contributor.authorAllahviranloo, Tofigh
dc.contributor.authorO'Regan, Donal
dc.date.accessioned2024-05-19T14:46:46Z
dc.date.available2024-05-19T14:46:46Z
dc.date.issued2024
dc.departmentİstinye Üniversitesien_US
dc.description.abstractTo make better decisions on approximation, we may need to increase reliable and useful information on different aspects of approximation. To enhance information about the quality and certainty of approximating the solution of an Apollonius-type quadratic functional equation, we need to measure both the quality and the certainty of the approximation and the maximum errors. To measure the quality of it, we use fuzzy sets, and to achieve its certainty, we use the probability distribution function. To formulate the above problem, we apply the concept of Z-numbers and introduce a special matrix of the form diag(A,B,C)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\mathrm{diag}(A, B, C)$\end{document} (named the generalized Z-number) where A is a fuzzy time-stamped set, B is the probability distribution function, and C is a degree of reliability of A that is described as a value of A*B\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$A\ast B$\end{document}. Using generalized Z-numbers, we define a novel control function to investigate H-U-R stability to approximate the solution of an Apollonius-type quadratic functional equation with quality and certainty of the approximation.en_US
dc.identifier.doi10.1186/s13660-024-03103-7
dc.identifier.issn1029-242X
dc.identifier.issue1en_US
dc.identifier.scopus2-s2.0-85185508568en_US
dc.identifier.scopusqualityQ2en_US
dc.identifier.urihttps://doi.org10.1186/s13660-024-03103-7
dc.identifier.urihttps://hdl.handle.net/20.500.12713/5590
dc.identifier.volume2024en_US
dc.identifier.wosWOS:001171699400003en_US
dc.identifier.wosqualityN/Aen_US
dc.indekslendigikaynakWeb of Scienceen_US
dc.indekslendigikaynakScopusen_US
dc.language.isoenen_US
dc.publisherSpringeren_US
dc.relation.ispartofJournal of Inequalities and Applicationsen_US
dc.relation.publicationcategoryMakale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanıen_US
dc.rightsinfo:eu-repo/semantics/openAccessen_US
dc.snmz20240519_kaen_US
dc.subjectStabilityen_US
dc.subjectDecision Theoryen_US
dc.subjectApproximationen_US
dc.subjectApollonius-Type Quadratic Functional Equationen_US
dc.subjectZ-Numberen_US
dc.titleAn application of decision theory on the approximation of a generalized Apollonius-type quadratic functional equationen_US
dc.typeArticleen_US

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