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

Table 9

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

(a) Based on the LSM

Number of solutions							Objective values
	Selected input variables	Number of MFs	Type	PI	V_PI	E_PI	E	H	N
1	1, 6, 11, 13	2, 2, 2, 2	1	3.529	2.888	5.093	3.209	16	16
2	1, 6, 13	2, 2, 2	1	3.680	3.312	5.713	3.496	8	8
3	6, 13	2, 2	1	4.662	3.299	4.859	3.980	4	4

(b) Based on the WLSM

Number of solutions							Objective values
	Selected input variables	Number of MFs	Type	PI	V_PI	E_PI	E	H	N
1	3, 6, 8, 11, 12, 13	2, 2, 2, 2, 2, 2	4	0.850	0.031	0.163	0.441	64	1408
2	5, 6, 8, 11, 13	2, 2, 2, 2, 2	4	1.087	0.448	0.510	0.768	32	512
3	6, 8, 11, 13	2, 2, 2, 2	4	1.652	1.210	1.738	1.431	16	176
4	1, 6, 13	2, 2, 2	4	2.841	2.321	2.246	2.581	8	56
5	3, 6, 7, 9, 13	2, 2, 2, 2, 2	1	3.965	3.300	4.678	3.633	32	32
6	4, 6, 13	2, 2, 2	1	5.042	3.487	4.623	4.264	8	8
7	10, 13	2, 2	1	5.720	5.347	7.020	5.533	4	4