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Based on the generated 10 alternatives, ideal and anti-ideal alternatives are determined using Equations (1) and (2). The criteria values are randomly sampled and normalized between the ideal and anti-ideal alternatives by Equations (3) and (6). Then the closeness coefficient is calculated through Equations (4) and (5), and 30 training samples are obtained, as shown in Table 2. The sample series from 1 to 25 are used for training, and the sample series from 26 to 30 are used for verification.

Table 2

Training samples of the BP neural network and the training results

Sample no.		Inputs										Target outputs	Actual outputs
Sample no.		Z_ch–Z_max (m)	Z_e–Z_id (m)	W_ab (10⁶ m³)	Q_max (m³/s)	T (h)	W_ex (10⁶ m³)	Z_f	Q_f	S_l (t)	Q_sd (m³/s)	Closeness coefficient
Training samples	1	6.09	4.21	2708	5314	83	97	0.2	0.23	255	847	0.286	0.269
	2	7.98	2.43	2272	5016	64	63	0.08	0.09	205	646	0.714	0.741
	3	5.86	4.42	2760	5350	85	101	0.21	0.24	261	871	0.246	0.222
	…	…	…	…	…	…	…	…	…	…	…	…	…
	24	9.05	1.41	2022	4846	53	44	0.01	0.02	176	532	0.95	0.914
	25	5.73	4.55	2792	5371	87	103	0.22	0.25	265	885	0.214	0.200
Verification samples	26	4.96	5.27	2968	5492	94	117	0.27	0.31	285	966	0.036	0.111
	27	7.66	2.73	2344	5066	67	69	0.1	0.12	213	680	0.636	0.666
	28	6.94	3.4	2511	5179	74	82	0.15	0.17	232	756	0.472	0.472
	29	9.05	1.41	2022	4846	53	44	0.01	0.02	176	532	0.95	0.918
	30	7.17	3.19	2459	5144	72	78	0.13	0.15	226	732	0.532	0.530

Sample no.		Inputs										Target outputs	Actual outputs
Sample no.		Z_ch–Z_max (m)	Z_e–Z_id (m)	W_ab (10⁶ m³)	Q_max (m³/s)	T (h)	W_ex (10⁶ m³)	Z_f	Q_f	S_l (t)	Q_sd (m³/s)	Closeness coefficient
Training samples	1	6.09	4.21	2708	5314	83	97	0.2	0.23	255	847	0.286	0.269
	2	7.98	2.43	2272	5016	64	63	0.08	0.09	205	646	0.714	0.741
	3	5.86	4.42	2760	5350	85	101	0.21	0.24	261	871	0.246	0.222
	…	…	…	…	…	…	…	…	…	…	…	…	…
	24	9.05	1.41	2022	4846	53	44	0.01	0.02	176	532	0.95	0.914
	25	5.73	4.55	2792	5371	87	103	0.22	0.25	265	885	0.214	0.200
Verification samples	26	4.96	5.27	2968	5492	94	117	0.27	0.31	285	966	0.036	0.111
	27	7.66	2.73	2344	5066	67	69	0.1	0.12	213	680	0.636	0.666
	28	6.94	3.4	2511	5179	74	82	0.15	0.17	232	756	0.472	0.472
	29	9.05	1.41	2022	4846	53	44	0.01	0.02	176	532	0.95	0.918
	30	7.17	3.19	2459	5144	72	78	0.13	0.15	226	732	0.532	0.530

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