On Group Consensus Modeling With Chance-Constrained Programming

Group decision-making is an important method to deal with complex decision-making problems.It aggregates the opinions of all decision-makers into group preferences.It mainly includes two processes:consensus process and selection process.The consensus process aims to obtain the group opinion.The selection process hopes to obtain the best alternative(s)or the ranking of alternatives.When there are coordinators in the decision-making system that consume costs leading to the decision-making individuals adjusting their opinions and forming a unified opinion(consensus),a cost consensus issue is formed.Because of the limited rationality of decision makers and the uncertainty of the decision-making environment,in addition to fuzzy numbers commonly used that can express decision makers' preference,this article assumes that their opinions obey random and uncertain distributions.On the basis of analyzing the uncertainty of preference information.the cost consensus models and group decision-making models with chance constraints are constructed.The study expands the theory system of group decision-making,and has important practical significance f-or solving the consensus of the negotiation and group decision-making issues.Concerning cost consensus with coordinators,goal programming is often applied to achieve the optimal solution.Exiting models focus on either the minimum cost(guaranteeing negotiation budget)or the maximum utility(improving satisfaction level).This paper constructs a stochastic optimization cost consensus model adopting the minimum budget and the maximum utility as objective functions simultaneously to study the negotiation consensus with decision makers' opinions expressed in the forms of utility functions and normal distributions.Thus,the proposed model is an extension of the existing cost consensus model and utility consensus model,respectively.Furthermore in this model,utility priority coefficients cause acceptable budget range and chance constraint shows the probability of reaching consensus.The proposed model adopts a Monte Carlo simulation combined with Genetic Algorithm to reach an optimal solution.The characteristics of random variables and uncertain variables that obey distributions are analyzed,and the deterministic equivalent models of the chance constrained models are studied.In group decision-making without coordinators,the priority weight vectors of an intuitionistic fuzzy preference relation(IFPR)with linear uniform uncertainty distribution characteristics in group decision making(GDM)are determined in this study.On the basis of an IFPR.the assumptions of information variables obeying the uncertainty distribution are defined.Afterwards,a priority model is constructed with a chance constraint based on additive consistency,and the ranking relations of the membership and non-membership matrices are analyzed.The change of the confidence level of the chance constraint controls the flexibility of realizing additive consistency.Moreover,it is proven that if the individual decision-makers' IFPR has a linear distribution,the group IFPR aggregated by the weighted methodology still obeys this distribution.A linear ranking consensus model based on uncertain preference information is developed.