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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Detalles Bibliográficos
Autores: Osuna Gómez, Rafaela, Costa, T.M., Chaico Cano, Y., Hernández Jiménez, Beatriz
Tipo de recurso: artículo
Estado:Versión publicada
Fecha de publicación:2022
País:España
Institución:Universidad de Sevilla (US)
Repositorio:idUS. Depósito de Investigación de la Universidad de Sevilla
OAI Identifier:oai:idus.us.es:11441/134894
Acceso en línea:https://hdl.handle.net/11441/134894
https://doi.org/10.1007/s40314-021-01746-6
Access Level:acceso abierto
Palabra clave:Interval-valued functions
Quasilinear functions
Generalized Hukuhara differentiability
Descripción
Sumario: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.