Study Of DEA Cross-efficiency Evaluation Based On Uncertain Information

Personnel assessment,scientific research evaluation,project evaluation,medal performance,performance evaluation of regional energy economy are important problems in management decision-making,these evaluated homogeneous unit are referred to as “decision units”.Evaluation work is hard to precede when there are multiple inputs and multiple outputs index in evaluation system,and complex or unknown relations between input and output indicators.Data envelopment analysis(DEA)as a non-parametric data driven approach and it is able to handle multiple index data and does not need to obtain clear functional form.It is because of the strong objectivity advantage of DEA,the method based on DEA to evaluate decision making units in theory and application research made a lot of progress.For classic DEA method,is generally believed that there are some defects,such as only divided evaluated decision making units into effective ones and ineffective ones,and it can't further rank for decision making units;Classic self-evaluation system will improve the weights of evaluation indicators of benefit itself and ignore ones against their own evaluation,which resulted in the problem of high efficiency value of evaluation.Aiming at these defects,DEA were research further and produced some new theories and methods.Cross-efficiency method is the typical representative of these methods and is one of the DEA ranking important methods.Cross-efficiency method effectively combines the self-assessment and peer-assessment system,it not only can give completely sort to all decision making units,but also can effectively solve the problems of the partial extreme weights so as to avoid high efficiency evaluation phenomenon.But cross-efficiency method still exists some shortages,such as still often there are a lot of solutions of the weights of cross-efficiency so that resulted in bigger cross-efficiency value randomness,and to facilitate the processing often only a set of solutions selected,resulting in a large number of useful information to ignore;Existing cross-efficiency methods rarely considered competition,cooperation even coexist among decision making units,at the same time it is hard to get valuable information to improve the shortage of their own,this made stability and practicability of this method was serious influenced;At the same time,in the actual problem,due to the influence of the randomness of economic phenomenon and economic law itself,and the measurement error and data noise limit,or in order not to lose some important information,all these problems make the efficiencies of decision making units scores' can not be accurately measured.Therefore,under the condition of uncertain system,efficiency evaluation has been at the forefront of DEA theory research and has important theoretical and practical significance.In this paper,on the basis of existing research,in view of the cross-efficiency method less consider weight uncertainty,competition and cooperation among decision-making units,compromise,fair of decision-making,and so on and so forth,integrated application of information entropy,the advantage relationship in rough set,mutual information,VIKOR,game theory,and other research tools in the relationship of cross-efficiency of decision making units,the gainning of efficiency score weight,the efficiency score attribute empowerment,efficiency score assembled,score ranking,etc launched a series of studies.This paper including eight chapters,the main research results are as follows:(1)In view of weight nonuniqueness problem in the peer-evaluate phase of decision-making unit,game theory and the singular index are put forward and introduced into the cross-efficiency method to determine the weights and efficiency score.First of all,through the mutual information size to determine competition or cooperation relation of the decision making units.Based on game theory,decision making units will show different preference in the phase of DEA peer-evalution,and will take different strategies allies and opponents,more over the input and output data of similar units with similar weight strategies.At the same time,to be evaluators,decision makers will consider is how to fully accept its performance,and can be reflect democratic ideas widely.Since the self-assesment result is consistent with their colleagues,the final evaluation results more reliable.Finally on the basis of considering competition and cooperation of the units to calculate mutual weight and efficiency score to obtain average competition-cooperation cross-efficiency.Chose 2007-2014 data of 16 banks of China,constructing evaluation index.The results show because of the same characteristics of state-owned Banks,so within the same group,and comparing the results among relevant methods,proved the assessment results widely acception of the proposed method.