# Evaluation of the Rural Informatization Level in Central China Based on Catastrophe Progression Method

Lingxian Zhang, Xue Liu, Zetian Fu, Daoliang Li

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Lingxian Zhang, Xue Liu, Zetian Fu, Daoliang Li. Evaluation of the Rural Informatization Level in Central China Based on Catastrophe Progression Method. 4th Conference on Computer and Computing Technologies in Agriculture (CCTA), Oct 2010, Nanchang, China. pp.672-679, 10.1007/978-3-642-18369-0_80. hal-01564887

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<figure><img src="image_1.png" /></figure>

Distributed under a Creative Commons Attribution 4.0 International License
Evaluation of the rural informatization level in the
central China based on Catastrophe Progression Method

Lingxian Zhang, Xue Liu, Zetian Fu, Daoliang Li *

College of Information & Electrical Engineering, China Agricultural University, P.O. Box 209,
17 Qinghua East Road, Haidian District, Beijing, China

**Abstract:** This paper developed a methodology based on the catastrophe theory for estimating the rural informatization level in central China, and took evaluation of the rural informatization level among the six provinces of central China as an example to test the effectiveness of the method. Taking data from reference and constructing the hierarchy based on catastrophe progression method, it was calculated the scores of rural informatization level among the six provinces of central China using normalizing formula. The results are found to be coincident with practical situation, so it proves the catastrophe progression method works well.

**Key words:** rural informatization ; level ; evaluation ; Catastrophe Progression Method; the central China

# 1 Introduction

As rural informatization is an important component of the national informatization development process, it is the basis for decision-making to make an objective assessment and analysis to national and regional level of development of rural informatization.

There have many methods for multiple object comprehensive evaluation [1-4], such as factor analysis, RITE's Index of Information, Information Society Index(ISI), UN's Information Utilization Potentials, fuzzy evaluation, analytic hierarchy process [5] and so on. But some methods have defects with more subjectivity on weight decision or too complex processes in calculation. The paper introduces the main steps and idea of a method using catastrophe theory (CT), namely, called catastrophe progression method (CPM). Its characteristic is combining catastrophe theory with fuzzy mathematics, and only considers the relative importance of the indices, so the method avoids the subjectivity for weight decision. Catastrophe progression method also has advantages in solving problems of fuzzy multiple object decision because the catastrophe progression is a multidimensional fuzzy membership function. With these characteristics, the method is easier and the results are more precise [6].

* Corresponding author. Tel.: +86 010 62736764; fax: +86 010 62737741.

E-mail address: zlx131@163.com (L.X. Zhang); dliangl@cau.edu.cn(D.L. Li).
## 2 The evaluation methodology for the rural informatization level in central China

### 2.1 Evaluation index system of the rural informatization level

According as the composition project of national informatization index issued by Information & Industry Ministry of China on July 29th, 2001, taking the literature [7] from reference, this paper presents the evaluation index system for the rural informatization level in the central China, which includes the 5 categories (secondary indices) of the Economic strength, Information infrastructure, Information terminal equipment, Human resource and Information utilization, and 14 tertiary indices (Table 1).

<table><caption>**Table 1.** Evaluation index system for the rural informatization level in the central China.</caption><thead><tr><th>Evaluation objective</th><th>Category</th><th>Indices</th><th>Index abbreviation</th></tr></thead><tbody><tr><td rowspan="12">informatization level of rural areas</td><td rowspan="3">Economic strength</td><td>GDP per capita</td><td>GDP</td></tr><tr><td>Revenue per capita</td><td>RP</td></tr><tr><td>Per capita income of rural households</td><td>PI</td></tr><tr><td rowspan="4">Information infrastructure</td><td>Long-distance telephone exchange capacity</td><td>TC</td></tr><tr><td>Mobile switching capacity</td><td>MC</td></tr><tr><td>Length of long-distance optical cable</td><td>OC</td></tr><tr><td>Internet broadband access ports</td><td>IB</td></tr><tr><td rowspan="3">Information terminal equipment</td><td>Color television ownership</td><td>TO</td></tr><tr><td>Computer ownership</td><td>CO</td></tr><tr><td>Mobile telephone ownership</td><td>MO</td></tr><tr><td rowspan="2">Human resource</td><td>Percentage of literate population to total aged 15 and over</td><td>LP</td></tr><tr><td>Number of rural information service employees</td><td>IEm</td></tr><tr><td rowspan="2">Information utilization</td><td>Proportion of per capita information consumption expenditure of rural households</td><td>IEx</td></tr><tr><td>Proportion of Internet users in rural areas</td><td>IU</td></tr></tbody></table>

