Abstract:

Due to the high complexity of real-life decision-making problems， the knowledge and experience of a single expert are often not sufficient to meet decision-making needs. Therefore， a group of experts is required to participate in the decision-making process. Because of the differences in experts’ fields of expertise and knowledge， the evaluations of experts may differ or even be oppose. In this case， it is necessary to measure the group consensus degree， i.e.， the distance between the consensus center and the evaluations of experts. When the group consensus degree is less than a given consensus threshold， the minimum adjustment consensus model is often used to help decision makers guide experts to revise their opinions so that the group can reach consensus. In the current study， the consensus center used in the minimum adjustment consensus model is the mean of experts’ evaluations derived from aggregation operators. However， influenced by the distribution of information in the group， the consensus center is uncertain. How should a decision maker determine the value of the consensus center？ Is there a risk of misjudgment in using a given value of the consensus center to judge if a group reaches the consensus degree？ Little research has been conducted on these issues.To answer these questions， firstly， in terms of consensus efficiency， the highly efficient consensus center is defined and then a minimum adjustment consensus model is proposed based on the highly efficient consensus center. Next， on account of the consensus misjudgment risk， the reliable consensus center is defined and propose a minimum adjustment consensus model based on the reliable consensus center. Afterwards， a risk-efficiency mixed consensus model is further proposed， which considers both consensus efficiency and consensus misjudgment risk. A numerical example shows that the proposed models have the following advantages： 1） the minimum adjustment consensus model based on the highly efficient consensus center has less expert evaluation adjustment than the classical minimum adjustment consensus model； 2） the minimum adjustment consensus model based on the reliable consensus center has lower group consensus misjudgment risk than the classical minimum adjustment consensus model； 3） the risk-efficiency mixed consensus model can balance the consensus misjudgment risk and efficiency flexibly by a weight.The problem of consensus misjudgment risk and efficiency caused by the uncertainty of consensus center is discussed and three types of models are proposed that can analyze both consensus misjudgment risk and efficiency， which enriches group decision theory.

Key words: group decision making, consensus model, consensus center, consensus efficiency, consensus misjudgment risk, consensus reaching probability