On the Analysis of Regularized Fuzzy Systems of Uncertain Differential Equations.

Abstract

This article analyzes a regularized set of fuzzy differential equations with respect to an uncertain parameter. We provide sufficient conditions for the correctness of a new regularization scheme. For the resulting family of regularized fuzzy differential equations, the following properties are analyzed, and efficient criteria are proposed: successive approximations, continuity, global existence of solutions, existence of approximate solutions, existence of solutions in the autonomous case. In addition, we develop stability criteria for the regularized family of fuzzy differential equations on the basis of the comparison technique and the method of nonlinear integral inequalities. We expect that the derived results will inspire future research work in this direction.