Research On The Asymmetric Minimum Cost Consensus Problem Based On Random Interval Opinions

In order to increase the scientificity and effectiveness of decision making,consensus decision making is more and more widely applied in practice.Its main research is how to coordinate the preferences among different decision makers to obtain the consensus or solution widely accepted within the group.Reaching consensus usually consumes a lot of time and resources,how to reach consensus at the lowest cost is one of the important goals of group decision-making.First of all,decision makers often expect different marginal compensation due to differences in the direction of opinion adjustment in the process of reaching consensus,so decision makers often have asymmetric unit adjustment cost.Secondly,due to the uncertainty of objective things,the fuzziness of human thinking and the objective existence of judgment errors,it is often difficult for decision-makers to give accurate opinion values in practical decision-making,for which the interval opinion is widely used.Most of the existing studies do not consider the asymmetry of adjustment cost and often ignore the internal characteristics of interval opinion.In order to solve the above problems,this paper introduces the interval opinion that follows the uniform distribution and the normal distribution respectively,and studies the consensus reaching problem under the asymmetric cost situation from the perspective of the optimal adjustment cost.The main work of this paper is as follows:(1)The consensus model of minimum cost based on the asymmetry of adjustment costs is constructed by introducing the opinion of decision-makers as a uniform distribution interval.Existing research is mainly to consider policymakers accurately,this paper embarks from the decision makers opinions for uniform distribution interval,characterization the needs of decision makers in the different level of consensus.A weight allocation method for decision makers based on interval opinion length is proposed,with soft consensus measure,establish the asymmetric adjustment cost minimum cost model of soft consensus.(2)The opinion of decision-maker is introduced as normal distribution interval,so the distribution form of opinion of decision-maker interval is expanded,and the minimum cost consensus model of adjustment cost asymmetry is constructed.Furthermore,the soft consensus measure is introduced and an asymmetric minimum cost soft consensus model based on the opinion of normal distribution interval is proposed.The consensus model is analyzed and compared through the case study of the negotiation between the government and the manufacturer on the emission of pollution.The results show that:(1)compared with the precise opinion,the range opinion can reduce the consensus cost;(2)Compared with the consensus model with symmetric adjustment cost,the total consensus cost of asymmetric adjustment cost does not increase infinitely with the increase of unit adjustment cost;(3)Compared with the opinion of uniform distribution interval,the consensus cost of the opinion of normal distribution interval is less;(4)The change of consensus threshold has an important impact on consensus results.In this paper,the relationship between consensus opinion and cost compensation is analyzed from the perspective of total cost optimization,and the effectiveness of the consensus model of asymmetric cost adjustment based on decision-maker’s interval opinion is verified by case study.At the same time,the research results provide reference for government departments to guide enterprises to make policies on emission reduction.