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.