4.1 Method for Allocating Weights to Early Warning Indexes
Given that the factors influencing China’s technological security are diverse, and these factors are interrelated and mutually constraining, they exhibit characteristics of complexity, dynamism, and uncertainty. Therefore, the use of purely quantitative methods to conduct a comprehensive assessment of technological security has limited explanatory power. Additionally, the factors influencing technological security have strong randomness, so relying solely on quantitative methods may lead to a significant discrepancy between the evaluation results and the actual situation. In view of the above circumstances, this study chooses to use the Analytic Hierarchy Process (AHP), which combines quantitative and qualitative methods, to determine the variable weighting and operational logic of the technological security comprehensive evaluation and warning in China. This method can deal with the complex relationships between various factors in a more comprehensive manner. It not only makes full use of the information from quantitative data but also combines expert experience and qualitative analysis to improve the comprehensiveness and accuracy of the evaluation. This integrated approach helps to more comprehensively understand and warn of the risks to China’s technological security.
AHP is a quantitative analysis method used to address multi-criteria decision-making problems. It breaks down a complex problem into manageable modules by structuring it into a hierarchy, consisting of the goal, the criteria, and the alternatives. By comparing and inducing, AHP can combine subjective judgment with objective data to obtain the relative weights of various factors, providing a scientific basis for decision-making[20].
The main idea of using AHP method to allocate weights to indexes in this paper is: Utilizing Saaty’s 1–9 scale method[21], to compare and score the importance of indexes within the same level two by two, and then construct the corresponding judgment matrix based on the scores obtained. Subsequently, conduct a consistency check of the judgment matrix. If it does not meet the consistency requirements, the judgment matrix needs to be reconstructed until the consistency requirements are satisfied. The specific steps are as follows.
4.1.1 Judgment Matrix Construction
The first step is to invite an expert panel to score the weights of the criteria layer and the index layer in accordance with the actual situation of early warning for public safety risks in county-level societies. The 1–9 scale method is used to determine the scores. For a given layer, when comparing the importance of the i-th element relative to the j-th element with respect to a factor of the previous layer, the quantified relative importance is represented by \({a}_{ij}\). If there are n elements involved in the comparison, the final Judgment Matrix A will be obtained as follows, with the corresponding elements being \({a}_{ij}\).
$$A=\left[\begin{array}{cccc}{a}_{11}& {a}_{12}& \cdots & {a}_{1n}\\ {a}_{21}& {a}_{22}& \cdots & {a}_{2n}\\ ⋮& ⋮& \ddots & ⋮\\ {a}_{n1}& {a}_{n2}& \cdots & {a}_{nn}\end{array}\right]$$
The Matrix A has the following characteristics:
(1) \({a}_{ij}\)represents the importance of index i compared to index j.
(2) When i = j, the two indexes are the same, and therefore equally important, denoted as 1, which means the main diagonal elements are 1.
(3) \({a}_{ij}>0\)and satisfies the condition \({a}_{ij}\times {a}_{ji}=1\).
4.1.2 Calculation of Single-Layer Weight Ranking and Consistency Check
The calculation of single-layer weight ranking is based on the established judgment matrix to calculate the weights representing the order of importance of relevant indexes at the current layer relative to a certain index at the previous layer. The calculation involves normalizing all elements in the Judgment Matrix A and then determining the value of \({\stackrel{-}{a}}_{ij}\) using Formula 1.
\({\stackrel{-}{a}}_{ij}=\frac{{a}_{ij}}{{\sum }_{k=1}^{n}{a}_{kj}}\) 1
After normalizing the matrix, sum up the columns in the same row to obtain \({\stackrel{-}{w}}_{i}\) using Formula 2.
\({\stackrel{-}{w}}_{i}=\sum _{j=1}^{n}{\stackrel{-}{a}}_{ij}\) 2
Divide the sum of the index vectors by n to get the weight vector, that is, \({w}_{i}=\frac{\stackrel{-}{{w}_{i}}}{n}\), and determine the largest characteristic root\({ \lambda }_{max}\) using Formula 3.
