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

Table 5

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

(a) Based on the LSM

Number of solutions						Objective values
	Selected input variables	Number of MFs	Type	PI	E_PI	E	H	N
1	4, 5, 6	2, 2, 2	2	2.535	2.372	2.454	8	32
2	4, 6	2, 2	2	2.792	2.718	2.755	4	12
3	4, 5, 6	2, 2, 2	1	2.893	2.585	2.739	8	8
4	4, 6	2, 2	1	2.982	2.728	2.855	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, 5, 6, 7	2, 2, 2, 2, 2, 2	4	0.646	0.245	0.445	64	1408
2	3, 4, 5, 6, 7	2, 2, 2, 2, 2	4	1.351	0.683	1.017	32	512
3	2, 5, 6, 7	2, 2, 2, 2	4	1.551	0.940	1.246	16	176
4	1, 4, 5, 6	2, 2, 2, 2	2	2.266	1.689	1.977	16	80
5	2, 5, 6	2, 2, 2	4	2.396	1.658	2.027	8	56
6	4, 5, 6	2, 2, 2	2	2.636	2.132	2.384	8	32
7	4, 6	2, 2	4	2.849	2.399	2.624	4	16
8	4, 6	2, 2	2	2.889	2.457	2.673	4	12
9	2, 3, 6	2, 2, 2	1	3.228	2.668	2.948	8	8
10	4, 6	2, 2	1	3.355	2.982	3.168	4	4