## 2 Methodology
### Improved High-Conflict Evidence Fusion  
Evidence conflicts can be categorized into Type I and Type II conflicts based on the fusion steps of the D-S evidence theory [35; 36; 37]. Type I are conflicts between bodies of evidence arising from the bodies of evidence themselves. Type II are conflicts arising from defects in the rules on fusion of evidence. To the above problems, the improvement process of this paper is as follows. Step (1). Calculate the conflict degree: Based on the traditional DS evidence theory, the degree of conflict is represented by the conflict coefficient K, which describes the overall degree of conflict among the evidence bodies. The smaller the degree of conflict, the smaller the conflict. In construction risk early warning, for the evidence body composed of different information sources, we let \(\alpha_{ij}\) be the degree of conflict between the \(i\)th information source and the \(i\)th information source. \[\alpha_{ij}=\sum_{i\
eq j}m_{i}(A)*m_{j}(A) \tag{3}\]  
where \(m_{i}\) (\(A\)) and \(m_{j}\) (\(A\)), respectively, represent the initial trust degree BPA corresponding to the \(i\)th information source and the \(j\)th information source when the early-warning level is \(A\). We suppose the initial trust degree of information source 1 is {m\({}_{1}\) (safe), m\({}_{1}\) (yellow), m\({}_{1}\) (orange), m\({}_{1}\) (alarm)} = {0.1, 0.7, 0.2, 0}, and the initial trust degree of information source 2 is {m\({}_{2}\) (safe), m\({}_{2}\) (yellow), m\({}_{2}\) (orange), m\({}_{2}\) (alarm)} = {0.2, 0.8, 0, 0}. So in the conflict degree calculation process for \(\alpha_{12}\) = 0.1 \(\times\) (0.8 + 0 + 0) + 0.7 \(\times\) (0.2 + 0 + 0) + 0.2 \(\times\) (0.2 + 0.8 + 0) + 0 \(\times\) (0.2 + 0.8 + 0), the result is 0.42. \(m_{i}\) (\(A\)) and \(m_{j}\) (\(A\)) denote the BPAs corresponding to the \(i\)th data source and the \(j\)th data source when the early-warning level is \(A\), respectively. Step (2). Calculate the uncertain degree: The focusing degree indicates the uncertainty of the data source itself: the smaller focusing degree, the smaller the uncertain degree. In order to keep the monotonicity of the conflict degree and uncertain degree consistent, the uncertain degree is represented by the focusing degree. We let \(\theta\) denote the focusing degree of the \(i\)th data source, and the corresponding uncertain degree is \(\beta\). \[\beta=1-\theta=1-\sqrt{\frac{1}{|\Theta|}{\sum\left(m(A)-\frac{1}{|\Theta|} \right)}^{2}} \tag{4}\]  
where \(|\Theta|\) is the base of the subset \(\Theta\) (the number of elements in the set \(\Theta\)). The greater the uncertainty, the greater the conflict between the evidence, the more likely fusion failure to occur. The smaller the uncertainty, the smaller the conflict between evidences pieces, and the greater the possibility of fusion failure. Step (3). Improve the conflict correction parameters: The distance from point (\(\alpha\), \(\beta\)) to (0, 0, 0) is defined as an improved evidence correction parameter. We let \(\delta\) denote the credibility of the \(i\)th data source and adjust for the data source. \[\delta=1-\sqrt{\frac{\alpha^{2}+\beta^{2}}{2}} \tag{5}\]  
Step (4). Type I conflict correction: By applying the improved evidence correction parameter to the initial BPA, the BPA corrected for Type I conflict is obtained. \[m_{corrected}(A)=(1-\delta)*m(A) \tag{6}\]  
where \(m_{corrected}\) (\(A\)) represents the underlying probability assignment of the data source to early-warning Level A. Step (5). Type II conflict adjustment: Type I conflict correction removes the differentiation between evidence pieces but does not resolve the global focal element allocation between evidences. Therefore, by adding the fine-tuning term \(L\) (\(A\)), the global conflict is decomposed into local conflicts to reduce the subjectivity of global focal element allocation. We let \(m_{adjust}\) (\(A\)) denote the adjusted BPA for the second type of conflict and \(m_{fusion}\) (\(A\)) be the final fusion result. \[\left\{