The Research And Application Of Index Preference DEA Problem

In recent decades,the DEA model has become one of the fastest-growing methods for system evaluation with its unique characteristics and advantages.The DEA model has no restrictions on the weight of the indicators in the decision-making process,and the most favorable weights for the evaluated decision-making units are selected,which are not affected by subjective factors.Although this evaluation method is objective that it completely ignores the difference in importance between indicators,but it is difficult to ensure the rationality of the evaluation results.In view of this,the paper proposes the index preference DEA model and deeply studies the nature of its solution.Firstly,the index preference DEA model and its dual model are constructed.Based on the C~2R model,according to the difference that the importance of objective existence between indicators and the preference of decision makers,the order of indicators'importance is given,and the corresponding weight constraint conditions are obtained;then the DEA model of index preference is constructed.The decision variables,constraints and objective functions are analyzed,so the dual model of the index preference DEA model is constructed.At the same time,the definition of the validity of the index preference DEA model is given.The relevance of the index preference DEA model and its dual model is studied,and the existence of the solution is discussed.The practicality of the index preference DEA model is verified by an example.Secondly,the DEA model of index preference based on the Archimedes'infinitesimal quantity and its dual model are constructed.The introduction of Archimedes infinitesimal quantity makes each indicator plays a corresponding role,which makes up for the defects of the indicator preference DEA model in the evaluation process.The comparison between the calculation results of the example and the data from the index preference DEA model is carried out to verify the rationality of the DEA based on the Archimedes infinitesimal indicator.Finally,the established index preference OC~2R model and the Archimedes'infinitesimal OC~2R model are applied to the comprehensive performance evaluation of universities,and the corresponding evaluation results are obtained respectively.By comparing with the C~2R model evaluation results,the rationality and practicability of the research results are verified.