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

Table 6

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

(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	2, 3, 6	2, 2, 2	4	2.284	2.632	3.174	2.458	8	56
2	3, 4, 6	2, 2, 2	2	2.450	2.757	2.536	2.603	8	32
3	3, 4, 5, 6	2, 2, 2, 2	1	2.679	2.704	2.292	2.692	16	16
4	4, 6	2, 2	2	2.781	2.819	2.592	2.800	4	12
5	3, 4, 6	2, 2, 2	1	2.772	2.895	2.290	2.834	8	8
6	4, 6	2, 2	1	3.037	2.792	2.773	2.914	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	2, 3, 4, 5, 6, 7	2, 2, 2, 2, 2, 2	4	0.451	0.083	0.096	0.267	64	1408
2	2, 3, 5, 6, 7	2, 2, 2, 2, 2	4	0.637	0.088	0.199	0.362	32	512
3	1, 2, 4, 5, 6, 7	2, 2, 2, 2, 2, 2	2	1.589	1.044	0.897	1.316	64	448
4	3, 5, 6, 7	2, 2, 2, 2	4	1.802	0.842	0.978	1.322	16	176
5	1, 4, 5, 6	2, 2, 2, 2	2	2.206	1.658	1.719	1.932	16	80
6	2, 5, 6	2, 2, 2	4	2.368	1.618	1.282	1.993	8	56
7	3, 4, 6	2, 2, 2	2	2.548	2.284	1.708	2.416	8	32
8	4, 6	2, 2, 2	4	2.876	2.532	2.026	2.704	4	16
9	4, 6	2, 2	2	2.913	2.634	2.350	2.773	4	12
10	3, 4, 6	2, 2, 2	1	2.974	2.887	2.763	2.930	8	8
11	4, 6	2, 2	1	3.423	3.036	3.174	3.230	4	4