Fuzzy Data Envelopment Analysis for Fuzzy Overall Effectiveness

Aggregating measure scores is an important step in multiple criteria decision-making, determining the overall effectiveness from dissimilar measures. One of the most popular aggregating methods is Simple Additive Weighting (SAW), which assigns weights to measures based on subjective preference information, and sum weighted scores up. The quality of overall score is highly dependent on the quality of elicited preference information. Data Envelopment Analysis (DEA) technique for output-only model is another option to determine the overall effectiveness based on quantitative data. However, the original DEA model is limited to crisp data. Hence, this paper generalizes the crisp DEA model to fuzzy model. The solution procedures consist of decomposing fuzzy scores to levels of α -cuts, inserting α -cuts to crisp DEA model to estimate the α -cuts of fuzzy overall score by mathematical programming, and then constructing the fuzzy overall score membership function by derived α -cuts. Finally, there is a numerical example illustrating the proposed model for a set of hypothetical fuzzy data set, which is similar to performance evaluation with fuzzy data. The proposed model is effective for applications that need aggregate fuzzy data from different measures without preference information. Key-Words: DEA, data envelopment analysis, fuzzy, multiple criteria decision-making