On fuzzy TOPSIS method based on alpha level sets

In a paper by Wang and Elhag [Ying-Ming Wang and Taha M.S. Elhag, Fuzzy TOPSIS method based on alpha level sets with an application to bridge risk assessment, Expert Systems with Applications 31 (2006) 309-319], a fuzzy TOPSIS method on alpha level sets was introduced and a nonlinear programming solution procedure was presented. It is found that in the case that the fuzzy decision matrix is of the same dimension and needs no normalization, a pair of nonlinear programming models is incorrect for computing the relative closeness provided by the above paper. In this paper we present a correct pair of nonlinear programming models in the case of the same dimension and justify it from the viewpoint of monotonic function. An illustrated example for selecting the best supplier of metallic components used in a variety of transmission cables has been examined using the proposed programming models to fuzzy TOPSIS method and demonstrated its superiorities, rationalities.