Fuzzy Data Envelopment Analysis with Ordinal and Interval Data

Abstract

In this paper, we reformulate the conventional DEA models as an imprecise DEA problem and propose a novel method for evaluating the DMUs when the inputs and outputs are fuzzy and/or ordinal or vary in intervals. For this purpose, we convert all data into interval data. In order to convert each fuzzy number into interval data, we use the nearest weighted interval approximation of fuzzy numbers by applying the weighting function, and we convert each ordinal data into interval one. In this manner, we could convert all data into interval data. The presented models determine the interval efficiencies for DMUs. To rank DMUs based on their associated interval efficiencies, we first apply the Ω-index that is developed for ranking of interval numbers. Then, by introducing an ideal DMU, we rank efficient DMUs to present a complete ranking. Finally, we use one example to illustrate the process and one real application in health care to show the usefulness of the proposed approach. For this evaluation, we consider interval, ordinal, and fuzzy data alongside the precise data to evaluate 38 hospitals selected by OIG. The results reveal the capabilities of the presented method to deal with the imprecise data.