Minimal solution of fuzzy linear system of differential equations

Abstract

In this paper, a new approach to solve the fuzzy linear system of differential equations based on pseudo-inverse is presented. In this work, we discuss the minimal solution of a system of linear fuzzy differential equations such as $$A\dot{x}(t)=B\dot{x}(t)+Cx(t), x(0)=x_0$$ where A, B, and C are three real m × n matrices and the initial condition x 0 is described by a vector made up of n fuzzy numbers. In this paper, we investigated a necessary and sufficient conditions for the existence fuzzy derivative $$\dot{x}(t)$$ of a fuzzy process x(t) and a necessary and sufficient conditions for the minimal solution vector to be a fuzzy vector, given arbitrary input fuzzy vector x 0.