## 3 Fuzzy Generation  
Fuzzy mathematics is a mathematical tool for dealing with uncertain information, which is developed on the basis of fuzzy set theory. Different from traditional probability theory and statistics, fuzzy mathematics does not deal with the uncertainty of randomness but with the uncertainty caused by various reasons (such as fuzziness, incompleteness, imprecision, etc.). In view of the fuzzy phenomenon in the research, the introduction of fuzzy mathematics theory can deal with the shortcomings of traditional mathematics in dealing with fuzzy problems [13; 14; 15; 16]. In the study of sound quality, we found a fuzzy problem in that researchers only chose the mean of subjective evaluation scores as the final score. However, here is the fact that all scores for the same sample should be reasonable after the correlation test. There are subtle differences in how people perceive the same sample, and this uncertainty is reflected  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Sample** & **SPL** & **A-SPL** & **Loudness** & **Sharpness** & **Roughness** & **Fluctuation** & **AI** & **Score** \\ \hline
1 & 74.96 & 69.05 & 25.08 & 1.380 & 0.112 & 0.102 & 72.72 & 8.92 \\
2 & 75.18 & 69.62 & 27.83 & 1.555 & 0.120 & 0.095 & 75.64  
in the study of sound quality. Therefore, there is a certain fuzziness in the final results of subjective evaluation. In our study, 12 scores are given for one noise sample, and the minimum and maximum values constitute the maximum reasonable interval of subjective evaluation scores. To improve the universality of subjective evaluation results, we use a method of fuzzy generation to obtain a sufficient number of sample points within the maximum reasonable interval. The functions of the fuzzy generation method are as follows: it can not only be used to measure the ambiguity of each sample point in the interval but also to determine the interval range and way of sample generation. For the same sample, we set up a fuzzy interval of sample generation with the mean score as the kernel and the extreme score as a boundary. The fuzzy intervals of all samples are shown in Table 5, and then we define a mapping on this fuzzy interval as follows:  
\[ \begin{array}{l}H:V\rightarrow[0,1]\\ v\mapsto H(v)\end{array}  \tag{2}\]  
where \(V\) is the value field \([0,10]\), \(H\) is the fuzzy interval of \(V\), and \(H(v)\) is the membership function. Based on the kernel and boundary points of the fuzzy interval, we can construct the membership function as follows:  
\[\frac{H(v_{d})-0}{d-u}=\frac{1-0}{k-u}\Rightarrow H(v_{d})=\frac{1}{u-k}(u-d) \tag{3}\]  
\[\frac{H(v_{d})-0}{d-l}=\frac{1-0}{k-l}\Rightarrow H(v_{d})=\frac{1}{k-l}(d-l) \tag{4}\]  
where \(k\) is the kernel value, \(l\) is the minimum value, \(u\) is the maximum value, \(d\) is a random value, and \(H(v_{d})\) is the membership of \(d\). According to Equations (3) and (4), we calculate the membership functions of all samples, as shown in Figure 7.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Sample** & **Lower** & **Kernel** & **Upper** & **Sample** & **Lower** & **Kernel** & **Upper** \\ \hline
1 & 8 & 8.92 & 10 & 25 & 3 & 4.75 & 6 \\
2 & 8 & 8.50 & 9 & 26 & 3 & 3.83 & 5 \\
3 & 8 & 9.33 & 10 & 27 & 5 & 6.58 & 8 \\
4 & 8 & 8.83 & 9 & 28  
In Figure 7, when the score is as large as the kernel value, the membership reaches a maximum of 1. When the score gradually moves away from the kernel value from both sides, the membership gradually decreases until it reaches a minimum value of 0 at the two boundary points. In theory, the closer the generated sample point is to the kernel value, the closer it is to the real test result. However, if there is only a small disturbance around the kernel value, there is suspicion of data leakage. Therefore, it is most important to study how to choose a suitable membership value.