Two-stage logarithmic goal programming (TLGP) is one of the weighting technologies from fuzzy comparison matrices. But, it only present the interval weights at all alphacuts under each criterion when usage of the TLGP. In this paper, we improve this limitation of TLGP using an proposed index. Finally, the two real illustrative examples in literature are considered to show the verification of the proposed index. Manuscript profile

The technique for order of preference by similarity to ideal solution (TOPSIS) is a method based on the ideal solutions in which the most desirable alternative should have the shortest distance from positive ideal solution and the longest distance from negative ideal solution. Depending on type of evaluations or method of ranking, different approaches have been proposing to calculate distances in the TOPSIS method. In a recent paper, Dymova et al. (2015) extended the TOPSIS approach using interval type 2 fuzzy sets (IT2FSs) in which distances were calculated using alpha cuts. When investigating their paper, we found out that the extended method has some drawbacks such that it leads to the incorrect calculations and results when solving an IT2FSs-based multi-criteria decision making (MCDM) problem. In this note, the corrected version of extended TOPSIS method is being presented to eliminate its limitations. In order to show effectiveness and possibility of the proposed approach, it is also implemented in two illustrative examples and one case study. The results have showed that the optimal alternative obtained by the corrected TOPSIS approach has the similar rank to the others, whereas it is different from the results of existing TOPSIS approach. Manuscript profile