The Evaluation and Analysis of the Entropy Weight Method and the Fractional Grey Model Study on the Development Level of Modern Agriculture in Huizhou

From the level of agricultural material equipment, the level of agricultural output benefit, the level of agricultural economic structure, the level of agricultural industrialization management, the level of agricultural sustainable development, and the level of rural social and economic development, based on 15 indicators, an index system for evaluating the comprehensive capacity of modern agricultural development in Huizhou was constructed.+e comprehensive evaluation of the development level of modern agriculture in Huizhou from 2012 to 2018 was measured by the entropy weight method, and the evaluation was analyzed with the average level of Guangdong Province. We find out the gap between the development advantages of Huizhou and the average level of Guangdong Province, so as to promote the development of modern agriculture in Huizhou. Based on the comprehensive evaluation index of the development level of modern agriculture in Huizhou from 2012 to 2018 obtained by the entropy weight method, a fractional cumulative grey GM (1, 1) forecasting model was established, and its development ability was predicted and analyzed. +e forecast result has certain guiding significance to the development of modern agriculture in Huizhou.


Introduction
Agriculture is the most basic material production sector in the national economy. Whether in China or abroad, whether in the past, present, or in the future, agriculture is the foundation of the national economy. e policy of "agriculture, rural areas and farmers" put forward by the state emphasizes that the development of agriculture should be promoted as well as the increase of peasants' income. erefore, in order to realize the important goal of building Xiaokang in an all-round way and promoting socialist modernization in an all-round way, the most fundamental thing is to stress agriculture and strengthen agriculture and Huinong District in order to achieve sustainable and stable development of agriculture and long-term guarantee of effective supply of agricultural products. Modern agriculture, which has been formed since the Industrial Revolution, is gradually moving towards commercialization and marketization. Agricultural production and management activities have gradually become specialized, intensive, and large scale. Agricultural labor productivity has been greatly improved. Its main characteristics are as follows: the degree of market is increasingly mature, industrial equipment is widely used, advanced technology is widely used, the industrial system is improving day by day, and the ecological environment is valued. As one of the traditional agricultural cities and grain production areas in Guangdong Province, Huizhou has a very suitable climate for the development of crop production and has a relatively mild climate throughout the year. With plenty of rain and sunshine and fertile soil, agricultural resources are also relatively rich. According to the Huizhou Statistical Yearbook, the per capita net income of farmers in Huizhou has reached double-digit growth rate for five consecutive years and has made great achievements in agricultural development. Agriculture is an indispensable part of our city's national economy. At the same time, the development of modern agriculture can promote the development of other industries. erefore, scientific prediction of the economic development of modern agriculture is of great help to the prospect of the development of this city's agricultural economy. It is an extremely important basis for formulating the future agricultural development plan and also helps to promote the safe operation of our city's national economy. And the reasonable forecast method can also increase the science of the policy implementation and the persuasion to the masses, thus reducing the blindness of the decisionmaking. erefore, we should pay attention to the city's modern agricultural development in the future direction of the forecast. At present, accelerating the development of modern agriculture has become a consensus, many experts and scholars have explored the development of modern agriculture from different research perspectives. Zhang and Cang [1] set up indexes including the Agricultural Social Service Index, Agricultural Ecological Environment Index, Agricultural Security Level Index, and Agricultural Comprehensive Productive Capacity Index. Wang and Liu [2] constructed the first-class indexes of the agricultural economic function, agricultural ecological function, agricultural social function, and agricultural modernization level. According to the level of economic development, social development, and ecological development, an index system for evaluating the development level of modern urban agriculture in Tianjin, Hebei, was established by Gao [3]. Wan et al. [4] evaluated the modernization level of urban agriculture in Guangzhou from the classification indexes of production conditions, output benefit, scientific and technological level, ecological environment, and urban and rural overall planning. Fu and Luo [5] evaluated the modernization level of urban agriculture in Guangzhou from the aspects of urban agricultural quality and urban agricultural efficiency. Guo [6] constructed indexes including the comprehensive development level of agriculture, the safety level of agricultural ecological environment, the development level of agricultural society, the security level of urban agriculture, and the comprehensive production level of agriculture to evaluate the sustainable development ability of urban agriculture in Xi'an.
Focusing on the perspective of modern rural areas, Cai et al. [7] pushed forward the optimization of the agricultural structure, innovated the input methods of basic elements in agriculture, brought into play the leading role of the newtype agricultural management main body, and constructed a perfect socialized agricultural service system, effective promotion of sound development of agricultural economy. Liu and Na [8] promoted modern material conditions and equipment agriculture and modern science and technology to transform the agriculture and modern industrial system to upgrade agriculture from a green, circular, and high-end perspective. Luan [9] constantly expanded the quantity and quality of high-quality agricultural products, focused on the cultivation of scientific and technological innovation, and provided the core competitiveness of agricultural products for the perspective of supply-side reform.
Agricultural leading enterprises can promote the level of agricultural industrialization, optimize and adjust the industrial structure, and promote the production, employment, and income of farmers through various forms [10][11][12][13]. In recent years, domestic scholars have studied the efficiency of agricultural industrialization and its influencing factors from different angles, mainly focusing on the cluster of agricultural industrialization and agricultural leading enterprises and measuring the efficiency [14][15][16]. Zhang and Liu [17] established an evaluation index system for highquality development of agriculture from the aspects of agricultural resources, economic benefits, ecological environment and workers, etc., and through the mold and analytic hierarchy process for the comprehensive evaluation of agricultural high-quality development. ere are also some references to rural revitalization and modern agricultural development studies [18][19][20][21][22][23][24][25]. At present, scholars and experts focus on the entropy weight method and fractional grey model to study the development of modern agriculture which is still less. Based on the entropy weight method, this paper constructs the evaluation index system of the development level of modern agriculture, calculates the development status of modern agriculture in Huizhou from 2012 to 2018, and compares it with the average development level of modern agriculture in Guangdong Province from 2012 to 2018, a more accurate and comprehensive assessment of the level of modern agricultural development in Huizhou. We use fractional grey models to predict the level of modern agricultural development in Huizhou.

