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

Abstract

Envelopment Analysis (DEA) is a very e ective method to evaluate the relative e ciency of decision-<br />making units (DMUs). DEA models divided all DMUs in two categories: e cient and ine cient<br />DMUs, and don't able to discriminant between e cient DMUs. On the other hand, the observed<br />values of the input and output data in real-life problems are sometimes imprecise or vague, such<br />as interval data, ordinal data and fuzzy data. This paper develops a new ranking system under the<br />condition of constant returns to scale (CRS) in the presence of imprecise data, In other words, in<br />this paper, we reformulate the conventional ranking method by ideal point as an imprecise data<br />envelopment analysis (DEA) problem, and propose a novel method for ranking the DMUs when the<br />inputs and outputs are fuzzy and/or ordinal or vary in intervals. For this purpose we convert all<br />data into interval data. In order to convert each fuzzy number into interval data we use the nearest<br />weighted interval approximation of fuzzy numbers by applying the weighting function and also we<br />convert each ordinal data into interval one. By this manner we could convert all data into interval<br />data. The numerical example illustrates the process of ranking all the DMUs in the presence of fuzzy,<br />ordinal and interval data.