The purpose of this paper is to develop a projection-based compromising method for addressing multiple criteria decision-making problems based on interval-valued intuitionistic fuzzy sets. The concept of projections considers not only the distance but also the included angle between evaluative ratings of alternative actions with respect to a criterion. In the interval-valued intuitionistic fuzzy context, this paper determines the respective projections of the evaluative ratings of each alternative on the positive-ideal and negative-ideal solutions and explores several essential properties. Next, this paper introduces the concepts of projection-based compromising indices and comprehensive compromising indices and further investigates relevant theorems for supporting the usefulness of these indices. Additionally, this paper proposes the projection-based comparative index and the comprehensive comparative index to serve as benchmark values for the comparison purpose. The improvement percentage of the comprehensive compromising value is acquired to determine the priority order of the alternatives, including the complete ranking order and the approval status for each alternative. The feasibility and the applicability of the proposed method are validated with an application problem of watershed site selection. Finally, several comparative analyses are conducted to verify the effectiveness and advantages of the proposed method over other relevant compromising decision-making methods. 
A projection-based compromising method for multiple criteria decision analysis with interval-valued intuitionistic fuzzy information