# RPC-EAU: Radar Plot Classification Algorithm Based on Evidence Adaptive Updating
## 3 Proposed Method
### Correction and Combination of Evidences  
Although each neighbor sample evidence can provide some decision information for radar plot classification, it is particularly important to effectively combine them when these pieces of evidence are not completely consistent. In this section, a specific mixing combination rule is developed to fusion mass functions of the evidences about radar plots. This rule can be referred to as the \"D-S + Yager\" rule, which can have the efficiency of D-S when processing evidences in the same group, while also having the rationality of Yager in conflict allocation when processing evidences between different groups. For a sample set \(\Phi_{K}=\{m_{i1},m_{i2},\cdots,m_{ik}\}\) with \(K\)-nearest neighbor evidence, the evidence correction and combination based on this rule are as follows:  
Step 1: According to the maximum confidence corresponding to target, clutter, or uncertainty, \(K\)-nearest neighbor evidence can mainly be divided into three subsets \(\Phi_{T}\), \(\Phi_{C}\) and \(\Phi_{U}\), where \(\Phi_{T}=\{O_{i}:\max_{A\subseteq\Omega}m_{i}(A)=m_{i}(\omega_{T})\}\),\(\Phi_{C}=\{O_{j}:\max_{A\subseteq\Omega}m_{j}(A)=m_{j}(\omega_{C})\}\) and \(\Phi_{U}=\{O_{l}:\max_{A\subseteq\Omega}m_{l}(A)=m_{l}(\Theta)\}\). The number of evidences contained in them is \(K_{1}\), \(K_{2}\), and \(K_{3}\). Step 2: There is no conflict between the mass functions in this same set. Therefore, the D-S rule can be chosen to combine the evidences in \(\Phi_{T}\) or \(\Phi_{C}\) separately. We use \(m_{T}\) and \(m_{C}\) to represent the combined mass functions, and they are defined as follows:  
\[\left\{ \begin{array}{l}m_{T}(\omega_{T})=1-\prod\limits_{m_{j}\in\Phi_{T}}m_ {i}(\Theta)\\ m_{T}(\Theta)=\prod\limits_{m_{i}\in\Phi_{T}}m_{i}(\Theta)\end{array} \right., \quad i=1,\cdots,K_{1} \tag{20}\]  
And  
\[\left\{ \begin{array}{l}m_{C}(\omega_{C})=1-\prod\limits_{m_{j}\in\Phi_{C}}m_ {j}(\Theta)\\ m_{C}(\Theta)=\prod\limits_{m_{j}\in\Phi_{C}}m_{j}(\Theta)\end{array} \right., \quad i=1,\cdots,K_{2} \tag{21}\]  
The reason why the evidences in subset \(\Phi_{U}\) are not directly combined in this step is that they assigned all confidence to unknown, which results in the combination not providing effective decision information. Step 3: Then, we need to combine \(m_{T}\) and \(m_{C}\), but there may be some conflicts between them, since, compared to the D-S rule, the Yager rule can perform better when combining these conflicting evidences. So, it is chosen at this step to fuse the conflicting mass function in sets \(\Phi_{T}\) and \(\Phi_{C}\) obtained in the previous step. The combined mass functions \(m_{T,C}\) obtained by \(m_{T}\) and \(m_{C}\) are given by:  
\[m_{T,C}(\omega_{T})=(1-\prod\limits_{m_{i}\in\Phi_{T}}m_{i}(\Theta))\prod \limits_{m_{j}\in\Phi_{C}}m_{j}(\Theta) \tag{22}\]  
\[m_{T,C}(\omega_{C})=(1-\prod\limits_{m_{j}\in\Phi_{C}}m_{j}(\Theta))\prod \limits_{m_{i}\in\Phi_{T}}m_{i}(\Theta) \tag{23}\]  
\[ \begin{array}{ll}m_{T,C}(\Theta)=&\prod\limits_{m_{i}\in\Phi_{T}}m_{i}( \Theta)\prod\limits_{m_{j}\in\Phi_{C}}m_{j}(\Theta)\\ &+(1-\prod\limits_{m_{j}\in\Phi_{T}}m_{i}(\Theta))(1-\prod\limits_{m_{j}\in \Phi_{C}}m_{j}(\Theta))\end{array}  \tag{24}\] \begin{table}
\begin{tabular}{c c c c c} \hline
**Mass Function** & **\#1** & **\#2** & **\#3** & **\#4** \\ \hline \(m(\omega_{T})\) & 1 & 0 & 0.641 & 0 \\ \(m(\omega_{C})\) & 0 & 0.895 & 0 & 0 \\ \(m(\Theta)\) & 0 & 0.105 & 0.359 & 1 \\ \hline \end{tabular}
\end{table} 
Table 2: The mass function constructed by different nearest neighbor samples in Example 1. Step 4: The evidences in \(\Phi_{U}\) have the relationship that \(m_{I}(\Theta)=1\), \(l=1,\cdots,K_{3}\). So, combining them without correction does not provide additional decision-making information. Therefore, it is necessary to modify these evidences based on \(m_{T}\) and \(m_{C}\), which can be seen as the fused confidence center of \(\omega_{T}\) and \(\omega_{C}\).