A consensus model for heterogeneous multi-attribute group decision making with several attribute sets

•A consensus model for heterogeneous MAGDM with several attribute sets is proposed.•The model transforms heterogeneous MAGDM into homogeneous MAGDM.•A flexible feedback mechanism based on consensus level is proposed.•Detailed adjustment suggestions for heterogeneous preferences are proposed. In most of the consensus models for multi-attribute group decision making (MAGDM), the decision makers are required to provide evaluation information in given expression domains under the same evaluation attributes, which cannot well represent the heterogeneity of evaluation information and the differences of decision makers to meet the realistic requirements. In this work, we propose a consensus model for heterogeneous MAGDM with several attribute sets, in which each decision maker can independently choose evaluation attributes, set attribute weights, express evaluation information, and then decision makers can reach an agreement through a consensus reaching process. The key of the proposed model is to transform the individual heterogeneous evaluation attributes of each decision maker into corresponding two homogeneous evaluation attributes, i.e. the distance from the alternatives to the Positive Ideal Solution (PIS) and the distance from the alternatives to the Negative Ideal Solution (NIS). More specifically, every evaluation attribute of each decision maker is regarded as a small module. Then, the heterogeneous TOPSIS method is used to calculate the separation from NIS and proximity to PIS of alternatives in small modules and aggregate these distances under different attributes of the same alternative using attribute weights for each decision maker; then, consensus process and selection process are implemented via the new homogeneous evaluation attributes of alternatives for decision makers. Two case studies illustrate the effectiveness of the proposed model.