Some connections between the generalized Hukuhara derivative and the fuzzy derivative based on strong linear independence
Küçük Resim Yok
Tarih
2023
Dergi Başlığı
Dergi ISSN
Cilt Başlığı
Yayıncı
Elsevier Science Inc
Erişim Hakkı
info:eu-repo/semantics/closedAccess
Özet
This article investigates some connections between the notions of the generalized Hukuhara derivative and the Psi- derivative of fuzzy number-valued functions. The concept of Psi- differentiability is defined on a fuzzy number-valued function.. in the form of phi(x) =rho(1)(x)A(1)+ ... +rho(n) (x)A(n) where rho(1), ... rho(n) are.. real-valued functions defined on an interval [a,b] and {A(1),..A(n)} is a strongly linearly independent subset of fuzzy numbers. The Psi- derivative of phi at some x is phi'(x) = rho'(1)(x)A(1)+ ... +rho'(n) (x) A(n) whenever the derivatives rho'(1)(x)(,) ... , rho'(n) (x) exist. This article provides conditions for these two notions of derivatives of such functions to coincide. Moreover, under some weak conditions, we show that an arbitrary continuously gH-differentiable function defined on an interval [a,b] and its gH-derivative can be uniformly approximated as closely as desired by a.- differentiable function and its.- derivative, respectively. Finally, we apply these results to obtain numerical and analytical solutions of a simple fuzzy decay model described by a fuzzy initial value problem under gH-derivative.
Açıklama
Anahtar Kelimeler
Fuzzy Numbers, Strong Linear Independence, Fuzzy Calculus, Banach Space, Approximation, Generalized Hukuhara Derivative, Psi-Derivative
Kaynak
Information Sciences
WoS Q Değeri
N/A
Scopus Q Değeri
Q1
Cilt
643
