Input-output Efficiency Set Models of Interval Number DEA

Abstract

The system relative Effectiveness evaluation under uncertainty factors is the frontier of DEA Theory, research on DEA model with fuzzy elements can help resolve problems of the uncertainty input-output in systematic evaluation. Li and Yan proposed a new to improve the Efficiency Index of Input-output DEA model. However, such model did not consider situation when input-output are uncertain number . In the practice of the economic system evaluation, due to various restrictions, people often use certain methods (such as prediction, simulation, etc.) to obtain the interval estimate of evaluation index based on their own experience and prior knowledge. In current DEA literatures, L-R Interval DEA (IDEA) model based on partial order theories of L-R fuzzy numbers was proposed, and the relationship between fuzzy DEA efficiency Index and deterministic one was discussed by Zhen and Wu . They also discussed the sufficient condition of decision making units (DMUs) in the L-R type DEA model . Zhou et al. discussed the ideas of the Interval CR model (ICR) based on CR (the basic and first DEA model) , and used a simple extension of BCC model to construct a sorting method for interval input-output DMUs [5, , the discussion from Interval DEA from maximum and minimum limit directions in their algorithm is worth learning, but they did not consider the model when all of the inputs and outputs of DMUs are interval numbers. In summary, the reported literature discussed the DEA Efficiency under the most extreme cases, so the corresponding model does not apply to most case in practice. Therefore, this paper proposed a new interval DEA Efficiency Set model to further study the relative effectiveness of DMUs when inputs and outputs are interval numbers.