## 3 Materials and Methods
### Measuring the Coupling Coordination Degree  
Mongolian urbanization and residents' livelihood can be seen as two systems that affect each other and interact with one another. On the one hand, rapid urbanization in Mongolia causes social and economic development [21] and improves residents' livelihood [22]. Meanwhile, it also creates environmental pollution, traffic congestion, and other serious problems that affect residents' livelihood  
\begin{table}
\begin{tabular}{l l c c c c c} \hline \hline \multirow{2}{*}{**Index**} & \multirow{2}{*}{**Sub-Indicator**} & \multicolumn{6}{c}{**Weight (\(f\))**} \\ \cline{3-8}  & & **2004** & **2007** & **2010** & **2013** & **2016** \\ \hline \multirow{4}{*}{Education index} & Children in kindergarten & 0.1467 & 0.1533 & 0.1344 & 0.1528 & 0.1649 \\ \cline{2-8}  & Pupils in primary and secondary schools & 0.1051 & 0.1204 & 0.1278 & 0.1443 & 0.1503 \\ \cline{2-8}  & Student–teacher ratio in primary and secondary schools & 0.0368 & 0.0307 & 0.0771 & 0.0249 & 0.0288 \\ \hline \multirow{4}{*}{Security index} & Summary of recorded offense rates per 10,000 people aged 18 and above & 0.0354 & 0.0247 & 0.0329 & 0.0307 & 0.0242 \\ \cline{2-8}  & Number of crimes against human life & & & & & \\ and health & 0.0092 & 0.0099 & 0.0096 & 0.0097 & 0.0090 \\ \cline{2-8}  & Number of crimes against social safety & 0.0094 & 0.0099 & 0.0097 & 0.0097 & 0.0090 \\ \hline \hline \end{tabular} Note: Physicians per urban resident refers to the number of physicians divided by the number of urban residents; similarly, nurses per urban resident and pharmacists per urban resident refer to the numbers of nurses and pharmacists, respectively, divided by the number of urban residents. Unemployment rate refers to the proportion of the unemployed population to the economically active population, tanker trucks are the transportation means for water distribution, the probability of seeing professional arts per urban resident is the number of professional artworks divided by the number of urban residents, and museum exhibits per urban resident refers to the number of museum exhibits divided by the number of urban residents. These data are from the Statistical Yearbooks of Mongolia and the National Statistical Bureau of Mongolia ([[http://www.1212.mn/en/](http://www.1212.mn/en/)]([http://www.1212.mn/en/](http://www.1212.mn/en/))).  
\end{table}
Table 2: _Cont._level [20; 21; 58]. On the other hand, promoting residents' livelihood stimulates the government to improve urban infrastructure construction [10; 15], and the expansion of urban land may gradually spiral out of control [7]. The CCD can be seen as the coupling and coordination relationship between the \"level of urbanization\" system and the \"livelihood level of urban residents\" system. The specific calculation steps that were used here are described as follows:  
\[C=\left\{(U*L)/\big{[}\frac{(U+L)}{2}\big{]}^{2}\right\}^{K}, \tag{6}\]  
where \(C\) represents the coupling degree, \(U\) is the level of urbanization, \(L\) is the livelihood level of urban residents, \(K\) is the regulation factor, and \(K=2\) (because there are two systems, namely, the \"level of urbanization\" system and the \"livelihood level of urban residents\" system) [28; 59]:  
\[T=aU+bL. \tag{7}\]  
Here, \(T\) represents the overall effect of the level of urbanization and the livelihood level of urban residents [19], \(a\) and \(b\) represent the contributions of the level of urbanization and the livelihood level of urban residents, respectively, and \(a+b=1\). Based on the equal importance of the level of urbanization and the livelihood level of urban residents, we assumed that their contributions were the same, and thus \(a\) and \(b\) are both equal to 0.5 [19; 30]:  
\[D=\sqrt{C*T}, \tag{8}\]  
where \(D\) is the coupling coordination degree and \(0\leq D\leq 1\). When the value of \(D\) is greater, the coupling and coordination between the level of urbanization and the livelihood level of urban residents is better [59].