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

Table 1

Comparing TrFNs using the ED and the COG methods.

Set	TrFNs		Euclidean distance	Centroid		C(M) − C(N)
	TrFN M	TrFN N		C(M)	C(N)
1	(1, 3, 5, 7)	(2, 4, 6, 8)	1	4	5	−1
2	(1, 3, 5, 8)	(2, 4, 6, 7)	1	4.296	4.714	−0.418
3	(1, 3, 6, 7)	(2, 4, 5, 8)	1	4.222	4.810	−0.588
4	(1, 4, 5, 7)	(2, 3, 6, 8)	1	4.19	4.778	−0.588
5	(2, 3, 5, 7)	(1, 4, 6, 8)	1	4.286	4.704	−0.418
6	(2, 3, 5, 8)	(1, 4, 6, 7)	1	4.583	4.417	0.166
7	(2, 3, 6, 7)	(1, 4, 5, 8)	1	4.5	4.5	0
8	(2, 4, 5, 7)	(1, 3, 6, 8)	1	4.5	4.5	0