Extension of the TOPSIS Considering the Dispersion among the Criteria of Each Alternative

TOPSIS is located in compensatory decision-making methods. The basic principle is that the chosen alternative should have the shortest distance from the positive ideal solution and the longest distance from the negative ideal solution. The existence of incremental and decreasing uniform trend in positive and negative criteria is one of the TOPSIS characteristics in determining positive and negative ideal points. While the utility assigned to the decision maker after a certain level in each criterion will be less tangible. Therefore, in the ranking of alternatives in addition to the value of each alternative in each indicator, the balance among criteria of each alternative should be considered so the alternative that has an appropriate place in an important indicator, but does not have an appropriate place in other criteria, not to be the first chance for selecting. For this purpose, in this paper by adding virtual dimension to the decision matrix that comes from the deviations among criteria of each alternative, we have tried to compensate the mentioned weakness. To evaluate the proposed method, three different examples are presented. Thus, each of the three provided examples, solved by proposed method, TOPSIS, VIKOR, Deng and SAW and then by using the Spearman correlation coefficient the number of significant correlation relationships between the proposed method and TOPSIS with the other three methods were compared. Then, the rating similarity percentage of the proposed method and TOPSIS were compared with VIKOR, Deng and SAW.