Osuna-Gómez, RafaelaMendoça da Costa, TiagoChalco-Cano, YurilevHernández-Jiménez, Beatriz2024-01-262024-01-262022-04-20Ahmad I, Singh D, Dar Bilal A (2016) Optimality conditions for invex interval valued nonlinear programming problems involving generalized H-derivative. Filomat 30(8):2121–2138. https://doi.org/10.2298/FIL1608121A10.1007/s40314-021-01746-6https://hdl.handle.net/10433/19488FEDER-UPO-1381297In 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.application/pdfenAttribution-NonCommercial-NoDerivatives 4.0 Internationalhttp://creativecommons.org/licenses/by-nc-nd/4.0/Interval-valued functionsQuasilinear functionsGeneralized Hukuhara differentiabilityjournal articleopen access