Ranking Alternatives in Multi-Criteria Decision Analysis using Common Weights Based on Ideal and Anti-ideal Frontiers

One of the most important issues in multi-criteria decision analysis (MCDA) is to determine the weights of criteria so that all alternatives can be compared based on the collective performance of criteria. In this paper, one of popular methods in data envelopment analysis (DEA) known as common weights (CWs) is used to determine the weights in MCDA. Two frontiers named ideal and anti-ideal frontiers, instead of ideal and anti-ideal alternatives, are defined based on two new proposed CWs models. Ideal and antiideal frontiers are more flexible than that of alternatives. According to the optimal solutions of these two models, the distances of an alternative from the ideal and anti-ideal frontiers are derived. Then, a relative distance is introduced to measure the value of each alternative. The suggested models are linear and despite weight restrictions are feasible. An example is presented for explaining the method and for comparing to the existing literature.

• Saber Saati Mohtadi
• Ali Payan
• Azizallah Kord

• Anti-ideal frontier
• Common weights (CWs)
• Ideal frontier
• Multi-criteria decision analysis (MCDA)

[1] J. Figueira, S. Greco, and M. Ehrgott, Multiple Criteria Decision
Analysis: State of the Art Surveys. Springer, 2005.
[2] Y. J. Lai, T. Y. Liu, and C. L. Hwang, "TOPSIS for MCDM," European
Journal of Operational Research, vol. 76, pp. 486-500, 1994.
[3] T. L. Saaty, "A scaling method for priorities in hierarchical structures,"
Journal of mathematical psychology, vol. 15, pp. 234-281, 1977.
[4] C. A. K. Lovell, and J. T. Pastor, "Radial DEA models without inputs or
without outputs," European Journal of Operational Research, vol. 118,
pp. 45-51, 1999.
[5] C. Kao, "Weight determination for consistently ranking alternatives in
multiple criteria decision analysis," Applied Mathematical Modelling,
vol. 34, pp. 1779-1787, 2010.
[6] A. Charnes, W. W. Cooper, and E. Rhodes, "Measuring the efficiency
of decision making units," European Journal of Operations Research,
vol. 2, pp. 429-444, 1978.
[7] S. Saati, "Determining a common set of weights in DEA by solving a
linear programming," Journal of Industrial Engineering International,
vol. 4, pp. 51-56, 2008.