## 2 Methods
### Prospect Strengths and Weaknesses Degree and Choquet Integral Solution Methods
#### 2.3.2 Comprehensive Prospect Strengths and Weaknesses Degree  
By portraying the differences between the Prospect Theory and the SIR method in the previous subsection, the prospect value function and the psychological weight function of the Prospect Theory are introduced to extend the classical SIR method, and the related methods are introduced into the recommendation of electricity sale packages. To summarize, in the actual decision-making process, the customer needs to judge the strengths and weaknesses of a certain electricity sale package compared with other electricity sale packages under each decision-making information, but the ordering of electricity sale packages under different decision-making information is not the same, and it needs to be combined with the corresponding ordering formula in order to arrive at the final ordering of electricity sale packages. The classical SIR method involves the use of the preference difference function to measure the advantages and disadvantages of an electricity sale package under each piece of decision information compared with other programs, and then weigh the decision information weight value to the advantages and disadvantages, and then the preference difference function can be defined independently. To this end, the prospect value function \(v(\Delta x)\) is expanded by replacing the comparison between the electricity sale package and the expected reference point (positive and negative ideal points) with a two-by-two comparison with the electricity sale package and utilizing the probabilistic linguistic deviation function to carve out the difference values between the electricity sale packages; the weighted psychological weighting function \(\omega(p)\) is used, and then the resultant function is defined as a preference difference function in the SIR method, in order to come up with a new degree of strengths and weaknesses that can take into account the customers' risk preference. The calculation formula is called prospect strengths and weaknesses degree. This innovation is a good solution to the problem of the subjectivity of customers in making decisions on electricity sale packages. To this end, we refer to the labeling system for evaluating electricity sale packages established in Section 2.2, and set \(U=\left\{u_{1},u_{2},\cdots,u_{l}\right\}(k=1,2,\cdots,l)\) as a finite set of customer sets, \(C=\left\{c_{1},c_{2},\cdots,c_{m}\right\}(i=1,2,\cdots,m)\) as a finite set of electricity sale packages, \(D=\left\{d_{1},d_{2},\cdots,d_{n}\right\}(j=1,2,\cdots,n)\) as a finite set of decision information, and \(Q=\left\{q_{1},d_{2},\cdots,q_{n}\right\}\) as the subjective weights of each decision information. Customermakes an evaluation matrix \(H_{k}=\left(h_{kjj}\right)_{m\gets n}\) of different electricity sale packages using probabilistic language under decision information \(d_{j}\), where \(h_{kjj}=<L_{kjj}\left(p_{kij}\right)>\) denotes the probabilistic language evaluation of electricity sale package \(c_{i}\) by customer \(u_{k}\) under decision information \(d_{j}\). When considering group decision-making, it is necessary to assemble the decision information of each customer. The Choquet integral described in the previous section is often used to determine the relevance of each piece of decision information, and the degree of correlation is solved by calculating the correlation coefficient. When dealing with non-negative functions in the context of electricity sale packages, we often encounter the need to define these functions in relation to a specific measure. Specifically, if \(f\) is a non-negative function defined on the set \(C\) of electricity sale packages, it becomes necessary to establish its relationship with a fuzzy measure \(u\) within the framework of the Choquet integral.