The Application Of Multi-attribute Group Decision-making Based On Uncertain Information In Investment Problems

Investment is closely related to economic growth,and plays an important role in the economic development of enterprises.For enterprises,investment is the fundamental driving force of theeconomic growth.It is difficult for an investor to make decisions with the limited information,while the investment problem involves a wide range of information and many negative factors.Therefore,in this case,it is necessary to gather the wisdom of several people to overcomethe disadvantages of individual decision.Investment decision-making process usually completed by a group of experts who come from different fields.They evaluate the investment projects and choose the optimal one for investing.The group decision making is useful for investment decision.However,the uncertainty in the real world has become the main obstacle of the investment decision-making.Based on this,this paper explores the uncertainty in the investment problem with group decision-making process.This paper analyzes the uncertainty of investment problem in the group decision-making process from two aspects:the evaluation process and consensus reaching process.Moreover,this paper explores the influence of the uncertainty on the investment decision-making results.On the one hand,the uncertain opinions provided by the experts,who participate in the investment decision-making process in the evaluation process,are considered;on the other hand,the determination of the evaluations adjusted by the experts in the consensus reaching process are considered.In the evaluation process,the hesitate fuzzy set and the probabilistic linguistic set are introduced to express the evaluations of experts,and the new evaluations are determined basedonthe trust relationshipsamong experts.The proposed methods are applied to the selection of the optimalportfolio and the investment project,respectively.To consider the influence of the uncertainty on the evaluation process,this paper introduces the prospect theory to reflect the psychological behavior of experts,and the method of portfolio selection based on prospect theory with group decision-making is proposed.The group decision-making method is usedto select the optimal portfolio that allocating the limited funds to multiple investment projects.Due to the limited experience or available information,experts may hesitate among multiplevalues when they evaluate the investment projects.Therefore,the hesitate fuzzy set is used to express experts' opinions,and the score function and deviation function of the hesitant fuzzy number are used to depict the return and risk of the portfolio.The experts make decisions in the uncertain environment,which forces them to make evaluationswith intuition to a great extent.Therefore,the prospect theory is introduced to consider the psychological behavior of experts.The prospect value function is improved to adapt the hesitate fuzzy environment,and reflects the impact of the psychological behavior on the decision results.The availability of the proposed method is verified by a numerical example.In addition,the proposed method is compared with other methods to illustrate its advantages.The proposed group decision-making method is not only more reasonable than individual decision,but also more realistic with considering the psychological behavior of experts.The uncertainty in the process of reaching consensus is the determination of the evaluations adjusted byexperts.In order to fully reflect the subjectivity of experts,a group decision-making method based on the particle swarm optimization(PSO)is proposed and applied to the selection of the optimal investment projects.In the process of evaluation,the probability linguistic set is used to express the evaluation opinions of experts.When the consensus levelsamong experts are not reached the threshold,experts are asked to adjust their evaluations.The new evaluationsare obtained by the expertsaccording to their will,it is difficult for the manager who moderates the group decision-making process to determine the adjusted evaluations of experts.In order toconsider the subjectivity of experts entirely in the decision-making process,this studyintroduces the trust relationships todetermine the adjustment coefficients of experts.Then,the new evaluations can be obtained.Based on the trust relationship,the original update function in the PSO is improved to derive the new evaluations.Furthermore,the improved PSO is used to simulate the group decision-making process in the investment decision.Each expert in the group is regarded as a particle,which moving toward the best position that represents the final evaluation.The fitness function is improved by using the distance function of the probabilistic linguistic set to measure the consensus levels.The feasibility of the proposed method is verified by a numerical example,and the method is compared with the group decision-making method without considering the trust relationship to show its novelty.