Research On Consensus Model For Large-scale Group Decision Making With Probabilistic Linguistic Information

In the age of Internet,decision making environments and problems are becoming more and more complex,and the size of the groups participating in decision making problem is getting larger and larger.For the sake of the fairness and rationality of the decision making results,and the group decision making(GDM)has evolved into the large-scale group decision making(LSGDM).In the decision making process,many vague and uncertain indicators are difficult to be expressed numerically or in terms of single linguistic variables.However,the probabilistic linguistic term set(PLTS)contains several possible linguistic variables and their probabilistic information,which can describe the evaluation information of decision makers.As an effective means to deal with complex information,which can be in line with the ambiguity of decision makers’ thinking in the actual decision making process.In addition,since the members involved in decision making are no longer limited to experts in a certain field,the decision makers have different knowledge backgrounds,and the decision making information comes from different time and area,it is difficult to avoid conflicts in decision making.Therefore,in order to obtain a satisfying result recognized by decision makers,it is necessary to coordinate the viewpoints of decision makers through the consensus reaching process(CRP),so as to increase the consensus degree of the group on the decision making problem.In this way,it can ensure that the decision making results are reasonable and scientific.Based on the above analysis,this paper focuses on exploring large-scale group consensus decision making model in probabilistic linguistic environment by utilizing the social network analysis(SNA)for the uncertain information representation and large group characteristics.The main work can be summarized into the following four aspects:(1)A social network-based consensus model for LSGDM with probabilistic linguistic information is studied.Aiming at the trust relationship among decision makers as well as the uncertainty and ambiguity in the trust relationship,the PLTS is utilized to describe the trust degree among decision members.In addition,considering that the trust information given by decision makers in real problems may be defective or incomplete,a probabilistic linguistic trust transfer mechanism and a trust aggregation operator are proposed based on the nature of the trust relationship to estimate the missing trust values.A trust-guided consensus model is proposed to study the LSGDM method based on trust relationships.This study not only mines the potential information of decision makers and improves the quality of decision making through social relationships,but also greatly reduces the complexity of large-scale group decision making problems by utilizing social network analysis tools.(2)A LSGDM method based on the opinion evolution model is proposed.First,according to the similarity,self-persistence,authority and social network between decision makers,different influence matrices are determined.Second,based on the different influence matrices,a probabilistic linguistic environment DeGroot model(PL-DeGroot)is constructed.Finally,aiming at the feedback mechanism in the CRP,a consensus method based on PL DeGroot model is proposed.When the decision making group fails to reach consensus,the feedback mechanism of opinion evolution is used to adjust the evaluation information of decision makers.It realizes the interaction of opinions among decision makers,and improves the consensus level of the decision making group.Compared with the existing methods,it shows the effectiveness of the proposed method to improve the decision making efficiency.(3)A consensus model based on particle swarm optimization(PSO)algorithm is constructed.For the characteristics of PLTSs,some relevant measures are given,including transformation function,operation rule and distance measure.Then,the traditional PSO algorithm is integrated into the probabilistic linguistic environment.The individuals are treated as particles,and the maximization of the group consensus level is taken as the adaptive function to design an adaptive feedback mechanism.Then a consensus model based on intelligent algorithm is proposed.In addition,during the selection process,for making the ranking results reasonable,VIKOR method in probabilistic linguistic environment is proposed by improving the ranking function,.This study reduces the complexity of processing large amounts of data and broadens the application scenarios of decision making methods through the combination of intelligent algorithms and GDM theory.(4)A consensus model based on personalized semantics of decision makers is proposed.First,considering the differences in the understanding of the same linguistic term by different decision makers.The ambiguity of evaluation information and personal semantics is introduced into the probabilistic linguistic preference relation(PLPR),then a programming model of individual preference consistency is constructed to determine the specific semantics of experts on each linguistic term.The PLPR is transformed into a fuzzy preference relation and the consensus level of the decision group can be obtained.Then,the fuzzy C mean clustering algorithm is used to classify experts into several subgroups,which simplifies the decision making process.Finally,a two-stage CRP is proposed to dynamically update the weights of decision makers according to their contribution to the group consensus,and a reasonable weight determination method is developed.The proposed method introduces personalized semantics into uncertain decision making,which ensures the consistency of individuals while ensuring the rationality of the decision results.