2013 **Abstract:** 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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“…[25,26] Given two fuzzy numbers u, v ∈ E 1 , the generalized Hukuhara difference (gH-difference for short) is the fuzzy number w, if it exists, such that…”

confidence: 99%

“…Definition 2.8. [26] Let t 0 ∈ (a, b) and h be such that t 0 +h ∈ (a, b). Then the generalized Hukuhara derivative of a function F : (a, b) → E 1 at t 0 is defined as…”

confidence: 99%

“…Definition 2.2.5: (Bede and Stefanini, 2013). Let , ∈ ℱ(ℝ) , the generalized Hukahara difference (gH-difference) of two fuzzy numbers and is the fuzzy number ∈ ℱ(ℝ), if it exists such that…”

confidence: 99%

“…Each of following conditions guarantees the existence of = ⊖ ∈ ℱ(ℝ) (see 24 for more details) Definition 2.2.6: (Bede and Stefanini, 2013). Let = ⊂ ℝ → ℱ(ℝ) and ∈ be a fixed number, then is called Gh-differentiable at ∈ if: …”

confidence: 99%

“…After the introduction and major innovations in the theory of fuzzy differential equations [4,6,14], the term fuzzy differential equation (FDE) is instantaneously growing as a new area in fuzzy calculus. These equations are acquired interchangeably by incorporating differential equations with fuzzy initial values, fuzzy boundary values or with fuzzy functions as well.…”

confidence: 99%