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

Table 3

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

(a) Based on LSM

Number of solutions							Objective values
	Selected input variables	Number of MFs	Type	PI	V_PI	E_PI	E	H	N
1	1, 4, 5	2, 2, 2	3	0.014	0.044	7.046	0.029	8	80
2	1, 4, 5	2, 2, 2	4	0.053	0.062	146.31	0.057	8	56
3	1, 4, 5	2, 2, 2	2	0.091	0.118	117.79	0.104	8	32
4	1, 4	2, 2	3	1.149	0.447	3.503	0.798	4	24
5	4, 5	2, 2	4	5.269	5.409	16.40	5.339	4	16
6	4, 5	2, 2	2	5.985	5.789	21.94	5.887	4	12
7	1, 4, 5	2, 2, 2	1	9.097	8.655	15.80	8.876	8	8
8	4, 5	2, 2	1	14.10	18.95	20.64	16.52	4	4

(b) Based on WLSM

Number of solutions							Objective values
	Selected input variables	Number of MFs	Type	PI	V_PI	E_PI	E	H	N
1	1, 2, 3, 4, 5	2, 2, 2, 2, 2	4	0.00068	0.00062	0.0000074	0.00065	32	512
2	1, 3, 4, 5	2, 2, 2, 2	4	0.0086	0.0068	0.0804	0.00765	16	176
3	1, 4, 5	2, 2, 2, 2, 2	4	0.097	0.122	0.135	0.109	8	56
4	1, 3, 5	2, 2, 2, 2	2	2.55	0.596	2.949	1.572	8	32
5	1, 4	2, 2	4	5.88	1.456	3.419	3.667	4	16
6	4, 5	2, 2	2	7.51	5.255	12.39	6.383	4	12
7	2, 4, 5	2, 2, 2	1	39.53	38.74	19.03	3.914	8	8
8	4, 5	2, 2	1	52.44	40.92	39.90	4.668	4	4