Identification of Fuzzy Inference Systems by Means of a Multiobjective Opposition-Based Space Search Algorithm

Table 2

Optimal solutions based on training data and testing data (NO_𝑥).

(a) Based on the LSM

Number of solutions						Objective values
	Selected input variables	Number of MFs	Type	PI	E_PI	E	H	N
1	1,4, 5	2, 2, 2	3	0.042	0.104	0.073	8	80
2	1, 4, 5	2, 2, 2	4	0.087	0.197	0.142	8	56
3	1, 4, 5	2, 2, 2	2	0.371	0.412	0.392	8	32
4	1, 4	2, 2	3	1.016	0.810	0.913	4	24
5	1, 2, 4, 5	2, 2, 2, 2	1	2.823	6.997	4.910	16	16
6	4, 5	2, 2	4	5.525	8.527	7.026	4	16
7	4, 5	2, 2	2	6.029	10.41	8.217	4	12
8	2, 4, 5	2, 2, 2	1	6.290	13.74	10.02	8	8
9	4, 5	2, 2	1	13.60	20.23	16.92	4	4

(b) Based on the WLSM

Number of solutions						Objective values
	Selected input variables	Number of MFs	Type	PI	E_PI	E	H	N
1	1, 2, 3, 4, 5	2, 2, 2, 2, 2	4	0.00085	0.00042	0.00064	32	512
2	1, 2, 4, 5	2, 2, 2, 2	4	0.022	0.036	0.029	16	176
3	1, 4, 5	2, 2, 2	4	0.096	0.14	0.12	8	56
4	1, 3, 5	2, 2, 2	2	3.11	2.07	2.59	8	32
5	4, 5	2, 2	4	5.69	6.80	6.24	4	16
6	4, 5	2, 2	2	7.55	9.20	8.38	4	12
7	2, 4, 5	2, 2, 2	1	39.45	32.55	36.01	8	8
8	2, 5	2, 2	1	57.86	58.86	58.36	4	4