# Two-Sided Matching Decision Method of Electricity Sales Package Based on Disappointment Theory
## 3 Matching Method between Power User Demand and Power-Selling Package of Power-Selling Company
### Two-Sided Matching Decision Based on Disappointment Theory
On the one hand, because the packages in the collection \(\left\{Q_{1},Q_{2},\ldots,Q_{j-1}\right\}\) are inferior to \(Q_{j}\), power user \(P_{i}\) will feel happy because they do not match them. On the other hand, because the packages in the collection \(\left\{Q_{j+1},Q_{j+2},\ldots,Q_{m}\right\}\) are better than \(Q_{j}\), power user \(P_{i}\) will be disappointed because they do not match them. In the same way, the same is true for the electricity sales package \(Q_{j}\). Therefore, to evaluate the satisfaction of electric power customers and electricity sales packages with the matching results, we need to consider the disappointment-elation perception of both sides, so that we can more accurately describe the satisfaction degree of electric power customers and electricity sales packages. Because there is a lack of subjective evaluation elements in the subjective satisfaction matrix of electric power customers \(U^{P}=\left(u_{ij}^{P}\right)_{n\times m}\) and the subjective satisfaction matrix of electricity sales packages \(U^{Q}=\left(u_{ij}^{Q}\right)_{n\times m}\), we build a collection:  
\[\Theta^{P_{i}}=\left\{Q_{j}\Big{|}u_{ij}^{P}\
eq-M\&u_{ij}^{Q}\
eq-M,j\in I \right\},\ i\in I \tag{21}\]  
\[\Theta^{Q_{j}}=\left\{P_{i}\Big{|}u_{ij}^{P}\
eq-M\&u_{ij}^{Q}\
eq-M,i\in I \right\},\ j\in I \tag{22}\]  
Set (21) refers to the set of electricity sales packages that can match each \(P_{i}\) in the electricity sales package set \(Q\). Set (22) represents the set of electric power customers that can match each \(Q_{j}\) in the power user set \(P\) for the power sales package. If the power user \(P_{i}\) matches the \(P_{i}\) electricity sales package \(Q_{j}\), \(\overline{u_{ij}^{P}}\) means that the correction of subjective satisfaction degree after adding the disappointment-elation feeling of the power user, according to the definition, \(\overline{u_{ij}^{P}}\) can be expressed as  
\[\overline{u_{ij}^{P}}=\left\{ \begin{array}{ll}u_{ij}^{P}-d_{ij}^{P}+e_{ij}^{ P}&Q_{j}\in\Theta^{P_{i}}\\ u_{ij}^{P}&,\ Q_{j}\
ot\in\Theta^{P_{i}}\end{array} \right.,\ i\in I \tag{23}\]  
In formula (23), \(d_{ij}^{P}\) represents the user \(P_{i}\)'s disappointment value, and \(e_{ij}^{P}\) represents the user \(P_{i}\)'s elution value. For the matching object \(Q_{j}\in\Theta^{P_{i}}\), if there is a certain electricity sales package \(Q_{l}\in\Theta^{P_{i}}\), leading to \(u_{ij}^{P}<u_{il}^{P}\), then the power user \(P_{i}\) will be disappointed when matching with the electricity sales package \(Q_{j}\) instead of matching \(Q_{l}\). Set the collection \(\Delta_{ij}^{DP}=\left\{Q_{l}\Big{|}u_{ij}^{P}<u_{il}^{P}\&Q_{l}\in\Theta^{P_{ i}}\right\}\) as a collection of objects that will cause \(P_{i}\) disappointment after matching with \(Q_{j}\). At this time, the user \(P_{i}\)'s disappointment value can be calculated using the following formula:  
\[d_{ij}^{P}=prob(P_{i},Q_{l})\sum_{Q_{l}\in\Delta_{ij}^{DP}}D_{i}(u_{il}^{P}-u_ {ij}^{P}),\ \forall Q_{l}\in\Delta_{ij}^{DP},\ Q_{j}\in\Theta^{P_{i}},\ i\in I \tag{24}\]  
In the same way, \(Q_{l}\in\Theta^{P_{i}}\) can also exist, leading to \(u_{ij}^{P}>u_{il}^{P}\), such that \(P_{i}\) will feel happy when matching with \(Q_{j}\) instead of \(Q_{l}\). Set the collection \(\Delta_{ij}^{EP}=\left\{Q_{l}\Big{|}u_{ij}^{P}>u_{il}^{P}\&Q_{l}\in\Theta^{P_{ i}}\right\}\) as the collection of objects for which \(P_{i}\) will produce a sense of elation after matching with \(Q_{j}\). At this time, the user \(P_{i}\)'s happiness value can be calculated using the following formula:  
\[e_{ij}^{P}=prob(P_{i},Q_{l})\sum_{Q_{l}\in\Delta_{ij}^{EP}}E_{i}(u_{ij}^{P}-u_ {il}^{P}),\ \forall Q_{l}\in\Delta_{ij}^{EP},\ Q_{j}\in\Theta^{P_{i}},\ i\in I \tag{25}\]  
In formulas (24) and (25), the \(prob(P_{i},Q_{l})\) reciprocal of the number of electricity sales packages that disappoint power user \(P_{i}\) and the reciprocal of the number of electricity sales packages that delight power user \(P_{i}\) are respectively expressed as follows:  
\[prob(P_{i},Q_{l})=\left\{