Data Envelopment Analysis Cross Evaluation Method With Fuzzy Information

The society is a complex system, in the actual decision-making activities such as the supplier selection?project investment and the housing location, the available information for decision-makers are often vague because of objective uncertainty or subjective cognitive limitations. These fuzzy information can be represented as linguistic variables?triangular fuzzy numbers. It has always been the research topic that how to make the decision with these information. The traditional DEA (data envelopment analysis) models have been widely applied for actual evaluation because it is a non-parametric method for measuring the relative efficiencies of a homogeneous sets of DMUs (decision making units), but it is based on the assumption that the data are crisp. Therefore, extending the classic DEA models to fuzzy environment is of great theoretical and realistic significance for reflecting the inherent uncertainty in real evaluation problems. Based on basic fuzzy DEA and fuzzy sets theory, this paper studies evaluation methods of DMUs under fuzzy information and then proposed a new cross evaluation method based on relative closeness and intuitionistic fuzzy entropy.This paper concludes three aspects:At first, in order to overcome the drawbacks that the present fuzzy cross evaluation methods remove the fuzziness of fuzzy information at the beginning and care too much about how to be benevolent to other DMUs, we extend the secondary goal model which is based on the relative closeness to the fuzzy environment at first, while considering the distance from the evaluated DMU to the ideal DMU and the anti ideal DMU; At second, in order to make full use of uncertainty of fuzzy information, we convert triangular fuzzy efficiency to intuitionistic fuzzy set, so that we can integrate the fuzzy efficiencies with intuitionistic fuzzy entropy, then ternary directional distance index is used to rank the whole fuzzy efficiencies; At last, the proposed method is applied to measure the citation efficiency of ten management science and system science journals which is identified as the important journals by Management Science Department of National Natural Science Foundation of China. Considering the delay of citation between academic journals, total citations and number of citing journals are interpreted as triangular fuzzy number.After analysis we find that the fuzzy efficiencies measured by the proposed method can get more information compared with exact values, and the order of journals is closed to their actual academic impact. The efficiencies of ten important journals are relatively low and less volatile. The propagation ability among regions?international degree and established time have a significant positive impact on citation efficiency, while the scale have a negative effect, that is to say, the ten journals are decreasing returns to scale at the present stage. The above conclusions indicate that the proposed method is feasible and valid. It takes the fuzziness into account so that it can provide guidance to the decision making problems under the fuzzy information in the future.