Evaluation Index System of Modern Agriculture Development.
is paper selects the agricultural data from 2012 to 2018 through the Huizhou Statistical Yearbook and Guangdong Statistical Yearbook and establishes a comprehensive evaluation index model of modern agriculture in Huizhou by using the entropy method. We combined the possibility and significance of obtaining relevant indicators, establishing a modern agricultural development evaluation index system with six secondary indicators, including the level of agricultural materials and equipment, the level of agricultural output and efficiency, the level of agricultural economic structure, the level of agricultural industrialization and management, the level of agricultural sustainable development, and the level of rural social and economic development and selected 15 three-level indicators, as detailed in Table 1.

e Fundamentals of the Model.
In information theory, entropy is a measure of uncertainty. e more the information, the less the uncertainty and the less the entropy; the less the information, the more the uncertainty and the more the entropy. According to the characteristics of entropy, we can judge the randomness and disorder degree of an event by calculating the entropy value, or we can judge the dispersion degree of an index by the entropy value; the more the dispersion degree of the index is, the greater the influence (weight) of the index on comprehensive evaluation is and the smaller the entropy value is. Using the entropy method to determine index weight can overcome the inevitable randomness and supposition of the subjective weighting method. So, this paper uses information entropy to determine index weight to make a comprehensive evaluation of agricultural development in Huizhou.

