Characterizations of Fuzzy Functions on Time Scales

This paper handles with the characterization theorem for ∆gH fuzzy functions on T (time scales) through the ∆-differentiability of their end point functions. We proposed a relationship between the ∆gH-derivative of level-wise function Fβ and the delta differentiability of the endpoint functions Fβ and Fβ. We extended the results to fuzzy integro dynamic equations (FIDEs) on T (FIDETs) which translates FIDET into an equivalent system of crisp FIDETs. This laid the foundation for the methods of finding the analytic and approximate solutions of FIDETs.