This paper is concerned with the guaranteed cost robust weighted fusion prediction problem for discrete-time systems with multiplicative noises, colored measurements noises and uncertain noise variances. Applying the augmented state approach and a fictitious noise technique, the original system is converted into a system only with uncertain noise variances. Two classes of guaranteed cost robust weighted fusion steady-state Kalman predictions weighted by matrix are presented based on the minimax robust estimation principle and parameterization representation of uncertain noise variances. One class is to find the maximal perturbation region of uncertain noise variances, such that for all perturbations in that region, the accuracy deviations remain within a prescribe range. The other class is to find the maximal lower bound and the minimal upper bound of the accuracy deviations over the given bounded perturbation region of noise variances. The proof of the guaranteed cost robustness is proved by the Lyapunov equation approach. A simulation example applied to the uninterruptible power system (UPS) shows the correctness and effectiveness of the proposed results.