2009 **Abstract:** 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 i…

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“…Bede and Stefanini [14] introduced the definition and theorem of the generalized Hukuhara as follows: …”

confidence: 99%

“…From ( (2) is not a linear space since an interval does not have inverse element and therefore subtraction does not have adequate properties (see [3,13]). More recently, Stefanini and Bede in [13] have introduced the following difference between two intervals.…”

confidence: 99%

“…More recently, Stefanini and Bede in [13] have introduced the following difference between two intervals.…”

confidence: 99%

“…Based on the results established in [5], when both f (x) and f + (x) are differentiable w.r.t. x for all 's, then thecuts of the gH-derivative of f are As f (x) and f + (x) de ne the -cuts of the fuzzy number f (x) for each x, clearly they are monotonic and almost everywhere differentiable w.r.t.…”

confidence: 99%

“…From then on, the theory of interval analysis and its application developed greatly with the joint effort of many researchers. Especially, in order to build the theory of optimization of interval value [5,7,8], theory of differential equation of interval value [1,2,6] and the differential theory of fuzzy value [3], several kinds of differentiability of interval-valued functions were invented, and the related theories were built.…”

confidence: 99%