Set differential equations versus fuzzy differential equations

The study of fuzzy differential equations (FDEs) forms a suitable setting for a mathematical modeling of real world problems in which uncertainties or vagueness pervades. In recent years, the theory of FDEs has been investigated extensively in the original formulation as well as in an alternative framework, which leads to ordinary multivalued differential inclusions. It has recently been realized that initiating the study of set differential equations in a metric space has several advantages, in addition to providing a natural setting for considering FDEs. In this paper, we present some interesting results in this direction with the necessary background material.