A novel improvement on rank reversal in TOPSIS based on the efficacy coefficient method

Abstract

Some papers present a simple and intuitive method for eliminating rank reversal in TOPSIS by replacing the relative ideal solution with the absolute ideal solution. Unfortunately, this method has some defects, because it creates new constraints on the initial data. Consequently, it will still result in rank reversal. However, these new constraints are neglected in the present studies. In this paper, the efficacy coefficient method is introduced to deal with these problems. Firstly, the merits and drawbacks of the absolute ideal solution are presented. Secondly, the efficacy coefficient method is used to restructure the initial data in order to eliminate these new constraints. Thirdly, it is proved that selecting a different preference weight coefficient in the efficacy coefficient method does not affect the relative rank, and can increase the discrimination degree of alternatives. Finally, based on an illustrative example, the results show that the novel improved method is valid and stable.