Although a lot of research has been done in studying and exploiting, both, interval valued fuzzy sets and intuitionistic fuzzy sets, we still believe a lot more focus is still required on interval-valued fuzzy preference relations (IVFPR). In this paper, our focus shall be IVFPRs as we put forward two algorithms, based on the additive and multiplicative consistencies, to select the best alternative from a certain set of alternatives. Fuzzy preference relations have few advantages in preciseness and consistency as they give the freedom, to the experts, to evaluate the alternatives relatively. Further, we also extend our algorithms to group decision making and demonstrate their efficacy through numerical illustrations. © Springer Science+Business Media Singapore 2017.