Minimal solution of fuzzy linear system of differential equations
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 mn 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.
minimal solution linear fuzzy differential equations fuzzy number fuzzy system