Generalized partial and directional differentiability of multi-dimensional fuzzy mappings and applications

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.

Keywords:

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