A direct interval extension of TOPSIS method

The TOPSIS method is a technique for order preference by similarity to ideal solution. This technique currently is one of the most popular methods for Multiple Criteria Decision Making (MCDM). The TOPSIS method was primary developed for dealing with only real-valued data. In many cases, it is hard to present precisely the exact ratings of alternatives with respect to local criteria and as a result these ratings are considered as intervals. There are some papers devoted to the interval extensions of TOPSIS method, but these extensions are based on different heuristic approaches to definition of positive and negative ideal solutions. These ideal solutions are presented by real values or intervals, which are not attainable in a decision matrix. Since this is in contradiction with basics of classical TOPSIS method, in this paper we propose a new direct approach to interval extension of TOPSIS method which is free of heuristic assumptions and limitations of known methods. Using numerical examples we show that “direct interval extension of TOPSIS method” may provide the final ranking of alternatives which is substantially different from the results obtained using known methods.

► In the known approaches to the interval extension of TOPSIS method ideal solutions are presented by real values or intervals, which are not attainable in a decision matrix.
► In our approach the ideal solutions are presented by intervals, which are attainable in a decision matrix.
► To solve our problem, we propose a new method for interval comparison.
► Using numerical examples, we show that “direct interval extension of TOPSIS method” may provide the final ranking of alternatives which is substantially different from the results obtained using known methods.