(2)For the problems of simple average gathered on the cross-efficiency of decision making units,considering the subjective weights of cross-efficiency aggregation and stability,acceptability of ranking result,introducing dominance relation to classify decision making units according efficiency score for decision making units,and proposed DEA efficiency aggregate model based on rough set theory and the ordinal number type directed distance index.DEA cross-efficiency score is the eventually gathering result between self-assessment and peer-assessment of the decision making units,so usually to get the weight of each decision-making unit,while existing weight measure method are easily affected by subjective factors,the evaluation results are not easily accepted by decision making units.Attribute reduction based on dominance relation can extract the important characteristic(evaluation unit)from the decision table constructed by decision unit first of all,while maintaining the precondition of classification ability unchanged of the self-assesment and peer-assesment cross-efficiency information system,remove the irrelevant or unimportant attributes so as to implement on the key attributes to ranking decision making units,which made the sorting result is more stable and easy to accept.Further ordinal distances index was put forward and proved its related properties,and so implements the non-critical attributes ranking of decision making units.Based on 16 banks data of China prove the effectiveness of the method.(3)In view of the preference in cross-efficiency assembled and efficiency score incomplete information characteristicsin of single value cross-efficiency system,so extended the single value efficiency to interval number of decision making units score.Because efficiency values based on the classical benevolent and aggressive cross-efficiency are based on crisp data,but the results of the two programming cannot guarantee the consistency of the sort and often unable to choose,therefore,based on the above two kinds of programming to build the interval cross-efficiency score model.At the same time,considering the communication,conflict and policymakers mentality can affect the value of information in the interval cross-efficiency,so according to VIKOR method combined with attitude indicator mechanism to ranking and selecting.Chose 16 Joint-stock banks' data of China in 2007-2014,researched the bank performance sorting of interval cross-efficiency and selecting mechanism,proved the effectiveness of the proposed method.Results show that the performance of the Joint-stock Banks are superior to State-owned Banks commonly,and the financial crisis make the efficiency gap become larger of different kinds banks.After 2008,the efficiency of all banks especially Joint-stock Banks turned for the better gradually along with the country's economic stimulus policy.(4)For the incomplete information problem in cross-efficiency interval value information system,constructed ternary efficiency interval model and based on dominance index and ternary directional distance index realized efficiency scores sorting.In order to be able to reflect upper and lower bounds of decision makers extreme assessment cases,but also efficiency evaluation of neutrality.Therefore,to get the efficiency range on the basis of benevolent and aggressive cross-efficiency model,joined the neutral cross-efficiency model,and made interval cross-efficiency further extended to ternary efficiency interval,and use adominance relationship to sort decision making units by comprehensive dominance of the;Ternary directional distance index model is also put forward and properties of the model proved,all decision making units are ranked based on the index.At last,the validity of model is proved by example.Based on the example of Chinese 16 Banks proved the effectiveness of the method.(5)In view of the cross-efficiency model had problems which often based on the optimal frontier and ignored the worst frontier,so put forward “double frontiers” of cross-efficiency model from the angle of the two front surfaces.Due to efficiency value is relatively one-sided evaluated from the single frontier of unit lead to ranking results may have bigger difference,thus it is difficult to gain recognition among the decisiom making units.Therefore,under the optimal and worst frontier to calculate CCR,aggressive and benevolent efficiency to construct the comprehensive efficiency of six models,and based on dominance relation of the rough set method and the ordinal directional number index to sort decision making units of comprehensive efficiency score information system.At last,the validity of model is proved by example.(6)For the problem of cross-efficiency model only considered radial scores and ignored the the non-radial slacks,at the same time considered the disposability of unexpected output in the energy and environment efficiency assessment based on DEA,put forward EBM model which combining radial and non-radial characters based on grey relational model.Due to non-radial model has higher distinguish power and does not consider proportion changes to input or output,and slack variable can gave improved direction and degree of decision making units more accurately.Therefore,combined radial and non-radial features of DEA model,thus grey relation can accord change of input to measure radial and non-radial characteristics of model.Based on typical grey correlation degree and new defined grey correlation degree to connecte two models,and weak disposbility more consistent with the actual condition.At last,take example of 29 provinces of energy efficiency and environment evaluation of China test the validity of model.This article research provideed a new research perspective and solutions for the calculation of the cross-efficiency and decision making units ranking under uncertain information and environment,this enriched and developed the cross-efficiency ranking decision theory and method.