عنوان مقاله [English]
In complex human social activities, practical problems involve more prominent uncertainty, and deterministic approaches of classical methods become powerless. Decision makers sometimes are distributed in different geographical regions and it may be difficult to reach an agreement on which unique preference relations format is used. On the other hand, decision makers usually do not have enough knowledge to express their preference relations completely. In this research, a new method for human group decision making is presented by using heterogeneous incomplete uncertain preference relations. The uncertain multiplicative preference relations, uncertain fuzzy preference relations, uncertain linguistic preference relations, intuitionistic fuzzy preference relations and Interval preference sequence can be included in this method. Our new method consists of nine steps. In the first step, decision-makers preferences in the form of heterogeneous comparison matrixes are driven. In the second step, we change them to the homogeneous form. This homogeneous form is interval multiplicative preference relation. In the third step, a preprocessing approach using an optimization framework is presented to obtain a complete consistent interval comparison matrix respect to each decision-maker preferences. In the fourth step, flexible and simple forms are obtained to show the robustness of the final weights. In the fifth step, rank sequences for each decision maker is obtained. In the sixth step, the importance weights of decision makers are calculated. In the seventh step, importance weights of alternatives respect to each decision maker preferences are derived. In the eighth step, a multi-objective model is established and in the final step a bi-an optimization model which aims to maximize simultaneously the group consensus, the individual consistency and weights robustness of each decision maker is solved. By solving the optimization model, the priority weights of alternatives can be obtained. Finally, an illustrative example is used to show the feasibility and effectiveness of the proposed method.