Ranking DMUs by ideal points in the presence of fuzzy and ordinal data

Envelopment Analysis (DEA) is a very effective method to evaluate the relative efficiency of decisionmaking units (DMUs). DEA models divided all DMUs in two categories: efficient and inefficient DMUs, and don’t able to discriminant between efficient DMUs. On the other hand, the observed values of the input and output data in real-life problems are sometimes imprecise or vague, such as interval data, ordinal data and fuzzy data. This paper develops a new ranking system under the condition of constant returns to scale (CRS) in the presence of imprecise data, In other words, in this paper, we reformulate the conventional ranking method by ideal point as an imprecise data envelopment analysis (DEA) problem, and propose a novel method for ranking 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 also we convert each ordinal data into interval one. By this manner we could convert all data into interval data. The numerical example illustrates the process of ranking all the DMUs in the presence of fuzzy, ordinal and interval data.