A method considering and adjusting individual consistency and group consensus for group decision making with incomplete linguistic preference relations

For group decision making with incomplete linguistic preference relations, this paper first make an analysis about individual consistency, based on which a goal programming model is established to estimate the missing values for incomplete linguistic preference relations. Different to the existing methods, the proposed model can cope with the problem in ignorance situations. Then, a multi-stage algorithm which takes both the individual consistency and group consensus into consideration is presented, including the following main stages: initial check for the incomplete preference relations, completion, check and adjustment of individual consistency, aggregation, check and adjustment of group consensus and final selection. In the aggregation stage of the algorithm, an experience and quality hybrid weight vector (EQWV) is defined to obtain the collective linguistic preference relation in group decision making. To prove the feasibility and efficiency of the proposed method, some examples and the corresponding comparisons with other methods are provided. Besides, the analysis on the threshold values proposed by the multi- stage algorithm is made, which can help the decision maker determine the threshold values according to his/her expectations. Finally, a further discussion about comparison analysis, extensible application and some details of the proposed method is presented.