Agriculture Crop Suitability Prediction Using Rough Set on Intuitionistic Fuzzy Approximation Space and Neural Network

Figures & data

Table 1. Information system.

Objects	Max temp $(a_1)$	Min temp $(a_2)$	Avg. wind speed $(a_3)$	Avg. relative humidity $(a_4)$	Avg. evaporation rate $(a_5)$
$x_1$	36.6	20.9	8.6	73	4.4
$x_2$	36.9	23.1	7.4	72	2.8
$x_3$	43.7	24.8	6.2	70	2.6
$x_4$	46.9	27.4	3.1	67	3.4
$x_5$	46.1	27.2	7.4	62	5.1
$x_6$	45.4	26.4	8.9	56	4.2

Figure 1. The proposed research design.

Figure 2. Design of back propagation neural network.

Figure 3 Index map of the study area.

Figure 4. Administrative blocks of the study area.

Table 2. Agricultural divisions in Vellore district

S. no.	Agriculture division	Blocks
1.	Vellore (1)	Vellore, Kaniyambadi, Anaicut
2.	Gudiyatham (2)	Gudiyatham, K.V.Kuppam and Katpadi
3.	Vaniyambadi (3)	Alangayam, Madhanur and Pernambattu
4.	Tirupathur (4)	Tirupathur, Kandhili, Natrampalli and Jolarpet
5.	Walajah (5)	Walajah and Sholingur
6.	Arcot (6)	Arcot and Thimiri
7.	Arakonam (7)	Arakonam, Nemili, Kaveripakkam
8	Ambur (8)	Madhanur
9	Katpadi (9)	K.V. Kuppam, and Katpadi

Table 3. Notation representation table

Attributes	Abbreviation	Notation	Possible values	Max value
Soil pH	SPH	$a_1$	[5.4–8.5]	8.5
Moisture	MOI	$a_2$	[5–12.2]	12.2
Organic matter	OM	$a_3$	[0.65–1.98]	1.98
Nitrogen	N	$a_4$	[ 200–800]	800
Phosphorous	P	$a_5$	[ 40–533]	533
Potassium	K	$a_6$	[115–1045]	1045
Copper	Cu	$a_7$	[0.05–2]	2
Zinc	Zn	$a_8$	[ 0.01–2]	2
Manganese	Mn	$a_9$	[0.7–4.6]	4.6
Iron	Fe	$a_{10}$	[1.98–99.6]	99.6
Water pH	WPH	$a_{11}$	[6.2–8.5]	8.5
Calcium	Ca	$a_{12}$	[11–420]	420
Nitrate	NO3	$a_{13}$	[ 16–140]	140
Magnesium rain	Mg	$a_{14}$	[ 21–280]	280
Rainfall R	R	$a_{15}$	[ 773.4–1111.2]	1111.2
Places	PL	$d$	–

Table 4. Sample agriculture information system

Obj.	$a_1$	$a_2$	$a_3$	$a_4$	$a_5$	$a_6$	$a_7$	$a_8$	$a_9$	$a_{10}$	$a_{11}$	$a_{12}$	$a_{13}$	$a_{14}$	$a_{15}$	Places
$x_1$	7.3	9	0.96	350	200	160	1.2	1.8	3.2	61.2	7.3	20	16	226.14	787.9	3
$x_2$	7.2	11.7	0.99	450	130	115	1.2	1.09	1.088	75	8.5	21	17	25	1045.4	1
$x_3$	7.21	11.5	0.91	360	200	645	0.5	1.5	0.8	69	7.1	72.3	45	77.3	1111.2	7
$x_4$	7.35	9.5	0.78	432	40	150	1.6	3.3	1.7	61	7.36	23	63	280	1052.2	6
$x_5$	7.5	7	0.78	200	44	162.86	0.05	1.2	2.49	57	6.3	39	78	259	995	2
$x_6$	5.4	6.1	1.23	560	476	486	0.5	3.5	4.6	47	6.2	40.8	84	166	890	4
$x_7$	7.47	8	1.32	475	120	310	0.45	1.1	1.2	1.98	7.43	11	78	26	999.3	2
$x_8$	6.2	6.7	0.98	345	527	1045	0.9	4.7	2.7	2.2	6.35	80	56	250	894.3	4
$x_9$	6.3	7	1.2	401	222	672	0.05	0.01	0.7	8.4	6.35	53.8	45	21	1037.5	1
$x_{10}$	7.1	5	1.32	400	160	160	1.9	2.1	2.4	51.1	8.3	148	25	176.63	1004.4	2
$x_{11}$	7.45	8	1.67	540	242	370	1.5	5	3.3	8.8	7.41	420	56	110	998.7	7
$x_{12}$	7.2	11.9	1.53	200	160	220	1.8	1.2	3.4	61.4	7.4	20	140	211.55	773.4	3
$x_{13}$	8.5	10	1.52	800	190	340	1.2	2.4	1.8	45	8.31	70	130	120	999	4
$x_{14}$	7.32	12.1	1.98	645	140	120	1.4	2.2	3.5	64	7.42	12	18	27	1008.6	7
$x_{15}$	7.4	9	1.32	450	160	325	1.6	1.6	1.8	62.1	7.2	45	41	23	885.2	3
$x_{16}$	8.47	8	0.65	340	533	477	0.51	2.5	1.68	7.57	7	138	45	71	891.2	5
$x_{17}$	7.1	11.8	0.98	340	349	476	0.5	3.6	0.8	4.5	7.2	128	23	211	1012.6	6
$x_{18}$	5.5	10	0.88	650	170	150	1.1	1.9	4.6	51.5	7.28	60	126	130	880.5	4
$x_{19}$	7.2	8	0.92	460	120	140	1.1	1.2	3.2	60.2	8.11	118	24	69.5	1032.2	1
$x_{20}$	7.21	12.2	1.68	340	480	240	2	3.8	4.2	99.6	7.21	51	57	206.4	1008.1	5

