Differentiability and convexity of fuzzy mappings

Goetschel and Voxman [1] have introduced the notion of a derivative for fuzzy mappings of one variable in a manner different from the usual one. In this paper, we define a differentiable fuzzy mapping of several variables in ways that parallel the definition, proposed by Goetschel and Voxman [1], for a fuzzy mapping of one variable, and then study some basic differentiability properties of fuzzy mappings from the standpoint of convex analysis.