# Accident Risk Analysis of Gas Tankers in Maritime Transport Using an Integrated Fuzzy Approach
## 3 Methodology
### Fuzzy Delphi Method  
The Delphi method, a hallmark of traditional research practice, endeavours to reach a consensus on intricate issues by collating expert opinions through successive survey rounds [41]. Nevertheless, it is important to note that conducting consecutive surveys to ensure the consistency of expert opinions--especially when accompanied by pressure to alter those opinions--has the potential to create negative outcomes [42]. [PERSON]'s 1965 development of fuzzy set theory provided a framework for the representation of uncertainty, facilitating the conversion of expert language into quantitative values [43]. This theory has  
Figure 1: Research methodology. been incorporated into the Delphi method, which has been shown to reduce the number of interviews and research time while facilitating more effective communication of expert opinions [44]. The initial step in the process is the creation of a fuzzy Delphi questionnaire. The fuzzy method employs various types of fuzzy numbers to convert expert opinions from linguistic terms into fuzzy numbers [43]. The present study employed Trigonometric Fuzzy Numbers (TFN). The TBS model is represented by three real numbers: the minimum possible value (a), the maximum possible value (b), and the minimum possible value (c) [43]. A questionnaire was developed using the linguistic variables in Table 2 to assess the degree of influence of the criteria identified through the literature review [45]. Step 2--Determining Average Fuzzy Evaluation Scores: The average fuzzy evaluation score for each factor is calculated using Equation (1). This calculation assumes that the estimated value for factor \(j\) is provided by expert \(i\) from a total of \(n\) experts [43; 46]. \[\widetilde{\omega}_{ij}=\left(a_{ij},b_{ij}\text{, }c_{ij}\right)\text{, }i=1,2,3 \ldots n\text{, }j=1,2,3\ldots m \tag{1}\]  
Using Equation (2), the average of the fuzzy numbers (\(\widetilde{\omega}_{j}\)) associated with factor \(j\) is calculated. \[\widetilde{\omega}_{j}=\left(a_{j},b_{j}\text{, }c_{j}\right)\text{, } \left(\text{ }\frac{1}{n}\text{$\sum_{i=1}^{n}a_{ij}$, }\text{ }\frac{1}{n}\text{$\sum_{i=1}^{n}b_{ij}$, }\text{ }\frac{1}{n}\text{$\sum_{i=1}^{n}c_{ij}$}\right)\text{, }j=1,2,3 \ldots m \tag{2}\]  
Step 3--Identifying the Most Influential Criterion: During the clarification process, the average fuzzy evaluation score (\(\widetilde{\omega}_{j}\)) of each factor \(j\) is converted into precise values. The combined fuzzy scores of the factors (\(S_{j}\)) are then finalised using Equation (3) with the simple centre of gravity method [43; 45]. \[S_{j}=\frac{a_{j}+b_{j}+c_{j}}{3}\text{, }j=1\text{, }2\text{, }3\text{, } \ldots m \tag{3}\]  
Evaluation scores (\(S_{j}\)) were used to rank the factors based on their importance. Factors with a score of 0.7 or higher were considered significant, while those with scores below this threshold were excluded from the study [43; 45]. The acceptability of the estimation domain is analysed by calculating the difference between the average fuzzy number for the factor and each expert's fuzzy estimate using Equation (4). The acceptability of the estimation domain is assessed by calculating the difference (\(D_{ij}\)) between the average fuzzy number for factor \(j\) (\(\widetilde{\omega}_{ij}\)) and each expert's fuzzy estimate (\(\widetilde{\omega}_{ij}\)) using Equation (4) [43]. \[D_{ij}=\sqrt{\frac{1}{3}}\left[\text{ }\left(a_{j}-a_{ij}\right)^{2}+ \left(b_{j}-b_{ij}\right)^{2}+\left(c_{j}-c_{ij}\right)^{2}\right] \tag{4}\] \begin{table}
\begin{tabular}{c c c} \hline \hline
**Symbols** & **Linguistic Variables** & **TBSs (\(a,b,c\))** \\ \hline VL & very low effective & (0,0,0.25) \\ \hline L & low effective & (0, 0.25, 0.5) \\ \hline M & medium effective & (0.25, 0.5, 0.75) \\ \hline H & high effective & (0.5, 0.75, 1) \\ \hline VH & very high effective & (0.75, 1, 1) \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Linguistic terms and corresponding TFNs [43]. The threshold value (\(d\)) of each factor \(j\) is calculated using Equation (5) [43].