# RPREC: A Radar Plot Recognition Algorithm Based on Adaptive Evidence Classification
## 3 Proposed Method
### Construction and Correction Fusion of Belief Functions
#### 3.2.3 Correction and Combination of Evidence  
This section mainly focuses on revising and combining decision evidence. Firstly, the evidence belonging to the same category is combined, and then the combination results belonging to different categories are fused. 1. Combining evidence with the same category  
Firstly, combine the evidence with the same category assignment in decision evidence set \(\Phi_{K}(i)\); that is, combine the evidence in the decision evidence subset \(T_{q}\) of each category. \[\left\{ \begin{array}{c}m_{t}^{T_{q}}(C_{q})=1-\prod\limits_{j\in T_{q}}m_{i, j}(\Theta)\\ m_{t}^{T_{q}}(\Theta)=\prod\limits_{j\in T_{q}}m_{i,j}(\Theta)\end{array} \right. \tag{15}\]  
Assuming that \(E_{\mathsf{r}}\) is the error rate of the radar plot, the setting of the evidence discount factor is defined as:  
\[W_{C_{q}}=\frac{(1-E_{\mathsf{r}})\times Bel(C_{q})}{\sum\limits_{C_{q}\in\{C_ {o},C_{n},\Theta\}}Bel(C_{q})} \tag{16}\]  
Based on the correction factor, the update of evidence can be achieved as follows:  
\[\left\{ \begin{array}{c}dm_{t}^{T_{q}}(C_{q})=W_{C_{q}}(1-\prod\limits_{j\in T _{q}}m_{t,j}(\Theta))\\ dm_{t}^{T_{q}}(\Theta)=1-W_{C_{q}}(1-\prod\limits_{j\in T_{q}}m_{t,j}(\Theta) )\end{array} \right. \tag{17}\]  
2. Combining the results under different categories  
There may be certain confidence conflicts between different categories of decision evidence. The definition of evidence conflict between different categories is as follows:  
\[T_{c}=\sum\limits_{q=1}^{c}dm_{t}^{T_{q}}(\omega_{q}) \tag{18}\]Therefore, for the initial fusion evidence \(dm_{t}^{T_{q}}\) of different categories \(T_{q}\), a combination based on conflict resolution rules can be obtained as follows:  
\[\left\{ \begin{array}{l}m_{t}(C_{q})=(dm_{t}^{T_{q}}(C_{q})\prod\limits_{h\in \{1,\cdots^{c}\},h,\
eq q}dm_{t}^{T_{h}}(\Theta))/(1-T_{c})\\ m_{t}(\Theta)=1-\sum\limits_{q=1}^{\xi}\,(dm_{t}^{T_{q}}(\omega_{q})\prod \limits_{h\in\{1,\cdots^{c}\},h,\
eq q}dm_{t}^{T_{h}}(\Theta))/(1-T_{c})\\ \end{array} \right. \tag{19}\]  
Here, \(m_{t}\) is the global mass function obtained from the fusion of decision evidence set \(\Phi_{K}(i)\). Then, the confidence level \(Bel\) and the probability level \(Pl\) of target \(o_{i}\) belonging to each pattern category \(C_{i}\) can be calculated. \[Bel_{i}(C_{i})=\sum\limits_{C_{i}\in\{C_{o},C_{n},\Theta\},C_{q}\subseteq C_{i }}m_{t}(C_{q}) \tag{20}\]  
\[Pl_{i}(C_{i})=\sum\limits_{C_{i}\in\{C_{o},C_{n},\Theta\},C_{q}\cap C_{q}\
eq \varnothing}m_{t}(C_{q}) \tag{21}\]  
The criteria for updating the category labels of radar plots are:  
Criterion 1: Update categories with maximum confidence;  
Criterion 2: The minimum confidence difference between the new category and other categories must be greater than the threshold \(T1\), which means that there must be sufficient confidence differences between different categories;  
Criterion 3: The difference between the probability and confidence of the updated category must be less than the threshold \(T2\), which means that the uncertainty of the category cannot be too high. For example, let us assume that there are four pieces of evidence in the decision evidence set \(\Phi_{K}(i)\):  
\[ \begin{array}{l}m_{1}(C_{o})=0.8,\ m_{1}(\Theta)=0.2\\ m_{2}(C_{o})=0.7,\ m_{2}(\Theta)=0.3\\ m_{3}(C_{n})=0.8,\ m_{3}(\Theta)=0.2\\ m_{4}(C_{n})=0.6,\ m_{3}(\Theta)=0.4\\ \end{array} \]  
Firstly, combine the evidence with the same category. That is, evidence 1 and 2 need to be combined, and evidence 3 and 4 need to be combined. One obtains:  
\[ \begin{array}{l}m_{1,2}(C_{o})=0.94,\ m_{1,2}(\Theta)=0.06\\ m_{3,4}(C_{n})=0.92,\ m_{3,4}(\Theta)=0.08\\ \end{array} \]  
Assuming that the error rate of the radar plot is 0.1, the setting of the evidence discount factor is:  
\[ \begin{array}{l}W_{C_{o}}=\frac{(1-0.1)\times 0.94}{(0.94+0.92}=0.455\\ W_{C_{n}}=\frac{(-0.1)\times 0.92}{0.94+0.92}=0.445\\ \end{array} \]  
Based on the correction factor, the update of evidence can be achieved as follows:  
\[