New neural fuzzy-based machine learning ensemble for enhancing the prediction accuracy of flood susceptibility mapping

Figures & data

Figure 1. Study area location

Figure 2. Flood predictors: (a) slope angle; (b) topographic position index (TPI); (c) land use; (d) plan curvature; (e) topographic wetness index (TWI); (f) aspect; (g) convergence index (CI); (h) hydrological soil group; (i) distance from rivers; (j) rainfall; (k) elevation; and (l) lithological category

Figure 2. (Continued)

Figure 3. Frequency distribution of flood pixels within the flood predictor classes

TPI - Topographic Position Index; P.C. - Plan curvature; TWI - Topographic Wetness Index; C.I. - Convergence Index; HSG - Hydrological Soil Groups; D.f.R. - Distance from Rivers.

Figure 4. General ANFIS architecture of first-order Takagi-Sugeno fuzzy model

MFs - Membership Functions.

Figure 5. Flowchart of the developed methodology. ANFIS - Adaptive Neuro-Fuzzy Inference System; AHP - Analytical Hierarchy Process; CF - Certainty Factor; WOE - Weights of Evidence; RMSE - Root Mean Sqaured Error; K-index- Kappa Index; FPI - Flood Potential Index

Figure 6. Performance in terms of RMSE calculated for the training dataset: (a) ANFIS-AHP, (c) ANFIS-CF and (e) ANFIS-WOE, and the validation dataset: (b) ANFIS-AHP, (d) ANFIS-CF and (f) ANFIS-WOE

MSE - Mean Squared Error; RMSE - Root Mean Squared Error; StD - Standard Deviation.

Table 1. Random consistency index (RI; after Saaty 1980)

N	1	2	3	4	5	6	7	8	9	10	11	12	13	14	15
RI	0	0	0.58	0.9	1.12	1.24	1.32	1.41	1.45	1.49	1.51	1.53	1.56	1.57	1.59

Table 2. Multicollinearity analysis and predictive ability of independent variables. TPI: topographic position index; TWI: topographic wetness index; TOL: tolerance; VIF: variance inflation; IG: information gain

Flood predictor	TOL	VIF	IG
Slope angle	0.89	1.21	0.85
TPI	0.91	1.12	0.39
Land use	0.85	1.16	0.67
Plan curvature	0.83	1.12	0.46
TWI	0.84	1.09	0.41
Aspect	0.96	1.14	0.18
Convergence index	0.86	1.16	0.37
Hydrological soil groups	0.91	1.04	0.32
Distance from rivers	0.94	1.08	0.71
Rainfall	0.88	1.19	0.29
Elevation	0.85	1.11	0.48
Lithology	0.95	1.04	0.53

