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In the present paper we introduce and study a generalization of the Hukuhara di¤erence and also generalizations of the Hukuhara di¤erentiability to the case of interval valued functions. We consider several possible de…nitions for the derivative of an interval valued function and we study connections between them and their properties. Using these concepts we study interval di¤erential equations. Local existence and uniqueness of two solutions is obtained together with characterizations of the solutions of an interval di¤erential equation by ODE systems and by di¤erential algebraic equations. We also show some connection with di¤erential inclusions. The thoretical results are turned into practical algorithms to solve interval di¤erential equations.

In the present paper, using novel generalizations of the Hukuhara di¤erence for fuzzy sets, we introduce and study new generalized di¤erentiability concepts for fuzzy valued functions. Several properties of the new concepts are investigated and they are compared to similar fuzzy di¤erentiabilities …nding connections between them. Characterization and relatively simple expressions are provided for the new derivatives.

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