Focusing on multi-attribute group decision-making with interval-valued intuitionistic fuzzy numbers as the attribute values, this study uses the grey correlation coefficient method and the information entropy theory to determine the weights of experts and attributes and builds a comprehensive evaluation cloud model through information aggregation. For this purpose, the influences of fuzziness and randomness on the process and results of group decision-making are taken into account, and the cloud model theory and the characteristics of interval-valued intuitionistic fuzzy numbers are leveraged. Different from the traditional ranking method for interval-valued intuitionistic fuzzy numbers, this study uses the 3En rule of the cloud model to convert interval-valued intuitionistic fuzzy numbers into the cloud and determines the comprehensive evaluation value and hesitation degree of the scheme through cloud similarity. Then, the decision-making schemes are comparatively analyzed. The results show that the proposed method can make decisions scientifically and effectively and thereby provide a scientific basis for decision-makers.