Table 3. Pairwise comparison matrices

	Pairwise comparison matrix
Factor class/category	[1]	[2]	[3]	[4]	[5]	[6]	[7]	[8]	[9]	Weight	Normalized weight
Slope angle (°)
[1] 0–3	1									0.516	0.90
[2] 3.1 to 7	1/3	1								0.257	0.47
[3] 7.1 to 15	1/5	1/3	1							0.119	0.23
[4] 15.1 to 25	1/7	1/4	1/2	1						0.068	0.15
[5] 25.1 to 48.9	1/9	1/7	1/4	1/2	1					0.039	0.10
TPI
[1] −24.4 to −5.1	1									0.416	0.90
[2] −5 to −1.4	1/2	1								0.262	0.55
[3] −1.3 to 1.2	1/3	1/2	1							0.161	0.32
[4] 1.3 to 4.6	1/4	1/3	1/2	1						0.099	0.18
[5] 4.7 to 23.6	1/5	1/4	1/3	1/2	1					0.062	0.10
Land use
[1] Built-up area	1									0.268	0.90
[2] Agriculture area	1/3	1								0.108	0.37
[3] Vineyard	1/4	1/2	1							0.065	0.23
[4] Fruit trees	1/4	1/2	1	1						0.068	0.24
[5] Pasture	1/2	2	3	2	1					0.198	0.67
[6] Forest	1/7	1/4	1/3	1/4	1/5	1				0.026	0.10
[7] Shrub	1/4	1/2	1	2	1/3	3	1			0.072	0.25
[8] Marsh	1/4	1/2	1	1	1/4	3	1	1		0.063	0.22
[9] River	1/2	2	2	2	1/3	5	2	2	1	0.131	0.45
Plan curvature
[1] −2.82 to −0.1	1									0.175	0.10
[2] −0.09 to 0.1	4/3	1								0.303	0.40
[3] 0.11 to 2.67	4	4/3	1							0.521	0.90
TWI
[1] 3.3 to 6.2	1									0.428	0.90
[2] 6.3 to 8.2	1/2	1								0.259	0.55
[3] 8.3 to 11.1	1/3	2/3	1							0.187	0.40
[4] 11.2 to 15.9	1/5	1/4	1/3	1						0.084	0.19
[5] 16 to 26.8	1/7	1/6	1/5	1/3	1					0.042	0.10
Aspect
[1] Flat surfaces	1									0.032	0.10
[2] North	4	1								0.074	0.28
[3] Northeast	5	2	1							0.109	0.44
[4] East	5	3	4	1						0.216	0.90
[5] Southeast	4	4	2	3/4	1					0.169	0.70
[6] South	4	3/2	3/2	2/3	2/3	1				0.137	0.56
[7] Southwest	3	4/3	1	2/3	3/4	4/5	1			0.114	0.46
[8] West	3	5/4	2/3	2/5	2/5	3/5	4/5	1		0.087	0.34
[9] Northeast	2	1	1/2	1/3	1/2	1/3	3/7	3/4	1	0.062	0.23
Convergence index
[1] −91 to −3	1									0.431	0.90
[2] −2.9 to −2	1/2	1								0.253	0.53
[3] −1.9 to −1	1/3	1/2	1							0.182	0.39
[4] −0.9 to 0	1/5	1/3	1/3	1						0.090	0.19
[5] 0.1 to 97	1/7	1/5	1/5	1/3	1					0.044	0.10
Hydrological soil group
[1] A	1									0.108	0.10
[2] B	4/3	1								0.157	0.19
[3] C	2	4/3	1							0.201	0.27
[4] D	5	3	3	1						0.534	0.90
Distance from rivers (m)
[1] 0–50	1									0.321	0.90
[2] 50–100	1/2	1								0.220	0.63
[3] 100–150	1/3	1/2	1							0.151	0.45
[4] 150–200	1/4	1/3	1/2	1						0.103	0.32
[5] 200–400	1/5	1/4	1/3	1/2	1					0.082	0.26
[6] 400–700	1/6	1/5	1/4	1/3	1/3	1				0.062	0.21
[7] 700–1000	1/7	1/6	1/5	1/4	1/4	1/4	1			0.041	0.16
[8] >1000	1/9	1/7	1/6	1/5	1/5	1/6	1/7	1		0.020	0.10
Rainfall (mm/year)
[1] 504–600	1									0.046	0.10
[2] 601–700	2	1								0.075	0.15
[3] 701–800	4	3	1							0.157	0.31
[4] 801–900	6	4	2	1						0.247	0.48
[5] 901–962	7	5	4	3	1					0.475	0.90
Elevation (m)
[1] 68–200	1									0.318	0.90
[2] 201–400	1/2	1								0.217	0.63
[3] 401–600	1/3	1/2	1							0.151	0.45
[4] 601–800	1/4	1/3	1/2	1						0.132	0.40
[5] 801–1000	1/5	1/4	1/3	1/3	1					0.078	0.26
[6] 1001–1200	1/6	1/5	1/4	1/5	1/3	1				0.049	0.18
[7] 1201–1400	1/7	1/6	1/5	1/6	1/4	1/2	1			0.033	0.14
[8] 1401–1664	1/9	1/7	1/7	1/7	1/5	1/5	1/3	1		0.020	0.10
Lithology
[1] 1	1									0.061	0.20
[2] 2	3	1								0.120	0.38
[3] 3	2	2	1							0.135	0.42
[4] 4	2	1	1	1						0.128	0.40
[5] 5	1/3	1/4	1/4	1/5	1					0.026	0.10
[6] 6	2	1	1	1/2	5	1				0.113	0.36
[7] 7	1	1/2	1/2	1	3	1/2	1			0.123	0.39
[8] 8	7	3	3	2	9	5	1/2	1		0.294	0.90

Table 4. Pairwise comparison matrix properties. CI: consistency index; CR: consistency ratio; RI: random consistency index; TPI: topographic position index; TWI: topographic wetness index

Factor	N	λmax	CI	RI	CR
Slope angle	5	5.114	0.028	1.12	0.025
TPI	5	5.068	0.017	1.12	0.015
Land use	9	9.269	0.034	1.45	0.023
Plan curvature	3	3.074	0.037	0.58	0.064
TWI	5	5.120	0.030	1.12	0.027
Aspect	9	9.256	0.032	1.45	0.022
Convergence index	5	5.140	0.035	1.12	0.031
Hydrological soil group	4	4.011	0.004	0.90	0.004
Distance from rivers	8	8.255	0.036	1.41	0.026
Rainfall	5	5.158	0.040	1.12	0.035
Elevation	8	8.018	0.003	1.41	0.002
Lithology	8	8.119	0.017	1.41	0.012

