Direct interval extension of TOPSIS method

The technique for order preference by similarity to ideal solution (TOPSIS) currently is one of most popular methods for Multiple criteria decision making (MCDM).This technique was primary developed for dealing with only real-valued data. In some cases, determining precisely the exact values of local criteria is difficult and as a result their values are considered as intervals. There are several papers devoted to interval extensions of TOPSIS in the literature, but these extensions are not completed as ideal solutions are presented by real values, not by intervals. In this report, we show that these extensions may lead to the wrong results especially in the case of intersection of some intervals representing the values of criteria. Therefore, we propose a new direct approach to interval extension of TOPSIS method which is free of limitations of known methods.