Comprehensive Evaluation Model of the Agricultural Development Level Based on the Entropy Weight Method.
e entropy weight method is calculated as follows.
If there are m evaluated objects and n evaluation indexes and y ij (1 ≤ i ≤ m, 1 ≤ j ≤ n) is the i index of the j evaluated object, then the decision matrix is Y � (y ij ) m×n . Different algorithms are used to conduct data standardization processing for positive and negative indicators. e positive indicators are standardized according to equation (1), while the negative indicators are standardized according to equation (2): Secondly, in order to ensure that the weight of the entropy method can be carried out by the logarithmic operation, the translation data should be carried out according to the following formula: Again, the index value after translation is transformed according to the following formula: We obtain matrix H � (h ij ) m×n as the normalized value of the evaluation index of the modern agricultural development level.
Finally, we calculate the entropy value of each index according to formula (5) and calculate the entropy weight value of the j-th index according to formula (6): Using the data of various indicators in Huizhou from 2012 to 2018, after calculation, the weight vector of the evaluation indicators of the modern agricultural development level is finally obtained, as shown in Table 1.

Comprehensive Evaluation Index of the Modern Agricultural Development Level.
For calculation and comparison, the classification index and comprehensive evaluation index of the modern agricultural development level adopt the linear weighting method, and the calculation formula is Among them, s i is the evaluation index of the modern agricultural development level; W j is the weight of the j-th index; and H ij is the normalized value of the index.
Using the evaluation index system and evaluation criteria and the data and analysis results of Huizhou city and Guangdong Province, the vertical comparison (Tables 2 and 3) and horizontal comparison of the development level of modern agriculture in Huizhou city from 2012 to 2018 are carried out.

Fractional Cumulative Grey Model Predicts the Comprehensive Evaluation Index of the Modern Agricultural Development Level.
In 2013, Wu et al. [26] proposed a grey model, fractional cumulative grey GM (1, 1) prediction model, which is based on the new information priority principle, with the help of the "in between" idea contained in the fractional order [27]; by selecting a reasonable accumulation order, the high-growth data sequence becomes smooth, and the prediction accuracy of the model is improved. Wu et al. [28] applied the univariate nonhomogeneous grey model to study CO 2 emissions for BRICS countries without the consideration of external factors. Under several error metrics, one can see that grey forecasting models can provide excellent results for the five countries. Based on the definition of the conformable fractional derivative, Ma et al. [29] proposed the conformable fractional accumulation and difference. en, a novel conformable fractional grey model is proposed based on the conformable fractional accumulation and difference, and the brute force method is introduced to optimize its fractional order.
Wu et al. [30] proved that the nonhomogenous discrete grey model (abbreviated as NDGM) with the first accumulated generating operator violates the principle of new information priority and principle of minimal information of grey system theory. A new NDGM with the fractional-order accumulation is put forward. Grey convex relational analysis was used to describe the relationship between the electricity consumption and its related factors by Wu et al. [31]. A novel multivariable grey forecasting model which considered the total population was developed to forecast the electricity consumption in Shandong province. Based on the nonhomogeneous grey model, the conformable fractional nonhomogeneous grey Bernoulli model was developed by Zheng et al. [32] for estimating natural gas production and consumption. In the new method, the Bernoulli equation was first introduced into the existing differential equation. Liu et al. [33] reconstructed a dynamic background value for the fractional grey model by the composite integral median theorem; as a result, they proposed a novel fractional grey model-based variable background value. As far as we know, there are few literature studies on the study of the modern agricultural development index using the fractional-order grey prediction model. So, we apply this method to study the modern agriculture of Huizhou.

