A Geometric Approach to Solve Fuzzy Linear Systems of Differential Equations

In this paper, systems of linear differential equations with crisp real coefficients and with initial condition described by a vector of fuzzy numbers are studied. A new method based on geometric representations of linear transformations is proposed to find a solution. The most important difference between this method and methods offered in other papers is that the solution is considered to be a fuzzy set of real vector-functions rather than a vector of fuzzy functions. Each member of the solution set satisfies the given system with a certain possibility. It is shown that at any time the solution constitutes a fuzzy region in the coordinate space, alpha-cuts of which are nested parallelepipeds. The proposed method is illustrated on examples.