\({\lambda }_{max}=\frac{1}{n}\sum _{i=1}^{n}\frac{{\left(Aw\right)}_{i}}{{w}_{i}}\) 3
Perform a consistency check on the data to evaluate the rationality and reliability of the judgment matrix, ensuring that the decision-making results are reliable and credible. The Consistency Index (CI) is obtained using Formula 4.
\(CI=\frac{{\lambda }_{max}-n}{n-1}\) 4
CI = 0 indicates perfect consistency, and the larger the CI, the less consistent it is.
Finally, solve for the CR value using Formula 5 to determine if its consistency is acceptable.
\(CR=\frac{CI}{RI}\) 5
RI refers to the Random Consistency Index, obtained from a value table. When CR equals 0, the matrix has perfect consistency; when CR is less than 0, the matrix has satisfactory consistency; when CR is greater than 0.1, the matrix lacks consistency and should be adjusted.
4.1.3 Calculation of the Total Hierarchical Ranking of Weights
The calculation of the weights representing the relative importance of all factors at a certain layer with respect to the top layer is known as the total hierarchical ranking. To achieve the final objective of the AHP, the composite weights of the indexes at each layer with respect to the goal are calculated sequentially from the bottom up.
4.2 Determination of the Weights of the Early Warning Index System
4.2.1 Data Source
The data for determining the weights of early warning indexes for the public security risks of county-level societies in Yangtze River Delta region using the AHP method was obtained from expert consultations. The selected experts scored the questionnaire designed based on the public security risk early warning indexes of a certain county society in the Yangtze River Delta region, and then these data were collected and organized.
4.2.2 Construction of Judgment Matrix
To reasonably evaluate the factors of public security risk early warning in a certain county society of the Yangtze River Delta region, 8 experts were invited, including 3 government department personnel, 3 university researchers, and 2 security assessment agency managers. These experts possess a high theoretical level and rich practical experience in the management of public security risk early warning at the county level. Therefore, their scores for the relative impact of the public security risk early warning indexes in the said county society can ensure representative assessment results.
The expert review method was used. The highest and lowest values were eliminated, and then the average score was calculated to determine the value of the assessment factors. Pairwise comparisons are made between factors at the same layer to construct the Judgment Matrix A for the goal layer.
$$A=\left[\begin{array}{cccc}1& 3& 5& 2\\ \frac{1}{3}& 1& 2& \frac{1}{2}\\ \frac{1}{5}& \frac{1}{2}& 1& \frac{1}{4}\\ \frac{1}{2}& 2& 4& 1\end{array}\right]$$
The importance scores between the indexes at the index layer were compared using the same method to construct the Comparative Judgment Matrices\({ B}_{1}-{B}_{4}\).
\({B}_{1}=\left[\begin{array}{ccc}1& \frac{1}{2}& 3\\ 2& 1& 5\\ \frac{1}{3}& \frac{1}{5}& 1\end{array}\right]\) \({B}_{2}=\left[\begin{array}{ccccc}1& \frac{1}{3}& 3& 4& 2\\ 3& 1& 4& 5& 6\\ \frac{1}{3}& \frac{1}{4}& 1& 2& \frac{1}{2}\\ \frac{1}{4}& \frac{1}{5}& \frac{1}{2}& 1& \frac{1}{3}\\ \frac{1}{2}& \frac{1}{6}& 2& 3& 1\end{array}\right]\)
\({B}_{3}=\left[\begin{array}{ccc}1& \frac{1}{3}& 2\\ 3& 1& 5\\ \frac{1}{2}& \frac{1}{5}& 1\end{array}\right]\) \({B}_{4}=\left[\begin{array}{ccc}1& 2& 3\\ \frac{1}{2}& 1& 2\\ \frac{1}{3}& \frac{1}{2}& 1\end{array}\right]\)
4.2.3 Determination of Weights and Consistency Check
Considering the large amount of expert subjective experience involved in establishing the judgment matrix, a consistency check is required to eliminate obvious logical errors due to subjectivity. The weights of each judgment matrix were calculated using Formulas 1 and 2, and then the consistency check was conducted using Formulas 3, 4, and 5. The weight vectors of each matrix and the results of the consistency check are shown in Table 3.