Table 5. Certainty factor (CF) and weight-of-evidence (WOE) coefficients. TPI: topographic position index; TWI: topographic wetness index

Factors	Class	Class pixels	Flood	CF	WOE	CFN	WOEN
Slope angle (°)	0 to 3	534565	79	0.84	2.51	0.90	0.90
	3.1 to 7	680406	26	0.37	0.29	0.70	0.55
	7.1 to 15	2007111	10	−0.79	−2.28	0.19	0.14
	15.1 to 25	1421526	5	−0.85	−2.49	0.16	0.10
	25.1 to 48.9	312256	0	−1.00	−2.50	0.10	0.10
TPI	−24.4 to −5.1	309626	14	0.46	0.56	0.90	0.90
	−5 to −1.4	1098837	37	0.28	0.32	0.79	0.85
	−1.3 to 1.2	2082632	66	0.24	0.39	0.77	0.86
	1.3 to 4.6	1117893	2	−0.93	−2.97	0.10	0.10
	4.7 to 23.6	346876	1	−0.88	−2.32	0.13	0.25
Land use	Built-up area	277617	26	0.74	1.71	0.84	0.76
	Agriculture area	845085	39	0.48	1.03	0.73	0.62
	Vineyard	33450	0	−1.00	−1.55	0.10	0.10
	Fruit trees	22613	0	−1.00	−1.55	0.10	0.10
	Pasture	562104	16	0.15	0.36	0.59	0.49
	Forest	2851025	24	−0.65	−1.51	0.25	0.11
	Shrub	313819	5	−0.34	−0.27	0.38	0.36
	Marsh	2149	0	−1.00	−1.55	0.10	0.10
	River	47993	10	0.88	2.40	0.90	0.90
Plan curvature	−2.82 to −0.1	928127	21	−0.07	−0.43	0.66	0.59
	−0.09 to 0.1	2971217	92	0.22	0.44	0.90	0.90
	0.11 to 2.67	1056520	7	−0.73	−1.82	0.10	0.10
TWI	3.3 to 6.2	2239313	2	−0.96	−3.80	0.10	0.10
	6.3 to 8.2	1699284	23	−0.44	−0.70	0.32	0.45
	8.3 to 11.1	707081	29	0.41	0.74	0.68	0.62
	11.2 to 15.9	235882	35	0.84	2.20	0.86	0.78
	16 to 26.8	73946	31	0.94	3.22	0.90	0.90
Aspect	Flat surface	17914	0	−1.00	−0.65	0.10	0.10
	North	594014	18	0.20	0.25	0.84	0.78
	Northeast	691586	17	0.01	0.01	0.73	0.60
	East	719890	17	−0.02	−0.04	0.70	0.56
	Southeast	671671	23	0.29	0.41	0.90	0.90
	South	552529	12	−0.10	−0.13	0.65	0.49
	Southwest	560986	13	−0.04	−0.06	0.69	0.55
	West	571502	8	−0.42	−0.61	0.46	0.13
	Northeast	575772	12	−0.14	−0.17	0.63	0.46
Convergence index	−91 to −3	1133914	72	0.62	1.52	0.90	0.90
	−2.9 to −2	307398	2	−0.73	−1.46	0.10	0.10
	−1.9 to −1	405635	4	−0.59	−1.05	0.18	0.21
	−0.9 to 0	500461	10	−0.17	−0.31	0.43	0.41
	0.1–97	2608456	32	−0.49	−1.22	0.24	0.17
Hydrological soil group	A	1033758	16	−0.36	−0.62	0.10	0.10
	B	1788430	62	0.30	0.56	0.90	0.90
	C	1740316	35	−0.17	−0.35	0.33	0.28
	D	393351	7	−0.27	−0.41	0.22	0.24
Distance from rivers (m)	0–50	216627	56	0.91	2.85	0.90	0.90
	50–100	200304	40	0.88	2.37	0.89	0.84
	100–150	197815	11	0.56	0.78	0.75	0.64
	150–200	147651	4	0.11	0.01	0.56	0.55
	200–400	685596	3	−0.82	−1.94	0.16	0.31
	400–700	934459	2	−0.91	−2.72	0.12	0.21
	700–1000	792689	2	−0.90	−2.52	0.12	0.23
	>1000	1780723	2	−0.95	−3.60	0.10	0.10
Rainfall (mm/year)	504–600	1289813	38	0.18	0.26	0.90	0.90
	601–700	1062760	30	0.14	0.18	0.83	0.80
	701–800	920009	21	−0.06	−0.09	0.45	0.45
	801–900	1092026	20	−0.24	−0.36	0.10	0.10
	901–962	591332	11	−0.23	−0.31	0.12	0.17
Elevation (m)	68–200	169557	4	−0.03	−0.09	0.64	0.62
	201–400	1090021	47	0.44	0.77	0.90	0.90
	401–600	980645	25	0.05	0.01	0.68	0.65
	601–800	692803	16	−0.05	−0.11	0.63	0.61
	801–1000	724734	13	−0.26	−0.40	0.51	0.52
	1001–1200	858858	13	−0.37	−0.60	0.45	0.46
	1201–1400	385246	2	−0.79	−1.66	0.22	0.11
	1401–1664	54000	0	−1.00	−1.70	0.10	0.10
Lithology	1	58963	0	−1.00	−0.80	0.10	0.10
	2	44140	1	−0.06	−0.01	0.59	0.42
	3	29342	1	0.29	0.40	0.78	0.59
	4	2761921	43	−0.36	−0.76	0.44	0.12
	5	1055312	54	0.53	1.16	0.90	0.90
	6	885359	18	−0.16	−0.15	0.54	0.36
	7	78446	2	0.05	0.11	0.65	0.47
	8	42372	1	−0.03	0.03	0.61	0.44

