# Risk Factor Analysis of Elevator Brake Failure Based on DEMATEL-ISM
## 3 Improved DEMATEL-ISM Analytical Methods
### Grey DEMATEL Method  
DEMATEL analysis is based on expert judgement, but the numerical value given through expert judgement often fail to capture the inherent fuzziness in the relationships between factors. Grey System Theory offers a solution to this issue of system ambiguity by using grey numbers or intervals rather than precise values in the decision-making process. This approach introduces greater flexibility and aligns more closely with real-world scenarios. The specific numerical values of expert judgement and expert authority weights \begin{table}
\begin{tabular}{c c c c} \hline
**Category of Cause** & **Behavioral Stages** & **Main Category** & **Failure Risk Factors** \\ \hline \multirow{8}{*}{Internal Causes} & & Unsafe Actions & Error Action S1 \\  & & Unauthorized Action S2 \\ \cline{2-4}  & Stage I Disposable & & Brake Spring S3 \\ \cline{2-4}  & Behavior and & & Spring-loaded Rod S4 \\ \cline{2-4}  & Physical State & Unsafe Object State & Gate Tile Assemblies S5 \\ \cline{2-4}  & & & Solenoid Assembly S6 \\ \cline{2-4}  & & & Manual Release Assembly S7 \\ \hline \multirow{4}{*}{External Causes} & & Technical Qualification S8 \\  & & Personal Behavior & Safety Knowledge S9 \\ \cline{2-4}  & & Attitude of Responsibility S10 \\ \cline{2-4}  & Stage III & Safety Management & Policy Planning S11 \\ \cline{2-4}  & Operational Behavior & Systems & Management Control S12 \\ \cline{2-4}  & Stage IV Guiding Behavior & Safety Culture & Subjective Responsibility S13 \\ \cline{2-4}  & & & Safety Participation S14 \\ \hline \multirow{2}{*}{External Causes} & & & Contracting Units S15 \\ \cline{2-4}  & & External Factors & Government and Industry \\ \cline{1-1}  & & & Organizations S16 \\ \hline \end{tabular}
\end{table} 
Table 2: Comprehensive failure risk factor indicator system. are converted into grey number intervals to deal with the ambiguity in the decision-making process. To this end, grey system theory can be combined with DEMATEL to analyze the causal and logical relationships between the risk factors of elevator brake failure. The specific steps are as follows:  
1. Experts are organized to evaluate the mutual influence relationship of each influencing factor in the comprehensive failure risk factor indicator system, and the influence degree from low to high is classified into five categories: no influence, low influence, general influence, high influence and very high influence, respectively. The corresponding grey numbers of the intervals corresponding to the experts' scores were determined, as shown in Table 3. The experts, coming from various roles, provide different perspectives on elevator brake failure risks. Combined with the grey system theory, the grey number of intervals corresponding to the authority of the experts were determined, as shown in Table 4.  
2. The grey number matrix was formed by combining Table 3 with the direct influence matrix of elevator brake failure risk. 3. The grey number matrix is standardized and clarified through Formulas (1)-(3), while the same operation is performed for the authority of the experts according to Table 4, and the expert authority matrix \(Z\) is found using Formula (4), where \(Z_{ij}\) is the element of the \(i\)th row and the \(j\)th column in the expert authority matrix.