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

Table 8

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

(a) Based on the LSM

Number of solutions						Objective values
	Selected input variables	Number of MFs	Type	PI	E_PI	E	H	N
1	6, 9, 10, 11, 13	2, 2, 2, 2, 2	2	3.148	3.306	3.227	32	192
2	6, 7, 10, 11, 13	2, 2, 2, 2, 2	1	3.459	3.637	3.548	32	32
3	1, 5, 6	2, 2, 2	4	4.275	4.171	4.223	8	56
4	3, 6, 13	2, 2, 2	1	4.114	3.907	4.008	8	8
5	2, 3	2, 2	3	7.087	7.593	7.340	4	24
6	3, 11	2, 2	1	7.300	7.496	7.398	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	3, 6, 7, 8, 11, 13	2, 2, 2, 2, 2, 2	4	1.208	0.077	0.643	64	1408
2	1, 5, 6, 8, 13	2, 2, 2, 2, 2	4	1.319	0.726	1.022	32	512
3	6, 7, 10, 11, 12, 13	2, 2, 2, 2, 2, 2	2	2.134	1.410	1.772	64	448
4	1, 6, 9, 11, 13	2, 2, 2, 2, 2	2	2.776	2.105	2.440	32	192
5	1, 6, 13	2, 2, 2	4	2.872	2.272	2.572	8	56
6	6, 7, 10, 12, 13	2, 2, 2, 2, 2	1	3.939	3.687	3.813	32	32
7	2, 6, 10	2, 2, 2	2	5.533	3.893	4.713	8	32
8	6, 11, 13	2, 2, 2	1	4.776	3.970	4.373	8	8
9	3, 13	2, 2	1	5.824	5.961	5.892	4	4