3.1 Model Methodology
Analytic Hierarchy Process (AHP) decomposes the elements related to the decision object into goal level, indicator level and other levels, etc. It is an easy way to make decisions for some more complex and ambiguous problems, and the analysis process is more suitable for multi-level interleaved goal systems, and the goal values are difficult to describe the decision problem quantitatively [19, 20]. The steps to construct the hierarchical model are as follows.
(1) Construct a pairwise comparison judgment matrix.
(2) The matrix weights are calculated by normalizing the matrix corresponding to the maximum eigenvalue λmax.
\begin{equation} \lambda_{\max}=\frac{1}{n}\sum_{i=1}^{n}\frac{BW_{n}}{W_{i}}\text{\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ }\ (4)\nonumber \\ \end{equation}
(3) The eigenvectors corresponding to the maximum eigenvalues are used as the weight vectors to compare the influence of each factor on a factor in the upper level. The consistency index is calculated as.
\begin{equation} CI=\frac{\lambda-n}{n-1}\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ (5)\nonumber \\ \end{equation}
(4) Calculate the weights of the primary and secondary indicators respectively
(5) Calculate the Low Carbon Index (LCI). The scores of the second-level indicators are multiplied by the weights of the second-level indicators and added together to obtain the scores of the corresponding first-level indicators, and then the scores of the first-level indicators are weighted and added together to obtain the total score of the low-carbon evaluation of clean energy use, which is called the ”Low Carbon Index”, and the detailed calculation formula is as follows.
\begin{equation} Q_{i}=\sum_{i=1}^{n}{W_{j}Q_{j}}\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ (6)\nonumber \\ \end{equation}\begin{equation} LCI=\sum_{i=1}^{6}{W_{i}Q_{i}}\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ (7)\nonumber \\ \end{equation}
Where Qj denotes the evaluation score of secondary indicators, Wj denotes the weight of secondary indicators, Qi denotes the sum of the scores of primary indicators, Wi denotes the weight of primary indicators, and LCI denotes the low carbon index.
(6) Based on the above calculation results, the low-carbon performance of rural residential buildings is judged, and for high-carbon residential buildings, this study hopes to achieve low carbonization through retrofitting.