A class of linear differential dynamical systems with fuzzy initial condition

Abstract

This paper investigates linear first-order fuzzy differential dynamical systems where the initial condition is described by a fuzzy number. We use a complex number representation of the α -level sets of the fuzzy system and prove theorems that provide the solutions under such representation, which is applicable to practical computations and also has some implications for theory. Then the paper shows some properties of the two-dimensional dynamical systems, and their phase portraits are described by means of examples. There may be a significant difference between the solutions according to whether the matrix is nonnegative or not; finally, the paper points out future research on the fuzzy dynamical systems.