Uncertainty in Interval Type-2 Fuzzy Systems

Table 2

Basic IT2FS words: defuzzified output obtained by using the proposed method and difference percentage compared to the COG calculated by the KM algorithm.

	UMF	LMF	KM	Proposed	ARS	% E
(1)	[0, 0, 0.14, 1.97, 1]	[0, 0, 0.05, 0.66, 1]	0.47	0.49	0.27	1.0
(2)	[0, 0, 0.14, 1.97, 1]	[0, 0, 0.01, 0.13, 1]	0.56	0.61	0.96	2.5
(3)	[0, 0, 0.26, 2.63, 1]	[0, 0, 0.05, 0.63, 1]	0.63	0.66	0.47	1.1
(4)	[0, 0, 0.36, 2.63, 1]	[0, 0, 0.05, 0.63, 1]	0.64	0.67	0.49	1.1
(5)	[0, 0, 0.64, 2.47, 1]	[0, 0, 0.10, 1.16, 1]	0.66	0.66	0.24	0.0
(6)	[0, 0, 0.64, 2.63, 1]	[0, 0, 0.09, 0.99, 1]	0.67	0.68	0.29	0.3
(7)	[0.59, 1.50, 2.00, 3.41, 1]	[0.79, 1.68, 1.68, 2.21, 0.74]	1.75	1.74	0.45	0.3
(8)	[0.38, 1.50, 2.50, 4.62, 1]	[1.09, 1.83, 1.83, 2.21, 0.53]	2.13	2.11	0.75	0.5
(9)	[0.09, 1.25, 2.50, 4.62, 1]	[1.67, 1.92, 1.92, 2.21, 0.30]	2.19	2.28	0.99	0.2
(10)	[0.09, 1.50, 3.00, 4.62, 1]	[1.79, 2.28, 2.28, 2.81, 0.40]	2.32	2.33	0.91	0.2
(11)	[0.59, 2.00, 3.25, 4.41, 1]	[2.29, 2.70, 2.70, 3.21, 0.42]	2.59	2.59	0.93	0.0
(12)	[0.38, 2.50, 5.00, 7.83, 1]	[2.88, 3.61, 3.61, 4.21, 0.35]	3.90	3.94	0.93	0.5
(13)	[1.17, 3.50, 5.50, 7.83, 1]	[4.09, 4.65, 4.65, 5.41, 0.40]	4.56	4.57	0.95	0.1
(14)	[2.59, 4.00, 5.50, 7.62, 1]	[4.29, 4.75, 4.75, 5.21, 0.38]	4.95	4.98	0.89	0.6
(15)	[2.17, 4.25, 6.00, 7.83, 1]	[4.79, 5.29, 5.29, 6.02, 0.41]	5.13	5.13	0.98	0.0
(16)	[3.59, 4.75, 5.50, 6.91, 1]	[4.86, 5.03, 5.03, 5.14, 0.27]	5.19	5.21	0.90	0.6
(17)	[3.59, 4.75, 6.00, 7.41, 1]	[4.79, 5.30, 5.30, 5.71, 0.42]	5.41	5.41	0.99	0.0
(18)	[3.38, 5.50, 7.50, 9.62, 1]	[5.79, 6.50, 6.50, 7.21, 0.41]	6.50	6.50	0.82	0.0
(19)	[4.38, 6.50, 8.00, 9.41, 1]	[6.79, 7.38, 7.38, 8.21, 0.49]	7.16	7.15	0.82	0.2
(20)	[4.38, 6.50, 8.00, 9.41, 1]	[6.79, 7.38, 7.38, 8.21, 0.49]	7.16	7.15	0.90	0.2
(21)	[4.38, 6.50, 8.25, 9.62, 1]	[7.19, 7.58, 7.58, 8.21, 0.37]	7.25	7.21	0.86	0.7
(22)	[5.38, 7.50, 8.75, 9.81, 1]	[7.79, 8.22, 8.22, 8.81, 0.45]	7.90	7.87	0.86	0.6
(23)	[5.38, 7.50, 8.75, 9.83, 1]	[7.69, 8.19, 8.19, 8.81, 0.47]	7.91	7.88	0.45	0.6
(24)	[5.38, 7.50, 8.75, 9.81, 1]	[7.79, 8.30, 8.30, 9.21, 0.53]	8.01	8.01	0.65	0.0
(25)	[5.38, 7.50, 9.00, 9.81, 1]	[8.29, 8.56, 8.56, 9.21, 0.38]	8.03	7.97	0.90	1.3
(26)	[5.98, 7.75, 8.60, 9.52, 1]	[8.03, 8.36, 8.36, 9.17, 0.57]	8.12	8.12	0.65	0.0
(27)	[7.37, 9.41, 10, 10, 1]	[8.72, 9.91, 10, 10, 1]	9.30	9.31	0.24	0.3
(28)	[7.37, 9.82, 10, 10, 1]	[9.74, 9.98, 10, 10, 1]	9.31	9.23	0.28	3.0
(29)	[7.37, 9.59, 10, 10, 1]	[8.95, 9.93, 10, 10, 1]	9.34	9.35	0.28	0.3
(30)	[7.37, 9.73, 10, 10, 1]	[9.34, 9.95, 10, 10, 1]	9.37	9.34	0.47	1.1
(31)	[7.37, 9.82, 10, 10, 1]	[9.37, 9.95, 10, 10, 1]	9.38	9.34	0.48	1.5
(32)	[8.68, 9.91, 10, 10, 1]	[9.61, 9.97, 10, 10, 1]	9.69	9.67	0.36	1.5

Difference (error) RMS% compared to KM 0.95%.