### 2.2 Assessment model of the rural informatization level
**Establishment of the hierarchical structural model.** According to the regulation of indices grouping aforementioned, we constructed the catastrophe progression model for informatization level of rural areas in central China by four hierarchies, which was broken down in a manner as shown in Fig.1.

<figure><img src="image_2.png" /><figcaption>Fig.1. Catastrophe progression model for rural informatization level in the central China.</figcaption></figure>
**Confirming the catastrophe type in every catastrophe subordinate system.**

Catastrophe theory analyses critical degenerate points of the potential function, where not just the first derivative, but one or more higher derivatives of the potential function are also zero. There are seven fundamental types of Catastrophe models presented, three types of which, such as elliptic umbilic catastrophe, hyperbolic umbilic catastrophe, and parabolic umbilic catastrophe, are under behavior variation of two dimension. Among seven fundamental types, only four common catastrophe types are cusp catastrophe, swallowtail catastrophe and butterfly catastrophe, respectively, which potential functions are as follows [8]:

Fold catastrophe: $f(x) = x^3 + ax$.

Cusp catastrophe: $f(x) = x^4 + ax^2 + bx$.

Swallowtail catastrophe: $f(x) = \frac{1}{5}x^5 + \frac{1}{3}ax^3 + \frac{1}{2}bx^2 + cx$.

Butterfly catastrophe: $f(x) = \frac{1}{6}x^6 + \frac{1}{4}ax^4 + \frac{1}{3}bx^3 + \frac{1}{2}cx^2 + dx$.

Where $f(x)$ is the potential function of the state variable $x$, and a, b, c and d are control variables of the state variable.

In the catastrophe progression model for informatization level assessment of rural areas, the catastrophe type was confirmed in every evaluation index layer (see Fig.1). There were three catastrophe type, such as cusp catastrophe (one index divided into two sub-indices), swallowtail catastrophe (into three sub-indices) and butterfly catastrophe (into four sub-indices).

**Normalizing the control variables of the catastrophe model**

*Standardizing data.* The standardized data are in the value range of from 0 to 1. Equation (1) is adopted if the index is positive, equation (2) is applied if negative.

a) For The-Larger-The-Better indices, let

$$y_{ij} = \frac{x_{ij} - x_{\min(j)}}{x_{\max(j)} - x_{\min(j)}} \qquad x_{\min(j)} < x_{ij} < x_{\max(j)} \quad (1)$$

b) For The-Smaller-The-Better indices, let

$$y_{ij} = \frac{x_{\max(j)} - x_{ij}}{x_{\max(j)} - x_{\min(j)}} \qquad x_{\min(j)} < x_{ij} < x_{\max(j)} \quad (2)$$

Where $j$ is a sequence number for catastrophe subordinate systems, $i$ is a serial number of control variables in a catastrophe subordinate system; $x_{ij}$ is merely the values of $x$ corresponding to control variables in a hierarchy of $i$ and $j$, respectively;

$y_{ij}$ is only the standard transformation values of $x_{ij}$; $x_{\min(j)}$, $x_{\max(j)}$ are lower limit
or upper limit values of x corresponding to control variables in a catastrophe subordinate system, respectively.

Formulas for normalization of control variables. For the cusp, fold, swallowtail, and butterfly catastrophe system, the decomposition forms of the equation of the bifurcation point set and the normalization formulas are showed in Table 2.

