## 2 Methodology
### Setting of Reference Points  
First, let \(t\) represent the phase in which the sample customers give comprehensive ratings for electricity sales packages, where \(t\ =\ 1,2,\ldots,h\), and the corresponding weights are \(\lambda_{t}\), with \(0\ \leq\ \lambda_{t}\ \leq 1\) and \(\sum\limits_{t\ =\ 1}^{h}\lambda_{t}\ =\ 1\). The set of electricity sales packages is \(A\ =\ \{A_{1},A_{2},\ldots,A_{k},\ldots,A_{k}\}\), and the sample customer set is \(R\ =\ \{R_{1},R_{2},\ldots,R_{i},\ldots,R_{I}\}\), with corresponding customer weights \(\mu_{i}\), where \(i\ =\ 1,2,\ldots,I\) and \(0\ \leq\ \mu_{i}\ \leq 1\). For each sample customer within a given category, the sum of the customer weights within that category equals 1. The set of attributes used to comprehensively evaluate the electricity sales packages is \(C_{R}\ =\ \{C_{R,1},C_{R,2},\ldots,C_{R,j},\ldots,C_{R,J}\}\). Without loss of generality, consider the first \(y\) attributes as quantitative attributes and the remaining \(J-y\) attributes as qualitative attributes. Let the sets of quantitative and qualitative attributes be \(\{C_{1},C_{2},\ldots,C_{y}\}\) (where \(1\leq y\leq J\)) and \(\{C_{y+1},C_{y+2},\ldots,C_{J}\}\), respectively. The weights of each attribute are \(\omega_{j}\), where \(j\ =\ 1,2,\ldots,J,0\ \leq\ \omega_{j}\ \leq 1\), and \(\sum\limits_{j\ =\ 1}^{J}\omega_{j}\ =\ 1\).  
Next, in this paper, the quantitative attributes and qualitative attributes are described using three-parameter interval gray numbers and triangular fuzzy numbers, respectively. The specific calculation formulas are given below [34].  
Let \(a(\otimes)\ =\ [a_{1},a_{2},a_{3}]\) and \(b(\otimes)\ =\ [b_{1},b_{2},b_{3}]\) be three-parameter interval gray numbers (triangular fuzzy numbers), then  
\[d(a(\otimes),b(\otimes))\ =\ k_{1}|a_{2}-b_{2}|+k_{2}|a_{1}-b_{1}|+(1-k_{1}-k_{2} )|a_{3}-b_{3}|, \tag{15}\]  
where \(d(a(\otimes),b(\otimes))\) represents the distance between the three-parameter interval gray number (triangular fuzzy number) \(a(\otimes)\) and \(b(\otimes)\), with \(0\leq k_{1}\leq 0.5\) and \(0.5\leq k_{2}\leq 1\). This formula still applies when either \(a(\otimes)\) or \(b(\otimes)\) degenerates into a real number.  
Below is the method for comparing the size of three-parameter interval gray numbers (triangular fuzzy numbers).  
Let \(a(\otimes)\ =\ [a_{1},a_{2},a_{3}]\) and \(b(\otimes)\ =\ [b_{1},b_{2},b_{3}]\) be three-parameter interval gray numbers (triangular fuzzy numbers), where \(d(a_{3}-a_{2})\) represents the distance between the real numbers \(a_{3}\) and \(a_{2}\). The comparison rules are as follows:  
1. When \(a_{2}>b_{2}\), then \(a(\otimes)>b(\otimes)\).
2. When \(a_{2}\ =\ b_{2}\), the comparison is based on the following: * If \(d(a_{3}-a_{2})-d(a_{2}-a_{1})>d(b_{3}-b_{2})-d(b_{2}-b_{1})\), then \(a(\otimes)>b(\otimes)\). * If \(d(a_{2}-a_{1})\ =\ d(b_{2}-b_{1})\) and \(d(a_{3}-a_{2})\ =\ d(b_{3}-b_{2})\), then \(a(\otimes)\ =\ b(\otimes)\). * If \(d(a_{3}-a_{2})-d(a_{2}-a_{1})>d(b_{3}-b_{2})-d(b_{2}-b_{1})\) and \(d(a_{3}-a_{2})<d(b_{3}-b_{2})\), then \(a(\otimes)>b(\otimes)\).  
For the qualitative attributes of the electricity sales packages, the linguistic variables for the comprehensive ratings and their corresponding triangular fuzzy numbers are shown in Table 1.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Language Variables** & **Very Poor** & **Poor** & **Slightly** & **Fair** & **Slightly** & **Good** & **Very Good** \\ \hline Corresponding triangular fuzzy numbers & (0, 1, 2) & (1, 2, 3) & (2, 3, 4) & (3, 4, 5) & (4, 5, 6) & (5, 6, 7) & (6, 7, 8) \\ \hline \hline \end{tabular}
\end{table}
Table 1: Attribute linguistic variables and corresponding triangular fuzzy numbers.