The use of Fuzzy Preference Relations (FPRs) is prevalent in expert-driven decision-making, and thus obtaining the overall performance of each alternative from an FPR is a key topic in the area. This chapter proposes the notion of Mean Squared Error (MSE) utility vector associated with an FPR, which is defined as the utility vector that determines the pairwise comparison matrix that is closest to the original FPR. We demonstrate that this utility vector can be analytically computed and is a valid utility function since it assigns higher utility values to higher rated alternatives. Furthermore, we show that the MSE utilities can be computed although the comparison matrix is elicited using a multiplicative scale, or even when just one row and one column of the matrix are given. The applicability of the MSE utility vectors is then shown in a Large-Scale Group Decision-Making problem, in which we use them to accelerate the computational time necessary to reach a consensus. Additionally, we provide a comparative analysis with other classic methods for deriving priorities from pairwise comparison matrices.