## 2 Theory and Methodology
### Research Method
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Code** & **Factor** & **Description** \\ \hline B1 & Housing environment & Space, quality, structure, decoration, and utilization of the residents’ houses \\ \hline B2 & Road environment & Traffic convenience, accessibility, and road conditions \\ \hline B3 & Healthcare environment & Medical resources to cure diseases, health examination, and insurance of the physical and mental health of the residents. \\ \hline B4 & Hygienic environment & Clean water, fresh air, green food, and household waste disposal system \\ \hline B5 & Ecological environment & Conditions that influence the sustainable inter-relationship of the living organisms \\ \hline B6 & Security environment & Protection of people’s lives and property security \\ \hline B7 & Cultural activities & Celebration of traditional festivals and heritage of rural culture \\ \hline B8 & Inhabitation by outsiders & Immigrants who inhabit in the settlements because of work or vacation \\ \hline B9 & Policy support & Policy from the government to support the residents’ daily lives as well as tourism \\ \hline B10 & Distribution of benefits & Benefits received on land that is under collective ownership and are distributed by village officials \\ \hline B11 & Manage status & Government’s establishment of the rules, goals, and strategic plans, as well as the operation of it \\ \hline B12 & Land circulation subsidy & Money that is paid by the government to the residents to acquire their agriculture and housing land \\ \hline B13 & Working environment & Physical environment, facilities, tools, teamwork communication, and working atmosphere \\ \hline B14 & Economic income & Wage, welfare, bonus, social insurance, paid vacation, interests, business income \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Description of 14 factors. Ten experts were invited to score the relative importance of the factors from a scale of one to nine, based on a pairwise comparison proposed by [PERSON] [33; 34; 35]. Six of the experts were professors of rural development from the universities, and four of them were experts from government planning sectors. The factors within each layer were compared with each other, and a pairwise comparison matrix (aka. judgment matrix) were thus generated. The elements in the matrix represented the relative ratio of the corresponding two factors. Objective-criterion judgment matrix  
\[ZA= \begin{bmatrix}&A_{1}&A_{2}&A_{3}&A_{4}\\ A_{1}&1&2.353&1.270&1.455\\ A_{2}&0.425&1&0.540&0.618\\ A_{3}&0.787&1.853&1&1.145\\ A_{4}&0.688&1.618&0.873&1\end{bmatrix}  \tag{1}\]  
Criterion-index judgment matrix  
\[A_{1}B= \begin{bmatrix}&B_{1}&B_{2}&B_{3}&B_{4}&B_{5}\\ B_{1}&1&2.185&1.686&1.903&0.808\\ B_{2}&0.458&1&0.771&0.871&0.370\\ B_{3}&0.593&1.296&1&1.129&0.479\\ B_{4}&0.525&1.148&0.886&1&0.425\\ B_{5}&1.237&2.704&2.086&2.355&1\end{bmatrix}  \tag{2}\]  
\[A_{2}B= \begin{bmatrix}&B_{6}&B_{7}&B_{8}\\ B_{6}&1&1.093&3.105\\ B_{7}&0.915&1&2.842\\ B_{8}&0.322&0.352&1\end{bmatrix}  \tag{3}\]  
Figure 1: The hierarchical structure of multi-dimensional environment evaluation system. \[A_{3}B= \begin{bmatrix}&B_{9}&B_{10}&B_{11}&B_{12}\\ B_{9}&1&1.189&0.815&1.073\\ B_{10}&0.841&1&0.685&0.902\\ B_{11}&1.227&1.459&1&1.317\\ B_{12}&0.932&1.108&0.759&1\end{bmatrix}  \tag{4}\]  
\[A_{4}B= \begin{bmatrix}&B_{13}&B_{14}\\ B_{13}&1&0.893\\ B_{14}&1.120&1\end{bmatrix}  \tag{5}\]  
(2) Calculate the indicators' weight  
The calculation of factor weights was performed by the sum-product method. The judgment matrix was first normalized by columns, and then summed by rows to obtain the row vector \(\alpha\). \[\alpha=(\alpha_{1},\alpha_{2},\ldots,\alpha_{n})^{T}, \tag{6}\]  
where \(\alpha_{i}=\sum_{j=1}^{m}q_{ij},\text{ and }q_{ij}=\frac{a_{ij}}{\sum_{k=1}^{n}a _{ij}}\). \(a_{ij}\) was the element of the \(i\)th row and \(j\)th column in the judgement matrix. The vector \(\alpha\) was normalized to obtain the weight coefficient vector W = (w1, w2, \(\cdots\), wn), and wi represented the weight of indicator \(i\).