An application of decision theory on the approximation of a generalized Apollonius-type quadratic functional equation
Küçük Resim Yok
Tarih
2024
Dergi Başlığı
Dergi ISSN
Cilt Başlığı
Yayıncı
Springer
Erişim Hakkı
info:eu-repo/semantics/openAccess
Özet
To 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.
Açıklama
Anahtar Kelimeler
Stability, Decision Theory, Approximation, Apollonius-Type Quadratic Functional Equation, Z-Number
Kaynak
Journal of Inequalities and Applications
WoS Q Değeri
N/A
Scopus Q Değeri
Q2
Cilt
2024
Sayı
1
