Itô type stochastic fuzzy differential equations with delay

In the paper we give some foundations for the studies of stochastic fuzzy delayed differential equations. We prove the existence and uniqueness of solutions to such the equations. To obtain our result we assume that the coefficients of the equation satisfy the Lipschitz condition together with linear growth condition. We estimate the distance between approximate solution and exact solution. Also the stability of solution with respect to the initial history is shown. An application of stochastic fuzzy delayed differential equations in the modeling of population growth is indicated.