Table 5. Intuitionistic fuzzy tolerance relation for the attribute a₁

${\text{IR}}_{(\alpha ,\beta )}^{a_1}$	$x_1$	$x_2$	$x_3$	$x_4$	$x_5$	$x_6^{}$	$x_7$	$x_8$	$x_9$	$x_{10}$	$x_{11}$
$x_1$	1, 0	0.99, 0.01	0.99, 0.00	0.99, 0,00	0.98, 0.01	0.79, 0.11	0.98, 0.01	0.88, 0.06	0.89, 0.06	0.98, 0.01	0.98, 0.01
$x_2$	0.99, 0.01	1,0	1.00, 0.00	0.98, 0.01	0.97, 0.02	0.80, 0.10	0.97, 0.02	0.89, 0.06	0.90, 0.05	0.99, 0.01	0.97, 0.01
$x_3$	0.99, 0.00	1.00, 0.00	1, 0	0.98, 0.01	0.97, 0.02	0.80, 0.10	0.97, 0.01	0.89 0.06	0.90, 0.05	0.99, 0.01	0.97. 0.01
$x_4$	0.99, 0.00	0.98, 0.01	0.98, 0.01	1, 0	0.98, 0.01	0.78, 0.11	0.99, 0.01	0.87, 0.06	0.88, 0.06	0.97, 0.01	0.99, 0.01
$x_5$	0.98. 0.01	0.97, 0.02	0.97, 0.02	0.98, 0.01	1, 0	0.77, 0.12	1.00, 0.00	0.86, 0.07	0.87, 0.07	0.96, 0.02	0.99, 0.00
$x_6$ $x_6$	0.79, 0.11	0.80, 0.10	0.80, 0.10	0.78, 0.11	0.77, 0.12	1,0	0.77,0.12	0.91,0.04	0.90,0.05	0.81,0.09	0.77,0.10
$x_7$	0.98,0.01	0.97,0.02	0.97,0.01	0.99,0.01	1.00,0.00	0.77,0.12	1,0	0.86,0.07	0.87,0.07	0.96,0.02	1.00,0.00
$x_8$	0.88,0.06	0.89,0.06	0.89,0.06	0.87,0.06	0.86,0.07	0.91,0.04	0.86,0.07	1,0	0.99,0.01	0.90,0.05	0.86,0.07
$x_9$	0.89,0.06	0.90,0.05	0.90,0.05	0.88,0.06	0.87,0.07	0.90,0.05	0.87,0.07	0.99,0.01	1,0	0.91,0.04	0.87,0.06
$x_{10}$	0.98,0.01	0.99,0.01	0.99,0.01	0.97,0.01	0.96,0.02	0.81,0.09	0.96,0.02	0.90,0.05	0.91,0.04	1, 0	0.96,0.02
$x_{11}$	0.98,0.01	0.97,0.01	0.97,0.01	0.99,0.01	0.99,0.00	0.77,0.11	1.00,0.00	0.86,0.06	0.87,0.06	0.96,0.02	1, 0

