An Extended Normal distribution on Fuzzy Stochastic Data Envelopment Analysis

Data Envelopment Analysis (DEA) is a widely used technique for measuring the relative efficiencies of Decision Making Units (DMUs) with multiple inputs and multiple outputs. However, in real-world problems, the observed values of the input and output data are often vague or random. Indeed, Decision Makers (DMs) may encounter a hybrid uncertain environment where fuzziness and randomness coexist in a problem. This paper introduces a normal distribution with fuzzy component. The proposed distribution interprets a class of fuzzy random variables. The extensions to the fuzzy-stochastic environment sometimes may be laid to disregard some of the properties in DEA models such linearity and feasibility. In this way, we apply an extended normal distribution with a modified fuzzy ranking method on a new version of CCR-DEA model.

Keywords:

Data envelopment analysis , Fuzzy random variable , Normal distribution , Ranking function