## 2 Methods
### Prospect Strengths and Weaknesses Degree and Choquet Integral Solution Methods  
#### 2.3.1 Prospect Theory and the SIR Method  
Synthesizing the results of a large number of experiments, it can be seen that the variable environmental factors will produce different degrees of interference to the customer's decision-making, and the customer's decision-making is not completely rational. In order to accurately reflect the irrational psychology of the customer's decision-making process, [PERSON] and [PERSON] [45] used the value function and the weight function to represent the utility and probability in the expected utility, and proposed the Prospect Theory for representing the psychological characteristics of risk preference and aversion. Prospect Theory is an analytical theory used to describe the psychological behavior of customers under different conditions. According to Prospect Theory, the criterion that customers judge in the decision-making process is the prospect value of an alternative determined by the prospect value function and the psychological weight function. Among other things, the prospect value function describes how people assess the value of gaining or losing something. The expression of the prospect value function \(v(\Delta x)\) is [31]:  
\[v(\Delta x)=\left\{\begin{array}{l}(\Delta x)^{\alpha},\Delta x\geq 0\\ -\theta(-\Delta x)^{\beta},\Delta x<0\end{array}\right. \tag{3}\]  
where \(\Delta x\) is the positive or negative deviation between the decision value and the reference point; \(\alpha\) and \(\beta\)\((0<\alpha,\beta<1)\) are the risk attitude coefficients; and \(\theta(\theta>1)\) is the loss aversion coefficient, with the larger the value, the higher the risk aversion of the customer.  
The mental weighting function \(\omega(p)\) serves as a crucial tool in understanding how individuals assign weights to different probabilistic events. This function is essential in capturing the subjective perception of risk and uncertainty that people hold. It is calculated as follows, based on established methodologies outlined in the literature [31]. By utilizing this function, researchers can gain insight into how people evaluate the likelihood and consequences of various outcomes, which in turn can influence their decision-makingprocesses. Understanding the mental weighting function is thus critical for predicting and explaining human behavior in situations involving uncertainty.  
\[\left\{\begin{array}{l}\omega^{+}(p)=\frac{p^{\delta}}{\left(p^{\delta}+(1-p)^{ \delta}\right)^{\frac{1}{\delta}}}\\ \omega^{-}(p)=\frac{p^{\delta}}{\left(p^{\delta}+(1-p)^{\delta}\right)^{\frac{1 }{\delta}}}\end{array}\right. \tag{4}\]  
where \(\omega^{+}(p)\) and \(\omega^{-}(p)\) are nonlinear weighting functions for gains and losses; p is the associated probability of occurrence; and \(\xi\) and \(\delta\) are the risk attitude coefficients for gains and losses, respectively.  
In summary, it can be seen that the prospect value function portrays the subjective judgment of the customer's decision-making, and the existing related studies have failed to compare the programs directly. If the objective factors can be considered comprehensively in the Prospect Theory and a function can be drawn to compare the two programs, it will be more in line with the real decision-making situation.  
In the ranking method of portraying the two-by-two differences in programs, some studies will use the classical SIR method [46]. The SIR method, i.e., Superiority-Inferiority Ranking method, constructs a clear strengths and weaknesses matrix by directly comparing the high and low values of each program. With the help of scientific multi-attribute information comprehensive processing technology, the SIR method can accurately calculate the strength and weakness flow of each program. Based on the results of these analyses, we can partially or fully determine the ranking of all options.