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.

The original formulation of fuzzy differential equations suffers from the disadvantage since the solutions increases as time increases. In this paper, employing the results of set differential equations obtained in V. Laksmikantham, S. Leela, A.S. Vatsala, Setvalued hybrid differential equations and stability in terms of two measures, J. Hybrid Systems 2 (2) (2002) 169–188, a new approach is suggested in order to capture the vagueness and the rich properties of solutions without fuzziness.