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

Theory of Approximation and Applications

مقاله 2، دوره 9، شماره 2، اسفند 2015، صفحه 13-36   

نوع مقاله: Research Articles

نویسندگان

M Izadikhah^{* 1}؛ Z Aliakbarpoor¹؛ H Sharafi²

¹Department of Mathematics, College of Science, Arak Branch, Islamic Azad University, Arak, Iran

²Department of Mathematics, Science and Research Branch, Islamic Azad University, Tehran, Iran

چکیده

Envelopment Analysis (DEA) is a very eective method to evaluate the relative eciency of decision-
making units (DMUs). DEA models divided all DMUs in two categories: ecient and inecient
DMUs, and don't able to discriminant between ecient 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.

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