Table 6. Statistical metrics used to evaluate model performance. TP: true positive; TN: true negative; FP: false positive; FN: false negative

Metric	Training dataset			Validation dataset
	ANFIS-AHP	ANFIS-CF	ANFIS-WOE	ANFIS-AHP	ANFIS-CF	ANFIS-WOE
TP	110	113	109	45	47	47
TN	109	111	108	46	48	46
FP	10	7	11	7	5	5
FN	11	9	12	6	4	6
Sensitivity	0.909	0.926	0.901	0.882	0.922	0.887
Specificity	0.916	0.941	0.908	0.868	0.906	0.902
Accuracy	0.913	0.933	0.904	0.875	0.913	0.894
k index	0.825	0.867	0.808	0.750	0.827	0.788

ANFIS - Adaptive Neuro-Fuzzy Inference System; AHP - Analytical Hierarchy Process; CF - Certainty Factor; WOE - Weights of Evidence.

Figure 7. Relative importance of flood conditioning factors

ANFIS - Adaptive Neuro-Fuzzy Inference System; AHP - Analytical Hierarchy Process; CF - Certainty Factor; WOE - Weights of Evidence.

Figure 8. Map of FPI_ANFIS-AHP values across the Trotuș River basin

FPI - Flood Potential Index; ANFIS - Adaptive Neuro-Fuzzy Inference System; AHP - Analytical Hierachy Process.

Figure 9. Map of FPI_ANFIS-CF values across the Trotuș River basin

FPI - Flood Potential Index; ANFIS - Adaptive Neuro-Fuzzy Inference System; CF - Certainty Factor.

Figure 10. Weights of the FPI classes

FPI - Flood Potential Index; ANFIS - Adaptive Neuro-Fuzzy Inference System; AHP - Analytical Hierarchy Process; CF - Certainty Factor; WOE - Weights of Evidence.

Figure 11. Map of FPI_ANFIS-WOE values across the Trotuș River basin

FPI - Flood Potential Index; ANFIS - Adaptive Neuro-Fuzzy Inference System; WOE - Weights of Evidence.

Figure 12. ROC curves: (a) success rate and (b) prediction. AUC: area under curve

ANFIS - Adaptive Neuro-Fuzzy Inference System; AHP - Analytical Hierarchy Process; CF - Certainty Factor; WOE - Weights of Evidence; AUC - Area Under Curve.

Table 7. Flood point distribution (%) within FPI classes

Sample	Class	ANFIS-AHP	ANFIS-CF	ANFIS-WOE
Training	Very low	0.0	0.8	1.7
	Low	4.2	0.8	1.7
	Medium	11.7	7.5	5.0
	High	30.0	16.7	22.4
	Very high	54.1	74.2	69.2
Validation	Very low	0.0	1.9	0.0
	Low	6.9	3.8	3.8
	Medium	12.8	5.8	3.8
	High	24.8	19.3	25.1
	Very high	55.5	69.2	67.3

FPI - Flood Potential Index; ANFIS - Adaptive Neuro-Fuzzy Inference System; AHP - Analytical Hierarchy Process; CF - Certainty Factor; WOE - Weights of Evidence.

Saaty, T.L., 1980. The analytical hierarchy process, planning, priority. Resource allocation. USA: RWS publications.

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