# Accident Risk Analysis of Gas Tankers in Maritime Transport Using an Integrated Fuzzy Approach
## 3 Methodology
### Fuzzy DEMATEL Method  
The DEMATEL method was first introduced by [PERSON] et al. in 1972 to analyse interactions between variables [45]. As with the Delphi Method, DEMATEL relies on expert \begin{table}
\begin{tabular}{l l l l l} \hline \hline
**Expert** & **Department** & **Experience (Years)** & **DWT Tonnage Range** &
\begin{tabular}{l} **Gas Tanker** \\ **Number** \\ \end{tabular} \\ \hline
1 & ship operation & 12 & 10–155 k & 10 \\
2 & chartering & 15 & 50–125 k & 13 \\
3 & ship operation & 10 & 40–130 k & 8 \\
4 & chartering & 11 & 30–200 k & 9 \\
5 & chartering & 10 & 50–150 k & 9 \\
6 & chartering & 13 & 10–250 k & 10 \\
7 & chartering & 11 & 50–250 k & 10 \\
8 & ship operation & 11 & 30–200 k & 9 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Expert specifications. judgments and transforms evaluations from linguistic factors to fuzzy numbers using TFN. The objective of this transformation is to circumvent uncertainty and attain consensus [47]. In 2008, [PERSON] applied DEMATEL in a fuzzy environment [48]. Fuzzy DEMATEL determines cause and effect criteria by analysing the relationships between criteria and sub-criteria [47]. The DEMATEL method is predicated on the acceptance of pairwise comparisons and relationships in the decision-making process, a factor that confers upon the method an advantage over competing techniques [49]. Fuzzy DEMATEL has been extensively utilised in a variety of fields, including risk analysis, security management, and human resources management. The DEMATEL method was utilised in conjunction with fuzzy logic, as illustrated in Figure 1. This method involves the transformation of raw data into a fuzzy set, followed by the application of defuzzification techniques to derive a precise result. Please see Appendix A for detailed mathematical equations of the fuzzy DEMATEL method. In this study, the fuzzy DEMATEL method is applied by following the steps in Figure 2.  
Step-1 The Collection of Raw Data from Experts: The selected number of experts was invited to evaluate the effect of the factor \(F_{i}\) on the factor \(F_{j}\) on a 5-point scale [50]. The categories are as follows: \"Very highly effective\" = 5, \"Highly effective\" = 4, \"Slightly effective\" = 3, \"Very slightly effective\" = 2, and \"No effect\" = 1 [51]. Step-2 Conversion of Linguistic Data into Fuzzy Values (Fuzzification): Different triangular values developed by [51; 52; 53] were employed to fuzzify the linguistic data of the participants. The triangular values utilised in this study and developed by [53] are demonstrated in Figure 3, and the fuzzy number equivalents of the linguistic expressions are presented in Table 4.  
Figure 3: Fuzzy triangular values. Figure 2: Fuzzy DEMATEL method. Step-3 The Creation of a Direct Effects Matrix (\(\widetilde{Z}\)\(k\)): Individual direct influence matrix \(\widetilde{Z}^{k}=\left[\widetilde{z}_{ij}^{k}\right]_{n\times n}\) were formed by taking the influence evaluation of \(F_{i}\) factor on \(F_{j}\) factor for n factors from \(k\) selected experts. \(\widetilde{Z}^{k}\) is an \(n\times n\) matrix that has been obtained through the process of pairwise comparisons. The purpose of this matrix is to demonstrate the effect that the criteria have on each other. Here (Equation (A1)) \(\widetilde{Z}_{ij}\) is the degree of influence of criterion \(i\) on criterion \(j\). Step-4 The Creation of an Average Direct Effects Matrix (\(\widetilde{Z}\)): The arithmetic mean of the individual direct influence matrix was defined as the average direct influence matrix \(\widetilde{Z}=\left[\widetilde{z}_{ij}^{\sim}\right]_{n\times n}\) (Equation (A2)). Step-5 Creating Normalised Direct Effects Matrix (\(\widetilde{X}\)): It was generated using Equations (A3) and (A4). Step-6 Creating A Total Effect Matrix (\(\widetilde{T}\)): Equations (A5)-(A9) are used to obtain the total association matrix \(\widetilde{T}=\left[t_{ij}\right]_{n\times n}\) from the normalised direct effect matrix.