Table 3
Judgment Matrix | w1 | w2 | w3 | w4 | w5 | \({\lambda }_{max}\) | CR |
A | 0.4758 | 0.1544 | 0.0813 | 0.2884 | - | 4.0211 | 0.0079 |
B1 | 0.3092 | 0.5813 | 0.1096 | - | - | 3.0037 | 0.0032 |
B2 | 0.2247 | 0.4855 | 0.0946 | 0.06 | 0.1352 | 5.2047 | 0.0457 |
B3 | 0.2299 | 0.6479 | 0.1222 | - | - | 3.0037 | 0.0032 |
B4 | 0.5390 | 0.2973 | 0.1638 | - | - | 3.0092 | 0.0079 |
4.2.4 Overall Weight Ranking
The final weights of the public security and health risk early warning index system for county-level societies in the Yangtze River Delta region were obtained by multiplying the weight values of the corresponding criteria and indexes, as shown in Table 4.
Table 4
Weighted Overall Ranking Table
A | B1 | B2 | B3 | B4 | Overall Weight Ranking |
0.4758 | 0.1544 | 0.0813 | 0.2884 |
b11 | 0.3092 | - | - | - | 0.1471 |
b12 | 0.5813 | - | - | - | 0.2766 |
b13 | 0.1096 | - | - | - | 0.0521 |
b21 | - | 0.2247 | - | - | 0.0347 |
b22 | - | 0.4855 | - | - | 0.0750 |
b23 | - | 0.0946 | - | - | 0.0146 |
b24 | - | 0.0600 | - | - | 0.0093 |
b25 | | 0.1352 | | | 0.0209 |
b31 | - | - | 0.2299 | - | 0.0187 |
b32 | - | - | 0.6479 | - | 0.0527 |
b33 | - | - | 0.1222 | - | 0.0099 |
b41 | - | - | - | 0.5390 | 0.1554 |
b42 | - | - | - | 0.2973 | 0.0857 |
b43 | - | - | - | 0.1638 | 0.0472 |
According to the data in Table 4, it can be seen that within the dimension of public security and health risks, the factor with the highest weight is the management system, with a weight value of 0.2766, followed by the risk response factor, and finally the collaborative cooperation factor. This indicates that urbanization has a significant impact on the management system, risk response, and collaborative cooperation factors within the dimension of public security and health risks in county-level societies in the Yangtze River Delta region, and is more likely to trigger social risks.
Within the dimension of migrant population risks, the factor with the highest weight is the social status of the migrant population, with a weight value of 0.0750, followed by the economic income of the migrant population, the public security situation of the county, the employment environment of the county, and the governance policies for the migrant population. This indicates that during the process of urbanization, the return of migrant workers to their hometowns and the integration of farmers into county towns are most sensitive to changes in their own social status and economic income. These two factors are also more likely to trigger the occurrence of social risks at the county level.
Within the dimension of the mass incident risks, the factor with the greatest weight is the public opinion following the occurrence of mass incidents, with a weight value of 0.0527, followed by work effectiveness and production accident factors. This suggests that urbanization has a significant impact on the public opinion factor within the dimension of the mass incident risks in the counties of the Yangtze River Delta region, making it more prone to social risks.
Within the dimension of natural disaster risks, the factor with the highest weight is disaster resilience, with a weight value of 0.1554, followed by the types of disasters affecting the county and the number of affected people and houses within the county. This indicates that in the process of response to natural disasters by the counties in the Yangtze River Delta, disaster resilience has the most significant impact on the risk of natural disasters.