A note on group decision-making based on concepts of ideal and anti-ideal points in a fuzzy environment

In a very recent paper by Kuo et al. [M.S. Kuo, G.H. Tzeng, W.C. Huang, Group decision-making based on concepts of ideal and anti-ideal points in a fuzzy environment, Mathematical and Computer Modelling 45 (3–4) (2007) 324–339], a fuzzy multicriteria decision analysis method based on the concepts of ideal and anti-ideal points was presented. This note illustrates with a numerical example that the method presented by Kuo et al. is not correct and can evaluate more than one decision alternative as the best even if they are not Pareto optimal at all. The fundamental reason for this is because the closeness coefficient values adopted by the authors do not reflect the superiority or inferiority of decision alternatives and cannot be used for ranking purpose. Corrections to their method are therefore suggested.