Fractional Cumulative Modeling
(1) Input the original time series data: select a small amount of the historical data according to the forecast target: (2) e r-order cumulative sequence of the original data Calculate U (r) � u (r) (1), u (r) (2), . . . , u (r) (n) ; if the future scene belongs to short memory, set the order r ∈ (0, 0.5); if the future scene belongs to long memory, set the order r ∈ (0.5, 1). Among them, GM (1, 1) model parameter estimation: calculate the background value of the r-order cumulative sequence: Obtain matrices Use least squares to find parameters Determine the model: substitute the parameters a and b into the time response function of the GM (1, 1) model: Predicted u (r) (1), u (r) (2), . . .. (3) Accumulation and subtraction of the r-order sequence: change U (r) � u (r) (1), u (r) (2), . . . , u (r) (n), . . . to accumulate for order 1−r, and then accumulate and subtract for order 1, which is Calculate the fitted value u (0) (1), u (0) (2), . . . , u (0) (n) and the predicted value u (0) (n + 1), u (0) (n + 2), . . .. (4) Error test: perform the residual test, correlation test, or calibration error probability test for u (0) (1), u (0) (2), . . . , u (0) (n), judge the fitting effect of the model according to the test result, and qualitatively analyze the prediction accuracy of the model; if the fitting accuracy is not ideal, the cumulative order can be adjusted r, that is, return to formula (1) until the accuracy reaches the ideal state.

Analysis of Classification Index Evaluation Results. (1)
Agricultural material equipment level indicators: according to Figure 1, the agricultural material index of Huizhou city has shown a clear downward trend. It was 0.0100 in 2018, which was about 0.47 times that of 2012, mainly due to the continuous decline in electricity consumption per unit of the cultivated land. As shown in Figure 2, from 2012 to 2018, the agricultural material equipment level index of Guangdong Province increased first and then decreased and remained basically the same as Huizhou in the next two years.
(2) Index of the agricultural output benefit level: as shown in Figure 1, Huizhou's agricultural output benefit level index showed a clear trend of injury. e index in 2018 was more than 500 times that in 2012. As shown in Figure 2, from 2012 to 2018, Huizhou's agricultural output benefit level index was higher than the average level of Guangdong Province, increasing from 0.0027 in 2013 to 0.0099 in 2018; in 2014, it was lower than the evaluation level of Guangdong Province and lower than 0.0047.

Analysis of Comprehensive Evaluation Results.
According to Table 2

Using the Fractional Cumulative Grey Model to Predict the Comprehensive Evaluation Index of Modern Agriculture
From the data in Table 2, we obtain the original data sequence: In order to achieve the best simulation prediction effect, the optimal fractional order r should be determined, and the average relative error function (MAPE) should be constructed here. en, the relationship between the fractional order r and the parameter a, b is used as the constraint condition, and Python software is used to program the nonlinear optimization problem with the minimum average relative error as the objective function.
rough Python programming and the formula in Section 2.6, the optimal fractional order r is 0.8. e simulation value of the comprehensive evaluation index of the modern agricultural development level from 2012 to 2018 and the predicted value from 2019 to 2021 are given in Table 4. We use the grey prediction model and time series model to estimate and forecast the original data. We also get MAPE � 8.510% of the fractional cumulative grey model, which is smaller than that of the other two methods.

Conclusion
After research and analysis, Huizhou's modern agricultural construction has achieved positive results. e level of agricultural output and the level of agricultural industrialization management are higher than the average level of Guangdong Province, indicators such as agricultural material equipment level, agricultural economic structure, agricultural sustainable development level and rural social and economic development level are slightly lower than the average level of Guangdong Province. ese are the focus of Huizhou's future modern agricultural construction and development. In the research of grey forecasting, the fractional cumulative model is a hot spot in recent years. is paper established a fractional cumulative grey GM (1, 1) model to predict the comprehensive evaluation index of modern agricultural development in Huizhou. We obtained the predicted value of such indicators from 2019 to 2021. We found that the prediction worked very well. Using the novel conformable fractional nonhomogeneous grey model and nonhomogenous discrete grey model with fractional-order accumulation for forecasting Huizhou's modern agriculture is our future work.
Data Availability e data that support the findings of this study are openly available in Statistical Yearbook of Guangdong Province at https://data.cnki.net/area/Yearbook/Single/N2011090056? z=D19.

Conflicts of Interest
e authors declare that they have no conflicts of interest.  Mathematical Problems in Engineering 7