# Two-Sided Matching Decision Method of Electricity Sales Package Based on Disappointment Theory
## 4 Actual Case Analysis
### Case Analysis
#### 4.2.3 Calculation of the Disappointment Value and Elation Value of Both Parties  
After obtaining the subjective satisfaction matrix of both parties, the disappointment value, elation value, and adjusted satisfaction of the matching objects in \(P\) and \(Q\) can be calculated. For each power user \(P_{i}\) and electricity sales package \(Q_{j}\), set the sensitivity parameters of disappointment \(\alpha_{i}^{P}=\alpha_{j}^{Q}=0.8\), the degree of aversion to disappointment to \(\gamma_{i}^{P}=\gamma_{j}^{Q}=0.5\), and the sensitivity parameters of elation to \(\beta_{i}^{P}=\beta_{j}^{Q}=0.8\), where \(i=1,2,\ldots,5\), \(j=1,2,\ldots,6\). Taking \(R^{1}\) as an example, the disappointment value, elation value, and adjusted satisfaction of the power user are calculated. According to the subjective satisfaction matrix, the potential object set \(\theta^{P_{1}}=\{Q_{3},Q_{4},Q_{5},Q_{6}\}\) in \(Q\) that can match \(P_{1}\) is derived. We can get  
\[prob(P_{1},Q_{1})=prob(P_{1},Q_{2})=0,\] \[prob(P_{1},Q_{3})=prob(P_{1},Q_{4})=prob(P_{1},Q_{5})=prob(P_{1},Q _{6})=\frac{1}{4}\]  
It is known from the above results that \(P_{1}\) cannot match \(Q_{1}\) and \(Q_{2}\), i.e., \(\overline{u_{11}^{P}}=\overline{u_{12}^{P}}=1\). If \(P_{1}\) matches \(Q_{3}\) not \(Q_{4}\), \(P_{1}\) will be disappointed because \(u_{13}^{P}<u_{14}^{P}\). If \(P_{1}\) matches \(Q_{3}\), the set of matched objects that cause \(P_{1}\) to experience disappointment is \(\Delta_{13}^{DP}=\{Q_{4}\}\), and the value of disappointment is \(d_{13}^{P}=\frac{1}{4}\{1-\exp((0.7692-0.6468)\ln 0.8)\}=0.0029\). Similarly, if \(P_{1}\) matches \(Q_{4}\), \(Q_{5}\) or \(Q_{6}\), the disappointment value is  
\(d_{14}^{P}=0\)  
\(d_{15}^{P}=\frac{1}{4}\{1-\exp((0.6078-0.1708)\ln 0.8)+1-\exp((0.7592-0.1708) \ln 0.8)\}=0.0248\)  
\(d_{16}^{P}=\frac{1}{4}\{1-\exp((0.6468-0)\ln 0.8)\}+(1-\exp((0.7692-0)\ln 0.8))+(1- \exp((0.1818-0)\ln 0.8))\}=0.0376\). In addition, if \(Q_{3}\) matches \(P_{1}\), but not with \(Q_{5}\) or \(Q_{6}\), \(P_{1}\) will feel happy because \(u_{13}^{P}>u_{16}^{P},u_{13}^{P}>u_{15}^{P}\).Therefore, if \(Q_{3}\) matches \(P_{1}\), the set of matching objects that make \(P_{1}\) feel happy is \(\Delta_{13}^{EP}=\{Q_{5},Q_{6}\}\); then, the elation value is  
\[e_{13}^{P}=\frac{1}{4}\{(0.5-0.5\exp((0.6468-0.1818)\ln 0.8))+0.5-0.5\exp((0.6468 -0)\ln 0.8))=0.0131.\]  
Similarly, if \(P_{1}\) matches \(Q_{4}\), \(Q_{5}\), or \(Q_{6}\), \(P_{1}\)'s happy value is  
\(e_{14}^{P}=\frac{1}{4}\{0.5-0.5\exp((0.7692-0.6468)\ln 0.8)+0.5-0.5\exp((0.7692-0.1818)\ln 0.8)+0.5-0.5\exp((0.7692-0)\ln 0.8)=0.0174\)  
\(e_{15}^{P}=\frac{1}{4}\{(0.5-0.5\exp((0.1818-0)\ln 0.8))\}=0.0022\)  
\(e_{16}^{P}=0\). Further, the \(P_{1}\) satisfaction of other objects after adjustment is calculated. \[\overline{u_{13}^{P}}=0.6570,\overline{u_{14}^{P}}=0.7866,\overline{u_{15}^{P }}=0.1556,\overline{u_{16}^{P}}=-0.0376\]Similarly, the disappointment value \(d_{ij}^{P}\) and elation value \(e_{ij}^{P}\) (\(i=1,2\ldots 5\), \(j=1,2\ldots 6\)) of each power user for each electricity sales package can be calculated. Set \(D^{P}=(d_{ij}^{P})_{5\times 6}\), \(E^{P}=(e_{ij}^{P})_{5\times 6}\), \[D^{P}= \begin{pmatrix}-&-&0.0029&0&0.0248&0.0376\\ 0.0066&0.0031&0&-&-&0.0375\\ 0.0097&0.0361&-&0&0.0032&-\\ 0&-&0.0064&0.0444&0.0040&0.0114\\ 0&0.0343&-&0.0329&0.0089&0.0058\end{pmatrix} \] (61) \[E^{P}= \begin{pmatrix}-&-&0.0131&0.0174&0.0022&0\\ 0&0.0025&0.0650&-&-&0.0071\\ 0&0.0090&-&0.0611&0.0043&-\\ 0.0446&-&0.0064&0&0.0075&0.0135\\ 0.0536&0&-&0.0005&0.0102&0.0275\end{pmatrix} \] (62)  
The disappointment value \(d_{ij}^{Q}\) and elation value \(e_{ij}^{Q}\) (\(i=1,2\ldots 5\), \(j=1,2\ldots 6\)) of each power-selling company's power-selling package to electric power customers are calculated:  
\[D^{Q}= \begin{pmatrix}-&-&0.0499&0.0969&0.0749&0.0180\\ 0.0216&0.0599&0&-&-&0.0494\\ 0.0168&0&-&0.0114&0.0740&-\\ 0&-&0.0863&0.0796&0.0282&0.1039\\ 0.0431&0.0750&-&0&0&0\end{pmatrix}  \tag{63}\] \[E^{Q}=