<table><caption>**Table 2.** Catastrophe models under behavior variation of one dimension.</caption><thead><tr><th>Catastrophe type</th><th>Dimensions of control variation</th><th>Potential function</th><th>Bifurcation set</th><th>Normalization formula</th></tr></thead><tbody><tr><td>Fold</td><td>1</td><td>f(x) = x<sup>3</sup> + ax</td><td>a = -3x<sup>2</sup></td><td>x<sub>a</sub> = &radic;a</td></tr><tr><td>Cusp</td><td>2</td><td>f(x) = x<sup>4</sup> + ax<sup>2</sup> + bx</td><td>a = -6x<sup>2</sup>, b = 8x<sup>3</sup></td><td>x<sub>a</sub> = &radic;a, x<sub>b</sub> = &radic;3b</td></tr><tr><td rowspan="2">Swallowtail</td><td rowspan="2">3</td><td>f(x) = (1/5)x<sup>5</sup> + (1/3)ax<sup>3</sup></td><td>a = -6x<sup>2</sup>, b = 8x<sup>3</sup>,</td><td>x<sub>a</sub> = &radic;a, x<sub>b</sub> = &radic;3b,</td></tr><tr><td>+ (1/2)bx<sup>2</sup> + cx</td><td>c = -3x<sup>4</sup></td><td>x<sub>c</sub> = &radic;4c</td></tr><tr><td rowspan="2">Butterfly</td><td rowspan="2">4</td><td>f(x) = (1/6)x<sup>6</sup> + (1/4)ax<sup>4</sup> + (1/3)bx<sup>3</sup></td><td>a = -10x<sup>2</sup>, b = 20x<sup>3</sup>,</td><td>x<sub>a</sub> = &radic;a, x<sub>b</sub> = &radic;3b,</td></tr><tr><td>+ (1/2)cx<sup>2</sup> + dx</td><td>c = -15x<sup>4</sup>, d = 4x<sup>5</sup></td><td>x<sub>c</sub> = &radic;4c, x<sub>d</sub> = &radic;5d</td></tr></tbody></table>

**Principles of finding values of catastrophe subordinate functions.** During the process of computation, we must follow two principles, i.e., a complementary and a non-complementary principle. The non-complementary principle means that the smallest of the state variable values corresponding to the control variables (x_a, x_b, x_c and x_d) is chosen as the state variable value of the whole system; However, the complementary principle implies x=(x_a+x_b+x_c+x_d)/4. Hierarchically doing the calculation in the same way, the value of the overall catastrophe subordinate function can be found [9].
**3 Results and discussion**

In the light of the evaluation methodology of rural informatization level
aforementioned, the paper take evaluation of rural informatization level among the six
provinces of central China as an example to test the effectiveness of the Catastrophe
Progression Method, and referred to interrelated data on Beijing and nationally
average in the mainland of China.

The central China is a central region, including six provinces, such as Shanxi, Anhui, Jiangxi, Henan, Hubei, and Hunan (see Fig.2), with total population of 360 million people in the end of 2008. It plays an important role on the pattern of economic and social development in China, which land area is 1.03 million square kilometers, Gross Regional Product of which reached 6.3188 trillion RMB Yuan in 2008, accounting for 19.3% of GDP in China.

<figure><img src="image_3.png" /><figcaption>**Fig.2.** Space diagram of the six provinces of central China.</figcaption></figure>

Taking data from reference [7], the region's overall number of communication
facilities was in place of four indices of information infrastructure in rural areas,
telecommunications and other information transfer service employees in place of
indices about the number of rural information service personnel, the proportion of
local comprehensive internet users in place of the proportion of internet users in rural
areas.

