The concept of interval-valued fuzzy sets is the generalization of the concept of fuzzy sets. The theory of interval-valued fuzzy sets is well suited to dealing with vagueness. Recently, interval-valued fuzzy sets have been used to build soft decision making models that can accommodate imprecise information. However, it seems that there is little investigation on multicriteria decision making using interval-valued fuzzy sets with multiple criteria being explicitly taken into account. In this paper, multiattribute decision making using interval-valued fuzzy sets is investigated, in which multiple criteria are explicitly considered, several linear programming models are constructed to generate optimal weights for attributes, and the corresponding decision-making methods have also been proposed. Feasibility and effectiveness of the proposed method are illustrated using a numerical example.