Quasilinear approximation for interval-valued functions via generalized Hukuhara differentiability

In this paper, a new generalized Hukuhara differentiability concept for interval-valued functions defined on Rn is proposed, which extends the classical Fréchet differentiability notion and provides an interval quasilinear approximation for an interval-valued function in a neighborhood of a point at...

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Bibliographic Details
Authors: Osuna-Gómez, Rafaela, Mendoça da Costa, Tiago, Chalco-Cano, Yurilev, Hernández-Jiménez, Beatriz
Format: article
Publication Date:2022
Country:España
Institution:Universidad Pablo de Olavide (UPO)
Repository:RIO. Repositorio Institucional Olavide
Language:English
OAI Identifier:oai:rio.upo.es:10433/19488
Online Access:https://hdl.handle.net/10433/19488
Access Level:Open access
Keyword:Interval-valued functions
Quasilinear functions
Generalized Hukuhara differentiability
Description
Summary:In this paper, a new generalized Hukuhara differentiability concept for interval-valued functions defined on Rn is proposed, which extends the classical Fréchet differentiability notion and provides an interval quasilinear approximation for an interval-valued function in a neighborhood of a point at which such function is gH-differentiable. Moreover, it overcomes the shortcomings generated by the use of the gH-differentiability concept previously presented in the literature, and this presents a good perspective on interval and fuzzy environments. Several properties of this new concept are investigated and compared with the previous concept properties. Furthermore, the gH-differentiability concept is extended for a fuzzy function, and its introduction is argued and illustrated with examples.