# A Tolerance Type Screening Method Based on Similarity Evaluation
## 5 Discussion  
### Comparative Analysis with or Without Relative Scales  
As shown in Figure 7, Figure 7a is the target case; Figure 7b,c are the resource cases. The tolerance elements of the target case and the resource cases are cylindrical feature surfaces. According to the method of tolerance element similarity assessment proposed in this paper, the set of tolerance element similarity elements of the target case is \(\mathbf{SE_{t_{0}}}=\) [cylindricity, coaxiality, full runout, medium-long], the set of tolerance element  
\begin{table}
\begin{tabular}{l l} \hline \hline \multirow{4}{*}{algorithm} & Initiate the similarity list: create a list SimList to store each historical case \(T_{\text{c,k}}\) take part in \(T_{\text{o}}\) similarity. \\  & Calculate similarity: for each resource tolerance specification case \(T_{\text{c,k}}\) (k from 1 to \(n\)): \\  & Use the overall similarity calculation formula \(\mathbf{\hat{s}}\) to calculate \(T_{\text{c,k}}\) take part in \(T_{\text{o}}\) similarity between. \\  & Add the calculated similarity to SimList and compare it with case \(T_{\text{c,k}}\) corresponding. \\  & Screening similar cases: \\  & Traverse the SimList to find all historical tolerance specifications with a similarity greater than or equal to \\  & threshold \(t\), and store these cases and their similarity values in a temporary list FilteredList. \\  & Sort and output: \\  & Sort the cases in FilteredList in descending order of similarity value. If the number of cases in FilteredList is \\  & greater than N+, only output the first N+ cases; otherwise, output all cases in FilteredList. \\ \hline \hline \end{tabular}
\end{table}
Table 6: _Cont._  
Figure 6: The geometric tolerance types in the case with the highest similarity.  
similarity elements of the resource case 7b is \(SE_{\text{tc1}}=\{\text{straightness, roundness, cylindricity, coaxiality, runout, circular runout, medium-long}\}\), and the set of tolerance element similarity elements of the resource case 7c is \(SE_{\text{tc2}}=\{\text{linearity, circularity, cylindricity, coaxiality, runout, circular runout, more-long}\}\). Without considering the relative scale, the sets of tolerance element similarity elements \(SE_{\text{tc}}\), \(SE_{\text{tc1}}\), and \(SE_{\text{tc2}}\) have the elements \"medium-long\", \"medium-long\", and \"more-long\" removed, respectively.  
Using Equation (4), calculate the similarity between the target case and the resource cases as shown in Table 7. Considering the relative scale, \(SY(E_{\text{tc1}},E_{\text{tc}})\) is 0.6523 and \(SY(E_{\text{tc2}},E_{\text{to}})\) is 0.4594, calculated by using Equation (4), while \(SN(E_{\text{tc1}},E_{\text{to}})\) is equal to \(SN(E_{\text{tc2}},E_{\text{to}})\) without considering the relative scale and its similarity evaluation value is 0.5850.  
From the above comparative analysis of similarity assessment, it can be seen that, without considering the relative scale, the similarity between the target part in Figure 7a and the case parts in Figures 7b and 7c, respectively, are equal. However, after considering the relative scales of the tolerance elements, there is a significant difference in the similarity between them. The addition of the relative scale similarity element to the set of tolerance element similarity elements results in a more discriminating similarity assessment, and, the larger its value, the more similar the structural shape of the parts.