Table 3 showed some practical index values of the rural informatization level
among the six provinces of central in 2006, Table 4 showed the standardized data of
practical index values for the rural informatization level from the six provinces of
central China transformed by equations (1) and (2). At the same time, the scores of
rural informatization level among the six provinces of central China were calculated
using normalizing formula (see Table 5).
<table><caption>**Table 3.** Collected data from the six provinces of central China [7].</caption><thead><tr><th>Region</th><th>x<sub>11</sub></th><th>x<sub>12</sub></th><th>x<sub>13</sub></th><th>X<sub>21</sub></th><th>X<sub>22</sub></th><th>X<sub>23</sub></th><th>X<sub>24</sub></th><th>X<sub>31</sub></th><th>X<sub>32</sub></th><th>X<sub>33</sub></th><th>X<sub>41</sub></th><th>X<sub>42</sub></th><th>X<sub>51</sub></th><th>X<sub>52</sub></th></tr></thead><tbody><tr><td>Beijing</td><td>4.98</td><td>7066.08275</td><td>365</td><td>129</td><td>1788</td><td>21</td><td>133.2</td><td>36.1</td><td>104.3</td><td>95.5</td><td>37.6</td><td>1542.2</td><td>30.4</td></tr><tr><td>Shanxi</td><td>1.41</td><td>1729</td><td>3181</td><td>86.2</td><td>43.2</td><td>1445</td><td>4.4</td><td>98.4</td><td>1.38</td><td>72.1</td><td>95.6</td><td>9.8</td><td>564</td><td>11.3</td></tr><tr><td>Anhui</td><td>1.01</td><td>701</td><td>2969</td><td>78.5</td><td>23.7</td><td>1873</td><td>2.2</td><td>91.8</td><td>1.16</td><td>79.2</td><td>83.7</td><td>4.4</td><td>527.9</td><td>5.5</td></tr><tr><td>Jiangxi</td><td>1.08</td><td>704</td><td>3460108.0</td><td>40.3</td><td>1052</td><td>2.8</td><td>90.0</td><td>1.10</td><td>64.7</td><td>90.8</td><td>5.9</td><td>538.4</td><td>6.6</td></tr><tr><td>Henan</td><td>1.33</td><td>723</td><td>3261</td><td>62.4</td><td>31.3</td><td>1764</td><td>2.5</td><td>88.8</td><td>1.02</td><td>53.4</td><td>91.4</td><td>4.3</td><td>419.4</td><td>5.5</td></tr><tr><td>Hubei</td><td>1.33</td><td>836</td><td>3419</td><td>82.1</td><td>44.7</td><td>1234</td><td>3.9</td><td>92.1</td><td>2.33</td><td>57.3</td><td>90.2</td><td>8.6</td><td>538.4</td><td>9.3</td></tr><tr><td>Hunan</td><td>1.19</td><td>754</td><td>3390</td><td>73.4</td><td>31.7</td><td>1393</td><td>3.3</td><td>80.9</td><td>0.95</td><td>60.2</td><td>93.5</td><td>5.3</td><td>591.4</td><td>6.4</td></tr><tr><td>Nationally average</td><td>1.79</td><td>1417</td><td>3587106.8</td><td>47.3</td><td>752</td><td>5.02</td><td>89.4</td><td>2.7</td><td>62.5</td><td>90.69</td><td>7.4</td><td>593.9</td><td>10.5</td></tr></tbody></table>

Data source: Huang, 2009.

