M. R. Balooch Shahryari - Department of Mathematics, Kerman Branch, Islamic Azad University, Kerman, Iran.
M. Miri Karbasaki - Department of Mathematics, Kerman Branch, Islamic Azad University, Kerman, Iran.

In this paper, we introduce the concepts of multi-dimensional fuzzy mappings from ℝ? in to ℝℱ: using the new generalized difference (g-difference), we also present the concepts of fuzzy extended generalized Frechet g-differential, Gateux g-differentiability, directional g-differentiability, partial g-derivatives and g-subgradient, g-subdifferential. In the end, we have solved some examples to illustrate the ability and reliability of g-differentiability for multi-dimensional fuzzy mappings.

Generalized differentiability, Multi-dimentional convex fuzzy mapping, partial and directional diffrenetiability, generalized subdifferential differentiability