This paper presents a new approach to the treatment of uncertainty and imprecision in multi-criteria decision-making based on interval rough numbers (IRN). The IRN-based approach provides decision-making using only internal knowledge for the data and operational information of a decision-maker. A new normalized weighted geometric Bonferroni mean operator is developed on the basis of the IRN for the aggregation of the IRN (IRNWGBM). Testing of the IRNWGBM operator is performed through the application in a hybrid IR-DEMATEL-COPRAS multi-criteria model which is tested on real case of selection of optimal direction for the creation of a temporary military route. The first part of hybrid model is the IRN DEMATEL model, which provides objective expert evaluation of criteria under the conditions of uncertainty and imprecision. In the second part of the model, the evaluation is carried out using the new interval rough COPRAS technique.