<table><caption>**Table 4.** Standardized data from the six provinces of central China.</caption><thead><tr><th>Region</th><th>x<sub>11</sub></th><th>x<sub>12</sub></th><th>x<sub>13</sub></th><th>X<sub>21</sub></th><th>X<sub>22</sub></th><th>X<sub>23</sub></th><th>X<sub>24</sub></th><th>X<sub>31</sub></th><th>X<sub>32</sub></th><th>X<sub>33</sub></th><th>X<sub>41</sub></th><th>X<sub>42</sub></th><th>X<sub>51</sub></th><th>X<sub>52</sub></th></tr></thead><tbody><tr><td>Beijing</td><td>1.000</td><td>1.000</td><td>1.000</td><td>1.000</td><td>1.000</td><td>1.000</td><td>1.000</td><td>1.000</td><td>1.000</td><td>1.000</td><td>1.000</td><td>1.000</td><td>1.000</td><td>1.000</td></tr><tr><td>Shanxi</td><td>0.101</td><td>0.162</td><td>0.040</td><td>0.079</td><td>0.185</td><td>0.669</td><td>0.117</td><td>0.335</td><td>0.012</td><td>0.367</td><td>1.008</td><td>0.165</td><td>0.129</td><td>0.233</td></tr><tr><td>Anhui</td><td>0.000</td><td>0.000</td><td>0.000</td><td>0.053</td><td>0.000</td><td>1.082</td><td>0.000</td><td>0.208</td><td>0.006</td><td>0.507</td><td>0.000</td><td>0.003</td><td>0.097</td><td>0.000</td></tr><tr><td>Jiangxi</td><td>0.018</td><td>0.000</td><td>0.093</td><td>0.151</td><td>0.158</td><td>0.290</td><td>0.032</td><td>0.174</td><td>0.004</td><td>0.222</td><td>0.602</td><td>0.048</td><td>0.106</td><td>0.044</td></tr><tr><td>Henan</td><td>0.081</td><td>0.003</td><td>0.055</td><td>0.000</td><td>0.072</td><td>0.977</td><td>0.016</td><td>0.151</td><td>0.002</td><td>0.000</td><td>0.653</td><td>0.000</td><td>0.000</td><td>0.000</td></tr><tr><td>Hubei</td><td>0.081</td><td>0.021</td><td>0.085</td><td>0.065</td><td>0.199</td><td>0.465</td><td>0.090</td><td>0.214</td><td>0.039</td><td>0.077</td><td>0.551</td><td>0.129</td><td>0.106</td><td>0.153</td></tr><tr><td>Hunan</td><td>0.045</td><td>0.008</td><td>0.079</td><td>0.036</td><td>0.076</td><td>0.619</td><td>0.059</td><td>0.000</td><td>0.000</td><td>0.134</td><td>0.831</td><td>0.030</td><td>0.153</td><td>0.036</td></tr><tr><td>Nationally average</td><td>0.196</td><td>0.112</td><td>0.116</td><td>0.147</td><td>0.224</td><td>0.000</td><td>0.150</td><td>0.163</td><td>0.050</td><td>0.179</td><td>0.592</td><td>0.093</td><td>0.155</td><td>0.201</td></tr></tbody></table>

Table 5 showed catastrophe progression values of the rural informatization level among the six provinces in central China. From Table 5, catastrophe progression values (CPV) of the rural informatization level averaged 0.793 in the mainland of China; CPV is bigger in only one province of the six provinces in the central China than nationally average in the mainland of China. CPV is larger in Beijing Municipality than in each region of the six provinces in the central China. Among the six provinces in the central China, CPV of Shanxi province is first with 0.800, Hubei province second with 0.773, Jiangxi province third with 0.722, Hunan province fourth with 0.714, Henan province and Anhui province least with 0.354 and 0.222, respectively. The results are found to be coincident with practical situation.

<table><caption>**Table 5.** The evaluation result by CPM.</caption><thead><tr><th>Region</th><th>Catastrophe progression values</th><th>No.</th><th>Region</th><th>Catastrophe progression values</th><th>No.</th></tr></thead><tbody><tr><td>Beijing</td><td>1.000</td><td></td><td>Henan</td><td>0.354</td><td>5</td></tr></tbody></table>
<table><tr><td>Shanxi</td><td>0.800</td><td>1</td><td>Hubei</td><td>0.773</td><td>2</td></tr><tr><td>Anhui</td><td>0.222</td><td>6</td><td>Hunan</td><td>0.714</td><td>4</td></tr><tr><td>Jiangxi</td><td>0.722</td><td>3</td><td>Nationally average</td><td>0.793</td><td></td></tr></table>

## 4 Conclusion

The paper takes evaluation of rural informatization level among the six provinces of central China as an example to verify the effectiveness of the method. Based on catastrophe progression method, it calculated the scores of rural informatization level among the six provinces of central China using normalizing formula. The results are found to be coincident with practical situation, so it proves the catastrophe progression method works well.

From the calculation process, it was found that catastrophe progression method works simply and quickly. So the method was proved feasible in practice and provides us a new way in solving the problems of multiple objects comprehensive evaluation [6].

**Acknowledgments.** Thanks are due to National Science & Technology Support Program (2008BAB38B06) and Project from the Ministry of Agriculture of China (The twelfth five-year plan of agriculture and rural informatization development in China (2011-2015)) for financial support.

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