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Interval reciprocal preference relations (IRPRs) have been extensively applied to real-life decision-making problems. This paper aims at introducing two new decision-making methods with IRPRs. To overcome drawbacks of several extant order relations of intervals, a new admissible order relation of intervals is proposed. An algorithm is then introduced to rank a series of intervals. We define a new consistency index and the satisfactory consistency of IRPRs. For improving the consistency level of IRPRs, a linear programming model is built. Subsequently, a new individual decision-making (IDM) method with an IRPR is introduced. For group decision making, a group consensus index is proposed. To improve the group consensus degree, an interactive convergent iterative algorithm is designed. Decision makers' weights are determined by combining the logarithmic Manhattan distance between two IRPRs with the consistency indices of IRPRs. Accordingly, a novel consistent and consensus-based group decision-making (GDM) method with IRPRs is presented. Eventually, a decision support system is developed based on the proposed IDM method and GDM method. Illustrative examples and simulation experiments are provided to illustrate the superiority of the proposed IDM method and GDM method. [ABSTRACT FROM AUTHOR]