Uncertainty Avoider Interval Type II Defuzzification Method

Table 1

32 basic IT2FS words and their defuzzified output obtained by proposed equation (6) and their difference percentage compared to their COG calculated through the KM algorithm.

	UMF	LMF	KM	DMF	Difference
1	[0, 0, 0.14, 1.97, 1]	[0, 0, 0.05, 0.66, 1]	0.47	0.459	0.01
2	[0, 0, 0.14, 1.97,1]	[0, 0, 0.01, 0.13, 1]	0.56	0.693	−0.13
3	[0, 0, 0.26, 2.63, 1]	[0, 0, 0.05, 0.63, 1]	0.63	0.634	0.004
4	[0, 0, 0.36, 2.63, 1]	[0, 0, 0.05, 0.63, 1]	0.64	0.637	0.003
5	[0, 0, 0.64, 2.47, 1]	[0, 0, 0.10, 1.16, 1]	0.66	0.610	0.05
6	[0, 0, 0.64, 2.63, 1]	[0, 0, 0.09, 0.99, 1]	0.67	0.624	0.046
7	[0.59, 1.50, 2.00, 3.41, 1]	[0.79, 1.68, 1.68, 2.21, 0.74]	1.75	1.702	0.048
8	[0.38, 1.50, 2.50, 4.62, 1]	[1.09, 1.83, 1.83, 2.21, 0.53]	2.13	2.101	0.029
9	[0.09, 1.25, 2.50, 4.62, 1]	[1.67, 1.92, 1.92, 2.21, 0.30]	2.19	2.360	−0.17
10	[0.09, 1.50, 3.00, 4.62, 1]	[1.79, 2.28, 2.28, 2.81, 0.40]	2.32	2.347	−0.027
11	[0.59, 2.00, 3.25, 4.41, 1]	[2.29, 2.70, 2.70, 3.21, 0.42]	2.59	2.601	−0.011
12	[0.38, 2.50, 5.00, 7.83, 1]	[2.88, 3.61, 3.61, 4.21, 0.35]	3.90	3.969	−0.069
13	[1.17, 3.50, 5.50, 7.83, 1]	[4.09, 4.65, 4.65, 5.41, 0.40]	4.56	4.605	−0.045
14	[2.59, 4.00, 5.50, 7.62, 1]	[4.29, 4.75, 4.75, 5.21, 0.38]	4.95	5.028	−0.128
15	[2.17, 4.25, 6.00, 7.83, 1]	[4.79, 5.29, 5.29, 6.02, 0.41]	5.13	5.162	−0.032
16	[3.59, 4.75, 5.50, 6.91, 1]	[4.86, 5.03, 5.03, 5.14, 0.27]	5.19	5.231	−0.041
17	[3.59, 4.75, 6.00, 7.41, 1]	[4.79, 5.30, 5.30, 5.71, 0.42]	5.41	5.398	0.012
18	[3.38, 5.50, 7.50, 9.62, 1]	[5.79, 6.50, 6.50, 7.21, 0.41]	6.50	6.500	0.0
19	[4.38, 6.50, 8.00, 9.41, 1]	[6.79, 7.38, 7.38, 8.21, 0.49]	7.16	7.183	−0.023
20	[4.38, 6.50, 8.00, 9.41, 1]	[6.79, 7.38, 7.38, 8.21, 0.49]	7.16	7.183	−0.023
21	[4.38, 6.50, 8.25, 9.62, 1]	[7.19, 7.58, 7.58, 8.21, 0.37]	7.25	7.212	0.038
22	[5.38, 7.50, 8.75, 9.81, 1]	[7.79, 8.22, 8.22, 8.81, 0.45]	7.90	7.865	−0.035
23	[5.38, 7.50, 8.75, 9.83, 1]	[7.69, 8.19, 8.19, 8.81, 0.47]	7.91	7.874	0.036
24	[5.38, 7.50, 8.75, 9.81, 1]	[7.79, 8.30, 8.30, 9.21, 0.53]	8.01	8.062	−0.052
25	[5.38, 7.50, 9.00, 9.81, 1]	[8.29, 8.56, 8.56, 9.21, 0.38]	8.03	7.97	0.06
26	[5.98, 7.75, 8.60, 9.52, 1]	[8.03, 8.36, 8.36, 9.17, 0.57]	8.12	8.186	−0.066
27	[7.37, 9.41, 10, 10, 1]	[8.72, 9.91, 10, 10, 1]	9.30	9.344	−0.044
28	[7.37, 9.82, 10, 10, 1]	[9.74, 9.98, 10, 10, 1]	9.31	9.182	0.128
29	[7.37, 9.59, 10, 10, 1]	[8.95, 9.93, 10, 10, 1]	9.34	9.372	−0.032
30	[7.37, 9.73, 10, 10, 1]	[9.34, 9.95, 10, 10, 1]	9.37	9.369	0.001
31	[7.37, 9.82, 10, 10, 1]	[9.37, 9.95, 10, 10, 1]	9.38	9.368	0.012
32	[8.68, 9.91, 10, 10, 1]	[9.61, 9.97, 10, 10, 1]	9.69	9.693	−0.003
	Percentage of RMS of difference				1.2%