Research On Improvement Of Multi-index Comprehensive Evaluation Method Based On BoD

Multi-indicator comprehensive evaluation refers to a kind of measurement method that uses concepts,logic,mathematics and other methods to abstract and summarize the evaluation object(DMU)based on the comprehensive consideration of all aspects of the attribute characteristics,and obtains the score value or ranking result that can compare the merits and demerits of the evaluation object.In the process of multi-index comprehensive evaluation,weight is the key element to accurately express and reflect the value orientation of evaluation subjects,and is the core to determine the scientific,reasonable and fair results of multi-index comprehensive evaluation.Therefore,the weight assignment method is the important and difficult content of multi-index comprehensive evaluation theory.In particular,when the evaluation object or its stakeholders will receive corresponding compensation or punishment(such as reputation and reward,etc.)for its ranking results,the evaluation object with poor performance in the evaluation results will have enough incentives and reasons to question the fairness of the comprehensive evaluation weight of multiple indicators.Among them,the reliability,comprehensiveness and fairness of the external information required for weight calculation are more likely to be questioned if the weight calculation rules are given externally(such as AHP and Delphi,etc.).While,the weight calculation rules are represented by the weight assignment methods(such as PCA,entropy weight,DEA,etc.)of the evaluation object data.As the weight calculation results are difficult to be manually adjusted,this kind of model is seldom questioned by non-professional viewpoint.To alleviate such doubts,Cherchye(2005;2007)proposed an endogenous weighting method on the basis of DEA,to calculate weights via the performance of sub-indicators of evaluation objects.This method aims at maximizing the comprehensive score of all evaluation objects to calculate the weight,and can provide relatively fair evaluation results that are satisfactory to the evaluation objects and their stakeholders when the consistency of opinion on the importance of indicators is low.However,in practice,Cherchye and Nichey et al.found that the model still exists four theoretical issues,namely,1)Comparability issue;2)Over-flexibility issue(0-1 weight issue);3)Rank reversal issue caused by the change of evaluation object set;4)Multiple solution issue.Among them,the literature research on the first issue is relatively complete,while the corresponding theoretical research results of the other three questions are relatively inadequate.For theoretical problems 2-4,this paper firstly explores the weighting idea and logic of Bo D model from the mathematical perspective,and analyzes the essential properties of Bo D weight.Further,the formation conditions and inhibition methods are explored through mathematical proof.At last,two improved Bo D models,namely Pareto optimal group fuzzy Bo D model(POGF-BOD)and subgroup dominance Bo D(SD-BOD),were proposed by introducing the ideas for improving the rationality,robustness and scientificity of the models of MCDM theory.For issue 2),this paper firstly demonstrates the weight assignment idea and its logic in Bo D model from the mathematical perspective,and puts forward the weight importance calculation criterion based on the Pareto optimization.Then,based on what,the importance value of the sub-indicators for all DMU is given independently,to express the importance opinion of each DMU under the Pareto optimization criterion;Then,fuzzy subgroup idea is used to integrate the importance opinions of DMU index to obtain the endogenous weight boundary criterion.Finally,taking the HDI data of 28 European countries as an example,the robustness of the POGF-BOD model compared with other Bo D models is discussed by means of design experiments.The results show that compared with other directly-improved Bo D models,POGF-BOD model can not only effectively solve the over-flexible issue(including boundary weight),but also maintain relatively stable ranking results when the criteria change.For issue 3),this paper firstly gives a mathematic proof for the core reason of the rank reversal issue is determined,that is,the addition or deletion of DMU will affect the weight assignment by changing the frontier surface,so that the composite indicator value of DMU will be changed in different directions and degrees.Then,in order to solve this problem,based on the information of Bo D weight matrix,this paper uses the idea of pair-wise comparison to form the Bo D pair-wise comparison mechanism(BPCRM),and via which the frontier subgroup(FS)is partitioned.On the basis of the dominance relationship between each FSs,the subgroup dominant Bo D model(SD-BOD)is proposed.Finally,taking the human Development index(HDI)of28 European countries as an example,the change and reverse degree of HDI ranking under the condition of regional addition or deletion are discussed through comparative analysis,and the validity of SD-BOD method is verified.The results show that SD-BOD model can not only effectively suppress the reverse order problem,but also ensure the comparability of scores between DMUs and avoid other Bo D weight defects when grouping successfully.For issue 4),combining with the formula of Bo D model,this paper firstly discusses the essential attribute of the weight multiple solution issue in Bo D,that is,infinite optimal solution phenomenon in linear programming.Then,the causes of this issue are analyzed from the mathematical perspective.Secondly,by analyzing the algorithm ideas of common programming solvers,the expression and forming conditions of Bo D weight multiple solution issue in practice are further demonstrated.Thirdly,taking the augmented Lagrange algorithm as an example,the multi-solution problem of different Bo D models and its influence are discussed.Finally,combined with case analysis,the operational means of avoiding multiple solutions are given.The results show that the improved Bo D model is more stable than other models when the initial value of algorithm operation changes.Meanwhile,for the same operation environment and the same solver,the Bo D model results have unique repeatable display results.