In this paper, we have studied the system of differential equations with intuitionistic fuzzy initial values under the interpretation of (i,ii)-GH differentiability concepts and Zadeh's extension principle interpretation. And we have given some numerical examples.

In this paper, by using the properties of α and β cuts of intuitionistic fuzzy numbers, we have firstly proposed a method to find the general solution of the second order initial value problem with intuitionistic fuzzy initial values under intuitionistic Zadeh's extension principle interpretation. Then we have given some numerical examples for the proposed method. *

In this paper, by using \alpha- and \beta-cuts approach and the intuitionistic fuzzy Zadeh’s extension principle, we have proved a result which reveals that the \alpha- and \beta-cuts of an intuitionistic fuzzy number obtained by the intuitionistic fuzzy Zadeh’s extension principle coincide with the images of the \alpha- and \beta-cuts by the crisp function. Then we have given a corollary about monotonicity of the extension principle. Finally, we have extended these results to IF_N(\mathbb{R}) \times IF_N(\mathbb{R}).

In this paper we have firstly examined the properties of α and β cuts of intuitionistic fuzzy numbers in R n with the help of well-known Stacking and Characterization theorems in fuzzy set theory. Then, we have studied the generalized Hukuhara difference in intuitionistic fuzzy environment by using the properties of α and β cuts and support function. Finally, we have extended the strongly generalized differentiability concept from fuzzy set theory to intuitionistic fuzzy environment and proved the related theorems with this concept.

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