# Neighborhood Rough Fuzzy Penetration Control Method with Variable Precision Based on GMAW
## 3 Description of Fuzzy Control System
### VPNRS Feature Extraction and Classification Rule Acquisition  
In the neighborhood rough set, the size of the neighborhood is an important parameter in the neighborhood decision system. The size of the neighborhood determines the granularity of the domain information. Setting the neighborhood size threshold too high will cause the sample to be over-segmented, which will lead to less dependency of the decision attribute on the attribute. Standard deviation is a statistic that measures the dispersion of data. The smaller the standard deviation, the closer the data are to the mean. The larger the standard deviation, the further they are from the mean. The smaller the standard deviation, the smaller the neighborhood threshold needs to be. When the standard deviation is large, a larger threshold needs to be set. Therefore, \(SD/N\) is selected as the neighborhood \(\delta\) size to set the threshold [18], where \(N\) is the control parameter. When processing data, it is necessary to normalize the data for each attribute separately. Normalizing the data does not affect the data distribution. To verify the effectiveness of the VPNRS method, a description of the data in Table 2 is given in Table 3. Based on the sample number of data welding and the reduction output of the VPNRS algorithm, the appropriate parameter \(N\) range is set at [1.5-2.5], the step size is 0.05, and the variable precision threshold \(\beta\) is 0.8. In order to compare the classification ability of the selected features, the decision tree algorithm (C4.5) with elevated classification accuracy and the Naive Bayesian algorithm (NB) with stable classification are selected; the classification accuracy of 10-fold cross validation is used to evaluate the quality of the reduced features. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \(\mathbf{U}\) & \(\mathbf{L_{T}}\) & \(\mathbf{W_{T}}\) & \(\mathbf{R_{LW}}\) & \(\mathbf{S_{T}}\) & \(\mathbf{C_{TS}}\) & \(\mathbf{\alpha}\) & \(\mathbf{C_{TW}}\) & \(\mathbf{d}\) \\ \hline \(x_{1}\) & 203.5 & 227.4 & 1.0557 & 34,264.2 & 0.740344 & 58.38582 & 0.817982 & 0 \\ \(x_{2}\) & 227.1 & 246.4 & 1.11908 & 40,220 & 0.718398 & 56.95522 & 0.794792 & 0 \\ \(x_{3}\) & 287.2 & 279 & 1.24302 & 55,542.4 & 0.693106 & 51.83622 & 0.7656 & 0 \\ \(x_{4}\) & 388.2 & 303.2 & 1.28024 & 77,677.8 & 0.65948 & 42.6706 & 0.703328 & 0 \\ \(x_{5}\) & 380.7 & 294.6 & 1.29466 & 70,471.8 & 0.627972 & 42.30562 & 0.66299 & 1 \\ \(x_{6}\) & 209.2 & 230.4 & 0.90887 & 35,064.8 & 0.727834 & 57.69378 & 0.794246 & 0 \\ \(x_{7}\) & 228.2 & 241.6 & 0.94455 & 39,214.6 & 0.7711268 & 55.79898 & 0.781472 & 0 \\ \(x_{8}\) & 284.5 & 276.8 & 1.02794 & 54,364 & 0.69035 & 51.8864 & 0.752902 & 0 \\ \(x_{9}\) & 349.9 & 286.6 & 1.22096 & 63,152.8 & 0.629686 & 44.54132 & 0.653802 & 1 \\ \(x_{10}\) & 356.5 & 286.8 & 1.24315 & 61,489.8 & 0.601464 & 43.82376 & 0.639982 & 2 \\ \(x_{11}\) & 198.2 & 195.4 & 1.21924 & 25,912.6 & 0.669246 & 52.5764 & 0.72167 & 1 \\ \(x_{12}\) & 229 & 222.6 & 1.32878 & 33,977 & 0.66655 & 51.84138 & 0.708012 & 1 \\ \(x_{13}\) & 285.1 & 256.2 & 1.38284 & 47,002.4 & 0.643292 & 48.41272 & 0.660664 & 1 \\ \(x_{14}\) & 356.1 & 272.4 & 1.30719 & 58,891.8 & 0.60684 & 41.88194 & 0.620408 & 2 \\ \(x_{15}\) & 393.9 & 264.2 & 1.49169 & 62,363 & 0.599 & 37.07392 & 0.6063 & 2 \\ \(x_{16}\) & 225.5 & 192.2 & 1.17430 & 29,641 & 0.683952 & 46.16006 & 0.700376 & 1 \\ \(x_{17}\) & 264.5 & 207.4 & 1.27540 & 36,261.8 & 0.660962 & 42.82836 & 0.685534 & 1 \\ \(x_{18}\) & 306.1 & 223.2 & 1.37139 & 43,665 & 0.638984 & 40.07414 & 0.656882 & 2 \\ \(x_{19}\) & 397.1 & 240.2 & 1.65288 & 57,250 & 0.599762 & 33.69362 & 0.610434 & 2 \\ \(x_{20}\) & 448.5 & 244.2 & 1.83692 & 64,010 & 0.585122 & 30.5613 & 0.58698 & 2 \\ \(x_{21}\) & 222.7 & 184.4 & 1.45976 & 26,597 & 0.647332 & 45.05956 & 0.677862 & 1 \\ \(x_{22}\) & 250 & 210.8 & 1.52088 & 33,429.4 & 0.633874 & 45.73774 & 0.662322 & 1 \\ \(x_{23}\) & 323.8 & 222.4 & 1.77036 & 35,481.56 & 0.617926 & 37.93956 & 0.621488 & 2 \\ \hline \end{tabular}
\end{table} 
Table 2: Variable gap-current welding data sheet.