Table 6. Intuitionistic fuzzy proximity relation for the attribute a₂

${\text{IR}}_{(\alpha ,\beta )}^{a_2}$	$x_1$	$x_2$	$x_3$	$x_4$	$x_5$	$x_6^{}$	$x_7$	$x_8$	$x_9$	$x_{10}$	$x_{11}$
$x_1$	1, 0	0.78, 0.11	0.80, 0.10	0.96, 0.02	0.84, 0.08	0.76, 0.12	0.92, 0.04	0.81, 0.09	0.84, 0.08	0.67, 0.16	0.92, 0.04
$x_2$	0.78,0.11	1, 0	0.98, 0.01	0.82, 0.09	0.61, 0.19	0.54, 0.23	0.70, 0.15	0.59, 0.20	0.61, 0.19	0.45, 0.27	0.70, 0.15
$x_3$	0.80,0.10	0.98, 0.01	1, 0	0.84, 0.08	0.63, 0.18	0.56, 0.22	0.71, 0.14	0.61, 0.20	0.63, 0.18	0.47, 0.27	0.71 ,0.14
$x_4$	0.96,0.02	0.82,0.09	0.84,0.08	1, 0	0.80, 0,10	0.72,0.14	0.88,0.06	0.77,0.11	0.80,0.10	0.63,0.18	0.88,0.06
$x_5$	0.84,0.08	0.61,0.19	0.63,0.18	0.80,0.10	1, 0	0.93,0.04	0.92,0.04	0.98,0.01	1.00,0.00	0.84,0.08	0.92,0.04
$x_6{x}_6$	0.76,0.12	0.54,0.23	0.56,0.22	0.72,0.14	0.93,0.04	1, 0	0.84,0.08	0.95,0.02	0.93,0.04	0.91,0.05	0.84,0.08
$x_7$	0.92,0.04	0.70,0.15	0.71,0.14	0.88,0.06	0.92,0.01	0.84,0.08	1, 0	0.89,0.05	0.92,0.04	0.75,0.12	1.00,0.00
$x_8$	0.81,0.09	0.59,0.20	0.61,0.20	0.77,0.11	0.98,0.01	0.95,0.27	0.89,0.05	1, 0	0.98,0.01	0.86,0.07	0.89,0.05
$x_9$	0.84,0.08	0.61,0.19	0.63,0.18	0.80,0.10	1.00,0.00	0.93,0.04	0.92,0.04	0.98,0.01	1, 0	0.84,0.08	0.92,0.04
$x_{10}$	0.67,0.16	0.45,0.27	0.47,0.27	0.63,0.18	0.84,0.08	0.91,0.05	0.75,0.12	0.86,0.07	0.84,0.08	1, 0	0.75,0.12
$x_{11}$	0.92,0.04	0.70,0.15	0.71,0.14	0.88,0.06	0.92,0.04	0.84,0.08	1.00,0.00	0.89,0.05	0.92,0.04	0.75,0.12	1, 0

