Robust Group Consensus Optimization Modeling Under Uncertain Environmen

Group consensus decision making is a hot research issue in the field of group decisionmaking by coordinating the conflict between the views of decision makers and seeking a group solution that is widely supported by all decision-makers.As a classic consensus model,the optimal consensus model,such as the minimum cost consensus model and the maximum experts consensus model,can greatly improve the efficiency of consensus.In the past,the optimal consensus modeling was usually regarded as a deterministic optimization problem,or the stochastic programming method was used to deal with it,which often needed to obtain the specific distribution information of uncertain parameters.However,these are difficult to be satisfied in real life.Therefore,in order to overcome these shortcomings,based on the robust optimization method and uncertainty theory,this thesis extends the consensus model of minimum cost and maximum experts to the uncertain decision-making environment,so that the consensus process is more consistent with the reality.First of all,individual opinion is one of the important factors affecting consensus in group decision making and is often uncertain.Previous studies have mostly used probability distributions,interval distributions or uncertainty distribution functions to describe the uncertainty of individual opinions.However,this requires an accurate knowledge of the probability distribution of individual opinions,which is often difficult to satisfy in real life.To overcome this drawback,this paper uses a robust optimisation approach to construct three uncertainty sets to better characterise the uncertainty of an individual’s initial opinion.In addition,we use three different aggregation operators to obtain collective opinions,rather than using fixed values.Based on this,we apply numerical simulations to flood hazard assessment in South China to assess the robustness of the solutions obtained from our proposed robust consensus model.The results show that the proposed model is more robust than previous models.Finally,sensitivity analysis of uncertain parameters is discussed and compared to reveal the characteristics of the proposed model.Secondly,individual opinions and unit adjustment costs are key data for reaching collective consensus in group decision-making.However,in previous studies,most scholars have only considered the uncertainty of individual opinions and ignored the uncertainty of unit adjustment costs,or inaccurately described the uncertainty of unit adjustment costs,which undoubtedly increased the risk of decision makers.To address this issue,this paper constructs four types of uncertainty sets to more accurately describe the uncertainty of unit adjustment costs.In addition,based on multi-actor individual preference scenarios,this paper adopts a robust optimization approach to reduce model risk,and proposes a robust least-cost consensus model with multiple individual preference scenarios under the uncertainty of unit adjustment cost.The robust model is also applied to numerical experiments in Weihai Sea Ranch.The results show that the proposed robust model is more effective than the original model.Finally,this paper presents a sensitivity analysis of the relevant parameters for constructing the robust model,revealing the characteristics of the proposed model.Finally,ignoring the presence of uncertainty can lead to decision problems losing relevance.Therefore,this paper considers the uncertainty of the opinions of the three participating actors based on the maximum expert consensus model and the introduction of non-cooperators.Moreover,three different opinion uncertainty sets are constructed in order to characterize opinion uncertainty more accurately.Further,by applying robust optimization methods to the uncertainty sets,we propose a mixed integer robust maximum expert consensus model to reduce the uncertain opinion risk of decision makers.Numerical experiments are also conducted to verify the validity of the model in this paper,using the Shanghai Metro passenger satisfaction survey as an example.The characteristics of the model are revealed through sensitivity analysis.Finally,to overcome the problem that the results of classical robust optimization methods are relatively highly conservative,we construct a datadriven opinion uncertainty set and propose a data-driven robust optimization model.As a result,decision makers with different risk preferences can choose robust optimization models with different levels of risk depending on the situation.