Research On Maximum Expert Consensus Models Considering The Dual-consensus Constraints

The maximum expert consensus model which is aimed at maximizing the number of decision-makes who reach the consensus under the limited budget as many as possible.It is widely applicable to decision-making scenarios such as election voting,group recommendation and supplier selection,where consensus can be reached by obtaining the consent of a majority of decision-makers.However,the existing models mainly focus on maximizing the number of people who meet the type-ε consensus threshold,ignoring the type-α consensus threshold of the decision-making group.In order to solve this problem,this paper proposes a maximum expert consensus model with both type-α and type-ε constraints,and extends it to consider the limited compromise behavior of decision-makers.Furthermore,to determine the optimal range of the consensus budget,a minimum cost consensus model considering dual consensus constraints is proposed and the allocation of decision-makers’ weights is optimized.The main research work is as follows:First,in order to provide a reasonable budget for the following consensus-reaching process,a minimum cost consensus model with dual consensus constraints is constructed.At the same time,considering that the way in which the moderator directly gives the weight of the decision-makers is too subjective,this paper proposes a method to assign the decision-makers’weight considering attributes association.The moderator evaluates the decision-makers from multiple dimensions,prepossesses the evaluation data with entropy weight method,then measures the interaction between evaluation attributes with fuzzy measures,and finally uses Choquet integral to determine the weight of the decision-makers.Secondly,by constraining both type-α and type-ε consensus measures,a maximum expert consensus model with dual consensus constraints is constructed based on integer programming theory.Considering that decision-makers may have limited compromise behavior in real decision-making,we further develop a maximum expert consensus model considering limited compromise,which solves the problem that the traditional maximum expert consensus model adjusts the opinions of some decision-makers without limitation in order to pursue the optimal consensus opinion.At the same time,this paper also fully considers the role of the moderator in the consensus-researching process,and takes the opinion interval of the moderator as the consensus interval to ensure that the consensus results are produced within a reasonable range.Finally,taking drug centralized purchase pricing as the background,the relationships between the consensus models proposed in this paper and the traditional consensus models are discussed and a comparative analysis is conducted to verify the effectiveness of the models.The results show that the consensus cost of the minimum cost consensus model proposed in this paper increases with the increase of type-α consensus threshold.In addition,under the limited budget,the number of people who reach the consensus probably decreases due to considering type-α consensus threshold,and the higher the type-α consensus threshold,the fewer the number of people who reach the consensus.It has a certain inspiration to solve the decision-making problems that require a large number of people who reach a consensus and a relative high level of group consensus.