Calculus for linearly correlated fuzzy function using Fréchet derivative and Riemann integral

Abstract

In this manuscript we study integration and derivative theories for interactive fuzzy processes. These theories are based on the Fréchet derivative and the Riemann integral. In addition, we present a connection between these two theories, i.e., some problems may be formulated in both ways. We establish the fundamental theorem of calculus, theorem of existence and the local uniqueness of the solution of fuzzy differential equations and some techniques to solve fuzzy initial value problems. To illustrate the usefulness of the developed theory, we investigate the radioactive decay model.