A note to TOPSIS method in MADM problems under fuzzy environment

TOPSIS method has been widely used to solve various multiple attribute decision making and multiple criteria decision making problems since Hwang and Yoon first introduced it in 1981. The ranking results of TOPSIS are proved to be relatively convincing in many practical areas. However, in recent research we find that the traditional fuzzy TOPSIS method could not distinguish all of the alternatives in some circumstances. As stated later in this paper, several counter examples in triangular fuzzy number format will be demonstrated, where the fuzzy TOPSIS method fails to give alternatives respective rankings. And the reason for that phenomenon will be further discussed. Then a revised procedure is suggested in order to fully differentiate all of the alternatives. Finally a numerical example is given so as to testify the revised procedure.