Group decision making using incomplete fuzzy preference relations based on the additive consistency and the order consistency

In this paper, we present a new method for group decision making using incomplete fuzzy preference relations based on the additive consistency and the order consistency with consistency degrees to overcome the drawbacks of Lee's method [15], where Lee's method cannot obtain the correct preference order of alternatives in some situations. First, we estimate unknown preference values of incomplete fuzzy preference relations based on the additive consistency. Then, we construct modified consistency matrices of experts which satisfy the additive consistency and the order consistency simultaneously. We also prove some properties of the constructed modified consistency matrices. Finally, based on the constructed modified consistency matrices of experts, we present a new method for group decision making. The proposed method provides us with a useful way for group decision making using incomplete fuzzy preference relations based on the additive consistency and the order consistency with consistency degrees.