Revisiting the Interval and Fuzzy TOPSIS Methods: Is Euclidean Distance a Suitable Tool to Measure the Differences between Fuzzy Numbers?

Euclidean distance (ED) calculates the between n-coordinate points that n equals dimension of space these are located. Some studies extended its application to measure difference fuzzy numbers (FNs).This study shows this extension is not logical because although an point and FN denoted same, they conceptually different. An defined by components; however, equal where This illustrates misapplication ED FNs does necessarily reflect their difference. We also revisit triangular trapezoidal TOPSIS methods avoid misapplication. For purpose, we first defuzzify using center gravity (COG) method then apply crisp values. use example illustrate existing assign inaccurate weights alternatives may even rank them incorrectly.