The comminution process is very important in the mineral processing industry. Some characteristics of ore particles which occur as a product of this process have a significant impact on the effects of further ore processing and the separation of valuable minerals in froth flotation. At the same time, this process requires a significant amount of energy, which significantly affects the overall processing costs, and a significant amount of heavy equipment and corresponding installations, which affects investment costs. In addition, it is not so easy to accurately determine the correlation between energy consumption, the consumption of the grinding media, the utilization of valuable materials and the comminution circuit throughput. Therefore, the selection of an adequate comminution circuit design is recognized as a complex decision-making problem and a new multiple-criteria decision-making approach based on the use of interval-valued intuitionistic fuzzy sets is proposed for its efficient selection. In contrast to the use of a number of more precisely defined criteria, the use of a smaller number of the more complex criteria evaluated on the basis of the satisfaction and dissatisfaction levels is also proposed in this approach. In order to enable its use for solving various complex decision-making problems, the proposed approach is adapted so as to be used in a group environment. In addition, a new procedure for ranking interval valued intuitionistic fuzzy numbers based on the Hamming distance to a complex interval-valued intuitionistic fuzzy reference point is also proposed. The efficiency and usability of the proposed approach are considered on the illustrative example of the preliminary selection of three generic comminution circuit designs. The results obtained by applying the proposed approach are verified by the experts involved in the evaluation. The new procedure proposed for ranking interval-valued intuitionistic fuzzy numbers is also verified by comparing the results obtained by that procedure with those obtained by the proven procedure for ranking interval-valued intuitionistic fuzzy numbers based on an extension of the TOPSIS method.