# Fire Risk Assessment of Urban Utility Tunnels Based on Improved Cloud Model and Evidence Theory
## 3 Fire Risk Assessment Model of Urban Utility Tunnels
### Evidence Theory
#### 3.2.2 The Improved Synthesis Rules of Evidence Theory Based on Dynamic and Static Weights  
Evidence theory has unique advantages in multisource information fusion. Still, for the problem of strong conflicting evidence fusion, traditional combination rules may lead to conclusions contrary to the actual situation. The main reason is that each piece of evidence is assumed to be of the same importance when fused, while the importance of evidence is not the same. In addition, considering the impact on the weight of the evaluation index itself, this paper improves the synthesis rules by introducing the concept of dynamic and static weights and solving the optimal combination weight based on the combined weighting of game theory. This method not only takes into account the difference in the importance of the evidence but also corrects the conflicting evidence. It retains the original data information to the greatest extent and improves evidence fusion's credibility. (1) Dynamic weights  
Based on the identification framework in this paper, the fundamental probability distribution matrix \(M_{n\times(q+1)}\) was obtained by improving the cloud model. It shows that the identification framework has \(q+1\) groups of propositions, that is, a total of \(q+1\) levels, and each group of propositions has \(n\) groups of evidence, that is, \(n\) indicators. The steps for calculating the dynamic weights are as follows [29]. Step 1: Calculate the average membership degree of \(n\) indicators in each level using the formula shown in Equation (11). \[mass(\overline{u_{k}})=\frac{1}{n}\sum\limits_{i=1}^{n}mass(u_{k})\ k=1,2, \ldots,q+1 \tag{11}\]  
where \(u_{k}\) represents the \(k\)th membership degree. Step 2: Calculate the distance \(l_{i}\) between the membership degree of the \(i\)th indicator and the average membership degree using the formula shown in Equation (12). \[l_{i}=\sum\limits_{k=1}^{q+1}|mass_{i}(u_{k})-mass(\overline{u_{k}})|k=1,2, \ldots,q+1 \tag{12}\]  
Step 3: The distance \(l_{i}\) is used as the standard to assign the weight of indicators \(\omega_{i}\). It is believed that the greater the difference between the indicator membership and the average membership, the stronger the conflict between indicators and most indicators. Therefore,the weight assigned is inversely proportional to the distance, as shown in Equations (13) and (14). \[\rho_{i}=\frac{1}{l_{i}}\ \ i=1,2,\ldots,n \tag{13}\]  
\[\omega_{i}=\frac{l_{i}}{\sum\limits_{i=1}^{n}l_{i}}\ \ i=1,2,\ldots,n \tag{14}\]  
Since these weights change with evidence, they are called dynamic weights. The dynamic weights vector \(W_{\rm D}=[\omega_{1},\omega_{2},\ldots,\omega_{n}]\) (where \(n\) is the total number of indicators) can be obtained by this method. (2) Static weights  
In this paper, the G1 method (order relationship method) [30] is used to solve the static weights of the evaluation index. The G1 method does not require a consistency test, and its calculation process is easy to understand. It determines the order relationship between indicators based on the importance degree and derives the importance comparison coefficients between adjacent indicators. It also calculates the weight coefficients between indicators based on the comparison coefficients. Thus, the static weights vector \(W_{\rm G1}=[\omega_{1},\omega_{2},\ldots,\omega_{n}]\) (where \(n\) is the total number of indicators) can be obtained. (3) Combination weighting based on game theory  
The combination weighting based on game theory aims to minimize the deviation between the combined weights and the dynamic and static weights. It solves the optimal combined weights by the following steps [31].