| Summary: | Data envelopment analysis (DEA) is a model for evaluating the effectiveness of relative effectiveness of decision-making units with multiple input and output data based on non-parametric modeling using mathematical programming (including linear programming, multi-parameter programming, stochastic programming, etc.). Due to the complexity of real life, sometimes it is hard to get the exact value of the input and output data directly. The fuzzy DEA (FDEA) proposed to solve this problem well and is widely used in practice. However, the data of FDEA have certain subjectivity, and in addition, some indicators cannot be quantified intuitively. Owing to the complexity of society, there are often some causal relationships in the indicator system. As a method of combining uncertainty and graph theory for uncertainty reasoning, Bayesian network (BN) can effectively deal with the causal chain problem existing in the index and discover the potential relationship between data. The BN is often used to process accurate numerical information and does not handle uncertain information with ambiguity favorably. In order to solve the above issue, the interval-valued intuitionistic fuzzy number (IVIFN) is introduced into the BN to construct the interval-valued intuitionistic fuzzy BN (IVIFBN). Then, based on the index data obtained by the IVIFBN, the crossover efficiency is proposed, and the super efficiency interval FDEA (SEIFDEA) model is constructed. According to the different optimisms of the decision makers, the Hurwitz decision criterion is introduced for sorting. In addition, the model is applied to the performance evaluation system of logistics enterprises. Compared with the traditional DEA model, the validity and superiority of the model in fuzzy environment are verified.
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