Interval Efficiency of Two-stage Network DEA Model with Imprecise Data

Abstract

The conventional data envelopment analysis (DEA) models assume that the data of inputs and outputs are exactly known. However, inputs and outputs can be in ordinal relations or bounded data, or fuzzy data, which have been studied under the DEA approach by using fuzzy for calculating interval efficiency results. The current paper studies the situation when imprecise data is incorporated into the two-stage network DEA model, and construct new models to obtain the lower and upper bounds of the interval efficiency scores. Unlike the fuzzy number-based models, our proposed approach is based on DEA-like linear models. This paper shows that DEA optimality results can always be achieved at the input and output bounds, while can not be achieved at the upper or lower bonds of intermediate variables. We apply the proposed models to evaluate a set of life insurance companies in Taiwan for illustrating the use of our models and the differences of its results from that of existing fuzzy number-based models.