Table 7. Qualitative information system of sample dataset

Obj.	$a_1$	$a_2$	$a_3$	$a_4$	$a_5$	$a_6$	$a_7$	$a_8$	$a_9$	$a_{10}$	$a_{11}$	$a_{12}$	$a_{13}$	$a_{14}$	$a_{15}$	Places
$x_1$	H	H	Vl	L	M	Vl	M	L	M	M	M	Vl	P	M	L	Alangayam
$x_2$	H	Vh	Vl	L	M	Vl	M	Vl	Vl	H	H	Vl	P	Ne	H	Anaicut
$x_3$	H	Vh	Vl	L	M	H	Vl	L	Ne	M	M	L	Vl	P	H	Arakonam
$x_4$	H	H	Vl	L	L	Vl	H	M	P	M	M	Vl	L	Vh	H	Arcot
$x_5$	H	L	Vl	Vl	L	Vl	H	Vl	L	M	L	Vl	M	H	H	Gudiyatham
$x_6$	L	L	L	M	H	M	Vl	M	Vh	L	L	Vl	M	L	M	Jolarpet
$x_7$	H	M	L	L	M	L	Vl	Vl	Vl	Vl	M	Vl	M	Ne	H	K V Kuppam
$x_8$	M	L	Vl	L	Vh	Vh	L	H	L	Vl	L	L	L	H	M	Kandeli
$x_9$	M	L	L	L	M	H	H	P	Ne	Vl	L	L	Vl	Ne	H	Kaniyambadi
$x_{10}$	H	Vl	L	L	M	Vl	Vh	L	L	L	H	H	P	L	H	Katpadi
$x_{11}$	H	M	H	M	M	L	H	Vh	M	M	M	Vh	L	Vl	H	Kaveripakkam
$x_{12}$	H	Vh	M	Vl	M	Vl	Vh	Vl	M	M	M	Vl	Vh	M	L	Madhanur
$x_{13}$	Vh	H	M	Vh	M	L	M	L	P	L	H	L	H	Vl	H	Natrampalli
$x_{14}$	H	Vh	Vh	H	M	Vl	H	L	M	M	M	Vl	P	Ne	H	Nemili
$x_{15}$	H	H	L	L	M	L	H	L	P	M	M	Vl	Vl	Ne	M	Pemambattu
$x_{16}$	Vh	M	P	L	Vh	M	Vl	L	P	Vl	M	H	Vl	P	M	Sholingur
$x_{17}$	H	Vh	Vl	L	M	M	Vl	M	Ne	Vl	M	H	P	M	H	Thimiri
$x_{18}$	L	H	Vl	H	M	Vl	M	L	Vh	L	M	L	H	Vl	M	Tirupathur
$x_{19}$	H	M	Vl	L	M	Vl	M	Vl	M	M	H	H	P	P	H	Vellore
$x_{20}$	H	Vh	H	L	H	Vl	Vh	M	H	Vh	M	L	L	M	H	Walajahpet

Figure 5. Number of hidden nodes using MSE.

Figure 6. Number of hidden nodes using MPE.

Table 8. Validating the training data

Obj.	$a_1$	$a_2$	$a_3$	$a_4$	$a_5$	$a_6$	$a_7$	$a_8$	$a_9$	$a_{10}$	$a_{11}$	$a_{12}$	$a_{13}$	$a_{14}$	$a_{15}$	Recorded places	Observed Places
$x_{12}$	H	Vh	M	Vl	M	Vl	Vh	Vl	M	M	M	Vl	Vh	M	L	8	8
$x_{13}$	Vh	H	M	Vh	M	L	M	L	P	L	H	L	H	Vl	H	4	4
$x_{14}$	H	Vh	Vh	H	M	Vl	H	L	M	M	M	Vl	P	Ne	H	7	7
$x_{15}$	H	H	L	L	M	L	H	L	P	M	M	Vl	Vl	Ne	M	3	3
$x_{16}$	Vh	M	P	L	Vh	M	Vl	L	P	Vl	M	H	Vl	P	M	5	5
$x_{17}$	H	Vh	Vl	L	M	M	Vl	M	Ne	Vl	M	H	P	M	H	6	6
$x_{18}$	L	H	Vl	H	M	Vl	M	L	Vh	L	M	L	H	Vl	M	4	4
$x_{19}$	H	M	Vl	L	M	Vl	M	Vl	M	M	H	H	P	P	H	1	1
$x_{20}$	H	Vh	H	L	H	Vl	Vh	M	H	Vh	M	L	L	M	H	5	5

Table 9. Comparative analysis and results.

	Supporting objects			Accuracy obtained
Objects	RSIFASANN	RSFASANN	BCRSFAS	RSIFASANN	RSFASANN	BCRSFAS
220	203	198	184	0.923	0.900	0.836
440	408	399	370	0.927	0.907	0.841
660	616	611	560	0.933	0.926	0.848
880	823	825	750	0.935	0.938	0.852
1100	1031	1030	935	0.937	0.936	0.850
1320	1236	1240	1140	0.936	0.939	0.864
1540	1443	1443	1369	0.937	0.937	0.889
1760	1656	1645	1578	0.941	0.935	0.897
1980	1875	1874	1779	0.947	0.946	0.898
2193	2090	2076	1975	0.953	0.947	0.901
Average accuracy =				0.937	0.931	0.868

Figure 7. Experimental comparative graph.

Figure 8. Mean square error of Fold 1 for N = 10.

Figure 9. Overall mean square error over all folds for N = 10.

Table 10. Overall mean square error across various folds

Number of folds (N)	Overall MSE	Observations in test set
10	2.44	99
15	2.43	66
20	2.44	49
25	2.44	39
30	2.43	33
Average MSE	0.2436