A grey comprehensive evaluation model for wheat quality incorporating PCA-EWM

Miaolei DENG ^**Corresponding author: dengmiaolei@haut.edu.cn

School of Information Science and Engineering, Henan University of Technology, Zhengzhou, China

Bowen ZHANG

School of Information Science and Engineering, Henan University of Technology, Zhengzhou, China

Si CHEN

School of Information Science and Engineering, Henan University of Technology, Zhengzhou, China

No.	Physical and chemical indices	Index description	Type of index
a	Fatty acid value	An index of wheat freshness	Negative
b	Falling number	Greater impact on wheat eating quality	Negative
c	Sedimentation value	Reflects the protein content of wheat and its quality	Positive
d	Reducing sugar	Nutrients required for respiration	Intermediate
e	Germination rate	Reflects the ability to germinate under suitable conditions	Positive
f	Peroxidase	A protective enzyme against the ageing of organisms	Positive
g	Electrical conductivity	Reflects the degree of change in intracellular electrolytes	Negative
h	Malondialdehyde	End product of internal membrane lipid peroxidation in wheat	Negative

Batch	a/(mgKOH/100g)	b/s	c/mL	d/%	e/%	f/(U/g)	g/(μs/cm/g)	h/(μmol/g)
1	16	380	57	0.275	89	4000	26	2.95
2	17	330	62	0.275	90	3950	31	2.9
3	22.5	495	50	0.274	93	3000	43	3
4	23	415	55	0.28	92	3600	30	2.99
5	27	510	48	0.29	82	2600	52	3
6	16	345	60	0.27	93	4200	28	2
7	20	385	58	0.273	88	3900	25	2.75
8	24	430	49	0.276	87	3300	32	3.1
9	26	495	51	0.288	85	2750	42	3.4
10	30	495	50	0.288	80	2800	48	3.2
11	15	340	61	0.27	91	4000	25	2.8
12	18	360	59	0.27	93	4100	29	2.8
13	21	405	56	0.286	91	3800	27.5	3
14	25	330	61	0.286	89	3300	45	2.9
15	29	485	52	0.295	78	2940	40	3.3

Index	a	b	c	d	e	f	g	h
a	1.000
b	0.782	1.000
c	0.747	0.948	1.000
d	-0.409	-0.185	-0.236	1.000
e	0.783	0.645	0.584	-0.052	1.000
f	0.910	0.874	0.831	-0.346	0.723	1.000
g	0.819	0.686	0.625	-0.307	0.614	0.908	1.000
h	0.674	0.639	0.598	-0.429	0.600	0.695	0.471	1.000

Batch	Grey grade composite clustering coefficient				Maximum value	Evaluation level
Batch	Grade I	Grade II	Grade III	Grade IV	Maximum value	Evaluation level
1	0.30033	0.28549	0.23258	0.18160	0.30033	Grade I
2	0.32023	0.30133	0.22103	0.15741	0.32023	Grade I
3	0.16144	0.24646	0.30513	0.28696	0.30513	Grade III
4	0.24828	0.28293	0.26315	0.20565	0.28293	Grade II
5	0.17302	0.22213	0.28877	0.31608	0.31608	Grade IV
6	0.32180	0.29531	0.21915	0.16374	0.32180	Grade I
7	0.27390	0.27544	0.24955	0.20110	0.27544	Grade II
8	0.20626	0.27353	0.27811	0.24210	0.27811	Grade III
9	0.15998	0.23026	0.30071	0.30904	0.30904	Grade IV
10	0.17577	0.22594	0.28727	0.31102	0.31102	Grade IV
11	0.31792	0.28830	0.22218	0.17160	0.31792	Grade I
12	0.31204	0.29996	0.22632	0.16169	0.31204	Grade I
13	0.27076	0.28111	0.25371	0.19442	0.28111	Grade II
14	0.23367	0.26617	0.26805	0.23210	0.26805	Grade III
15	0.18212	0.23992	0.28591	0.29205	0.29205	Grade IV

Batch	PCA-EWM-GS evaluation model		PCA-EWM-TOPSIS evaluation model		PCA-RSR evaluation model
Batch	Evaluation value	Sort	Evaluation value	Sort	Evaluation value	Sort
1	2.70455	5	0.768	5	0.824	5
2	2.78438	1	0.882	3	0.889	3
3	2.28236	12	0.331	11	0.426	11
4	2.57386	8	0.583	9	0.668	8
5	2.25209	14	0.1	15	0.139	15
6	2.77517	2	0.91	2	0.937	2
7	2.62212	7	0.733	6	0.775	6
8	2.44395	10	0.41	10	0.486	10
9	2.24116	15	0.224	12	0.299	12
10	2.26646	13	0.112	14	0.165	14
11	2.75254	4	0.923	1	0.94	1
12	2.76237	3	0.839	4	0.877	4
13	2.62821	6	0.657	7	0.732	7
14	2.50139	9	0.636	8	0.641	9
15	2.31211	11	0.219	13	0.245	13

Evaluation model	PCA-EWM-GS evaluation model	PCA-EWM-TOPSIS evaluation model	PCA-RSR evaluation model
PCA-EWM-GS evaluation model	1	0.939	0.943
PCA-EWM-TOPSIS evaluation model	0.939	1	0.996
PCA-RSR evaluation model	0.943	0.996	1

{\hat{x}}_{i j} = \{\begin{cases} \frac{x_{i j} - x_{j \min}}{{\bar{x}}_{j} - x_{j \min}}, x_{i j} < {\bar{x}}_{j} \\ \frac{x_{j \max} - x_{i j}}{x_{j \max} - {\bar{x}}_{j}}, x_{i j} \geq {\bar{x}}_{j} \end{cases}

\begin{array}{l} ε_{k} (j) = \frac{\min \min |x_{0} (j) - x_{k} (j)| + ρ \max \max |x_{0} (j) - x_{k} (j)|}{|x_{0} (j) - x_{i} (j)| + ρ \max \max |x_{0} (j) - x_{i} (j)|} \\ = \frac{\min \min |1 - x_{k} (j)| + \frac{1}{2} \max \max |1 - x_{k} (j)|}{|1 - x_{k} (j)| + \frac{1}{2} \max \max |1 - x_{k} (j)|} \end{array}

U_{i} = [\begin{matrix} ε_{1} {(1)}_{i} & ε_{2} {(1)}_{i} & \dots & ε_{d} {(1)}_{i} \\ ε_{1} {(2)}_{i} & ε_{2} {(2)}_{i} & \dots & ε_{d} {(1)}_{i} \\ ⋮ & ⋮ & ⋱ & ⋮ \\ ε_{1} {(n)}_{i} & ε_{2} {(n)}_{i} & \dots & ε_{d} {(n)}_{i} \end{matrix}]

\begin{array}{l} Y_{i} = ω_{j} \cdot U_{i} = [\begin{matrix} ω_{1} & ω_{2} & \dots & ω_{n} \end{matrix}] \cdot [\begin{matrix} ε_{1} {(1)}_{i} & ε_{2} {(1)}_{i} & \dots & ε_{d} {(1)}_{i} \\ ε_{1} {(2)}_{i} & ε_{2} {(2)}_{i} & \dots & ε_{d} {(1)}_{i} \\ ⋮ & ⋮ & ⋱ & ⋮ \\ ε_{1} {(n)}_{i} & ε_{2} {(n)}_{i} & \dots & ε_{d} {(n)}_{i} \end{matrix}] \\ = [\begin{matrix} y_{1} & y_{2} & \dots & y_{d} \end{matrix}] \end{array}

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