## 5 Verification and Application
### Verification on Classification  
The applications in this study utilize several data sets sourced from the UCI machine learning database. These data sets include the Statlog (Australian Credit Approval) data set, Breast Cancer Wisconsin (Diagnostic) data set, Seeds data set, Climate Model Simulation Crashes data set (CMSC), Heart disease data set, Wine data set, and Ionosphere data set. The details are shown in Table 1.  
To demonstrate the effectiveness of the proposed method in classification, several algorithms are selected. These algorithms include XGBoost, Support Vector Machine (SVM), Random Forest (RF), Neural Network (NN), and Logistic Regression (LR). For each dataset, we have chosen ten classifiers from these five methods to generate a diverse set of classifiers. The specific classifiers used are as follows:  
1. XGBoost classifiers with booster options of gbtree and gblinear.
2. SVM classifiers with radial basis function kernel and linear kernel.
3. RF classifiers with criterion options of gini and entropy.
4. Multi-Layer Perceptron (MLP) classifiers with two hidden layers using either 10-10 or 20-10 nodes, and tansig activation function.
5. LR classifiers with LBFGS and Stochastic Average Gradient (SAG) solver, respectively.  
To combine the classifiers, the PHFET method is used. Five types of classifiers are utilized, resulting in five bodies of evidence. Each body of evidence includes information from two classifiers. The mass function of evidence is generated using the output of two classifiers and their accuracy, according to Equations (34) and (35). In the experiments, the 5-fold cross-validation method is employed, which is a common method to test the accuracy of the classification algorithm. The mean accuracy of different classifiers based on different data sets is provided in Table 2.  
As observed from Table 2, the PHFET method consistently achieves the highest accuracy across all seven data sets. These results clearly demonstrate the effectiveness of the  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Data Set** & \begin{tabular}{c} **Attribute** \\ **Type** \\ \end{tabular} & **Instances** & **Attributes** & **Class** & **Subject Area** \\ \hline Statlog & \
\begin{tabular}{c} Categorical, \\ Integer, Real \\ \end{tabular} & 690 & 14 & 2 & Financial \\ Breast Cancer & Real & 569 & 30 & 2 & Life \\ Seeds & Real & 210 & 7 & 3 & Life \\ CMSC & Real & 540 & 18 & 2 & Physical \\ Heart disease &
\begin{tabular}{c} Categorical, \\ Integer, Real \\ \end{tabular} & 303 & 13 & 5 & Life \\ Wine & Integer, Real & 178 & 13 & 3 & Physical \\ Ionosphere & Integer, Real & 351 & 34 & 2 & Physical \\ \hline \hline \end{tabular}
\end{table}
Table 1: Basic information of the data sets.  
\begin{table}
\begin{tabular}{c c c c c c c c c c c c} \hline \hline
**Data Set** & **XGBoost-1** & **XGBoost-2** & **SVM-1** & **SVM-2** & **RF-1** & **RF-2** & **MLP-1** & **MLP-2** & **LR-1** & **LR-2** & **PHFET** \\ \hline Statlog & 0.8810 & 0.8578 & 0.8564 & 0.8534 & 0.8810 & 0.8883 & 0.8549 & 0.8549 & 0.8593 & 0.8593 & 0.8905 \\ Breast cancer & 0.9701 & 0.9649 & 0.9210 & 0.9210 & 0.9649 & 0.9649 & 0.9139 & 0.8402 & 0.9438 & 0.9139 & 0.9912 \\ Seeds & 0.9191 & 0.9571 & 0.9381 & 0.9429 & 0.9143 & 0.8952 & 0.9143 & 0.9000 & 0.9381 & 0.9381 & 0.9762 \\ CMSC & 0.9204 & 0.9204 & 0.9204 & 0.9500 & 0.9550 & 0.9556 & 0.9574 & 0.9611 & 0.9630 & 0.9630 & 0.9630 \\ Heart disease & 0.5710 & 0.5876 & 0.5808 & 0.5842 & 0.5841 & 0.5775 & 0.5940 & 0.6007 & 0.5875 & 0.5875 & 0.6333 \\ Wine & 0.9492 & 0.9552 & 0.6571 & 0.9494 & 0.9776 & 0.9775 & 0.6356 & 0.6395 & 0.9494 & 0.7135 & 1.0000 \\ Ionoshpere & 0.9345 & 0.8805 & 0.9402 & 0.8804 & 0.9402 & 0.9375 & 0.8719 & 0.8803 & 0.8803 & 0.9486 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Classification accuracy of different methods.  
PHFET method in merging the information and advantages of multiple classifiers, leading to improved recognition accuracy.