Generalized differentiability for n-dimensional fuzzy-number-valued functions and fuzzy optimization

In this paper, we present a characteristic theorem for the generalized difference concept of n-dimensional fuzzy-numbers by means of support functions. The concepts of differentiability for n-dimensional fuzzy-number-valued functions are presented and discussed using the new generalized difference. The relationships of g-differentiability, s-differentiability, and l-differentiability are characterized. Furthermore, optimization problems with s-convex and s-differentiable fuzzy-number-valued functions are described.