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

Throughout this paper, we have presented the concept of one-dimensional convex fuzzy-valued functions from ℝ to the set of fuzzy numbers; using the new generalizeddifference (g-difference). Also the concept of generalized differentiability for convex fuzzy-valued functions is presented; by using the g-difference, and extended generalized g-subgradient and g-subdifferential. Furthermore, One-dimensional convex fuzzyvalued function and fuzzy optimality is described.

Fuzzy numbers; Onedimensional convex fuzzyvalued function; Generalized differentiability; Generalized subgradient and subdifferential; Fuzzyoptimality.