A Geometric Approach to Solve Fuzzy Linear Systems of Differential Equations
It offers a new perspective for handling fuzziness in differential equations, but the approach is incremental and lacks concrete performance comparisons.
The paper proposes a geometric method to solve fuzzy linear systems of differential equations, representing the solution as a fuzzy set of real vector-functions with nested parallelepiped alpha-cuts.
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 the geometric representations of linear transformations is proposed to find a solution. The most important difference between this method and methods offered in previous papers is that the solution is considered to be a fuzzy set of real vector-functions rather than a fuzzy vector-function. Each member of the 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, alfa-cuts of which are nested parallelepipeds. Proposed method is illustrated on examples.