# A Classification Model Based on Interval Rule Inference Network with Interpretability
## 6 Experiment and Analysis
### Performance Analysis of IRIN  
Parameters in IBRB such as attribute weight, rule weight, and belief degrees of consequents were determined by experts, where the belief degrees of consequents are interval values, complicating the problem of manual parameter setting. Therefore, IRIN effectively avoids this problem by automatically generated an IBRB in which both the antecedent and the consequent term of each rule are embedded in the interval belief distribution.  
In order to verify the classification performance of IRIN, the classification accuracy of IRIN is compared with some improved belief rule-based systems.  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**Rule**} & \multirow{2}{*}{**Rule Weight**} & \multicolumn{4}{c}{**Antecedent**} & \multicolumn{2}{c}{**Consequent**} \\ \cline{3-8}  & & \(A_{1}(0.2496)\) & \(A_{2}(0.6754)\) & \(A_{3}(0.1146)\) & \(A_{4}(0.8475)\) & \(D_{1}\) & \(D_{2}\) & \(D_{3}\) \\ \hline \multirow{3}{*}{\(R_{15}\)} & \multirow{3}{*}{0.4952} & \(L([0.3333,0.3544])\) & \(L([0.6667,0.7254)\) & \(L([0.0899,0.1509])\) & \(L([0.1667,0.2627])\) & \\  & & \(M([0.6456,0.6667])\) & \(M([0.2747,0.3333])\) & \(M([0.8492,0.9100])\) & \(M([0.7375,0.8334])\) & \([0.2907,0.3005]\) & \([0.3076,0.3769]\) & \([0.3322,0.3917]\) \\  & & \(H([0.0,0.0])\) & \(H([0.0,0.0])\) & \(H([0.0,0.0])\) & \(H([0.0,0.0])\) & & \\ \hline \multirow{3}{*}{\(\vdots\)} & \multirow{3}{*}{\(\vdots\)} & \(\vdots\) & \(\vdots\) & \(\vdots\) & \(\vdots\) & \(\vdots\) & \(\vdots\) & \(\vdots\) \\ \cline{3-8}  & & \(L([0.0002,0.008])\) & \(L([0.1667,0.1766])\) & \(L([0.0,0.0])\) & \(L([0.0,0.0])\) & \(L([0.0,0.0])\) & \\ \cline{3-8}  & & \(M([0.992,0.9998])\) & \(M([0.8234,0.8333])\) & \(M([0.6992,0.7799])\) & \(M([0.5833,0.6779])\) & \([0.2181,0.3661]\) & \([0.0595,0.0935]\) & \([0.5404,0.7224]\) \\ \cline{3-8}  & & \(H([0.0,0.0])\) & \(H([0.0,0.0])\) & \(H([0.2221,0.3008])\) & \(H([0.3221,0.4167])\) & & \\ \hline \multirow{3}{*}{\(\vdots\)} & \(\vdots\) & \(\vdots\) & \(\vdots\) & \(\vdots\) & \(\vdots\) & \(\vdots\) & \(\vdots\) & \(\vdots\) \\ \cline{3-8}  & & \(L([0.0,0.0])\) & \(L([0.0,0.1861])\) & \(L([0.0,0.0])\) & \(L([0.0,0.0])\) & & \\ \cline{3-8}  & 0.6762 & \(M([0.8333,0.8446])\) & \(M([0.8139,1.0])\) & \(M([0.8298,0.9136])\) & \(M([0.8333,0.8412])\) & \([0.1449,0.2777]\) & \([0.1119,0.4737]\) & \([0.3812,0.6103]\) \\ \cline{3-8}  & & \(H([0.1554,0.1667])\) & \(H([0.0,0.0])\) & \(H([0.1667,0.1701])\) & \(H([0.1588,0.1667])\) & & \\ \hline \hline \end{tabular}
\end{table}
Table 3: The IBRB of Iris.  
Figure 3: Belief distribution comparison.  
Table 4 shows the comparison results of classification accuracy with other BRB systems. As can be seen from Table 4, the classification accuracy of IRIN on the Diabetes, Glass, and Ecoli datasets are 75.3%, 76.7%, and 88.1%, respectively, which is 0.9%, 3.8%, and 1.0% higher compared to the second-ranked BRB system. The classification accuracy of the Seeds and Iris datasets is slightly lower than other BRB systems, ranking second and third, respectively. This may be due to the simplicity of the Seeds and Iris datasets, where the class distribution is relatively uniform and the feature dimensions are low. In such a case, the complexity and advantages of the IRIN method are not fully utilized. Nevertheless, the average ranking of IRIN is still better than that of other BRB systems. This fully shows that the IBRB automatically generated using the method proposed can effectively handle interval uncertainty, and the uncertainty can be expressed more carefully by using interval boundaries, so that the system can better distinguish boundary cases and reduce classification errors.