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...
| Authors: | , , , |
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| 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 |
| 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. |
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