### Fuzzy Calculation of Storage Tank Accident Factors Failure Probability  
In the quantitative calculation of storage tank probability, it is crucial to accurately assess the failure probability of basic events. Fuzzy set theory (FST) was proposed by [PERSON] in 1965 [10] to handle problems of imprecision and fuzziness in phenomena. Since the data and information provided in accident analysis and risk assessment often contain considerable uncertainty, FST has been applied in many fields. Well-known risk analysis techniques, such as FTA [29], FMEA [30], and HAZOP [31,32], have all been modified and enhanced using FST. This study combines fuzzy set theory (FST) and expert evaluation to calculate the basic events' failure probability to improve the accuracy and reliability of failure probability assessment [33]. Fuzzy numbers can be represented in various forms to express linguistic values. Common forms include triangular membership functions, trapezoidal membership functions, and Gaussian membership functions. The triangular membership function and the trapezoidal membership function are adopted as fuzzy set affiliation functions in this research. The steps for calculating the failure data of basic events using expert evaluation and fuzzy set theory are as follows:  
Step 1: Define the linguistic variables based on expert opinions and determine the corresponding membership functions \begin{table}
\begin{tabular}{c c c} \hline \hline
**Name** & **Illustration** & **Input Event** \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Introduction to Fault Tree Dynamic Logic Gates. Let \(x,a,b,c,d\in R\) (real numbers). Suppose a fuzzy number \(A\) in \(R\) is a triangular fuzzy number, then its membership function \(f_{A}\) is given by Equation (1):  
\[f_{A}(x)= \begin{cases}(x-a)/(b-a),&a\leq x\leq b,\\ (c-x)/(c-b),&b\leq x\leq c,\\ 0,&otherwise\end{cases}  \tag{1}\]  
where \(a\leq b\leq c\). A triangular fuzzy number is denoted as \(A=(a,b,c)\). The parameter '\(b\)' represents the maximum value of \(f_{A}(x)\), that is, \(f_{A}(b)=1\), which is the most likely value of the evaluation data. '\(a\)' and '\(c\)' are the lower and upper limits of the available evaluation range. Similarly, assume that a fuzzy number \(A\) in \(R\) is a trapezoidal fuzzy number, then its membership function \(f_{A}\) is given by Equation (2):  
\[f_{A}(x)= \begin{cases}(x-a)/(b-a),&a\leq x\leq b,\\ 1,&b\leq x\leq c,\\ (d-x)/(d-c),&c\leq x\leq d,\\ 0,&otherwise\end{cases}  \tag{2}\]  
where \(a\leq b\leq c\leq d\). A trapezoidal fuzzy number can be represented as \(A=(a,b,c,d)\). The interval [\(b,c\)] is the most likely value of \(f_{A}(x)\), '\(a\)' and '\(d\)' are the lower and upper limits of the available area for evaluating data. These two types of fuzzy numbers are used because, under some weak assumptions, these specific membership functions meet relevant optimization criteria and are also easy to evaluate intuitively evaluation [10; 34]. The fuzzy number is calculated based on the linguistic variables used by the experts to evaluate the risk factors, where each linguistic variable corresponds to a fuzzy set containing the affiliation function of that variable. The linguistic variables are {Very low (VL), Low (L), Mildly low (ML), Medium (M), Mildly high (MH), High (H), and Very high (VH)] [35] and their corresponding fuzzy numbers are shown in Figure 2. The triangular fuzzy numbers are converted into trapezoidal fuzzy numbers for ease of computation. Figure 2: Fuzzy membership functions. In order to obtain accurate and objective results, the ratings of multiple experts are aggregated and processed using the following Equation [5]:  
\[M_{i}=\sum_{j=1}^{m}A_{ij}w_{j}(i=1,2,...,n,j=1,2,...,m) \tag{3}\]  
where \(n\) is the number of basic events, \(m\) is the number of experts, \(w_{j}\) is the weight coefficient of each expert, \(A_{ij}\) is the value of the horizontal coordinates (\(a\), \(b\), \(c\), \(d\)), and \(M_{i}\) is the number of aggregated fuzzy numbers of basic events.