Ranking DMUs by ideal points in the presence of fuzzy and ordinal data
محورهای موضوعی : Applied MathematicsM Izadikhah 1 , Z Aliakbarpoor 2 , H Sharafi 3
1 - Department of Mathematics, College of Science, Arak Branch, Islamic Azad
University, Arak, Iran
2 - Department of Mathematics, College of Science, Arak Branch, Islamic Azad
University, Arak, Iran
3 - Department of Mathematics, Science and Research Branch, Islamic Azad
University, Tehran, Iran
کلید واژه:
چکیده مقاله :
Envelopment Analysis (DEA) is a very e ective method to evaluate the relative eciency of decision-making units (DMUs). DEA models divided all DMUs in two categories: ecient and inecientDMUs, and don't able to discriminant between ecient DMUs. On the other hand, the observedvalues of the input and output data in real-life problems are sometimes imprecise or vague, suchas interval data, ordinal data and fuzzy data. This paper develops a new ranking system under thecondition of constant returns to scale (CRS) in the presence of imprecise data, In other words, inthis paper, we reformulate the conventional ranking method by ideal point as an imprecise dataenvelopment analysis (DEA) problem, and propose a novel method for ranking the DMUs when theinputs and outputs are fuzzy and/or ordinal or vary in intervals. For this purpose we convert alldata into interval data. In order to convert each fuzzy number into interval data we use the nearestweighted interval approximation of fuzzy numbers by applying the weighting function and also weconvert each ordinal data into interval one. By this manner we could convert all data into intervaldata. The numerical example illustrates the process of ranking all the DMUs in the presence of fuzzy,ordinal and interval data.
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