Directional derivatives and subdifferential of convex fuzzy mapping on n-dimensional time scales and applications to fuzzy programming

Abstract

In this paper, we address the notions of directional derivative, differential and subdifferential of fuzzy mapping f:Λn→F1, where Λn denotes a n-dimensional time scale and F1 is the fuzzy number space. Through using the directional derivative and differential of two crisp functions that are determined by the fuzzy mapping on n-dimensional time scales, some characterizations of directional derivative and differential are discussed. Moreover, the existence of directional derivative for convex fuzzy mapping is considered on time scales and the relations among directional derivative, differential and subdifferential of fuzzy mapping are established. As applications, some examples of the convex fuzzy programming are given to show the feasibility of our obtained results.