# Fuzzy-FMEA Theory Approach for Prioritizing Supply Chain Nervousness Factors
## 3 Research Methodology
### SCN Model  
The integrated fuzzy-FMEA-gray correlation approach is used to rank the SCN factors based on their impacts and priorities. The proposed integrated FMEA model described in [58; 67] is applied in this study to analyze the nervousness modes estimation as follows:  
Step 1: Forming a rating index system. Based on Table 2, the following sets are defined:  
\[\text{Set of the level I elements}:\;l=\{P,\;V,\;S,\;D,\;F\},\]  
Set of the level II elements:  
\[l_{i}=\{P_{1},\;P_{2},\;P_{3},V_{1},\;V_{2},\;V_{3},S_{1},\;S_{2},\;S_{3},D_{1}, \;D_{2},\;D_{3},F_{1},\;F_{2},\;F_{3}\}\;\forall\;i=1,2,3\]  
Set of the level III elements : \(l_{i}I_{j}=\{P_{1}I_{1},\;\cdots,\;L_{3}I_{2}\}\;\forall\;i=1,2,3\;\&\;j=1,2\). Step 2: Defining the evaluation sets as shown in Table 3. The evaluation is based on seven semantic items: extremely unlikely (EU), very unlikely (VU), unlikely (UL), neutral (NE), likely (LK), very likely (VL), and extremely likely (EL). The experts give fuzzy scores for the semantic elements. Then, each interruption failure mode is given a semantic value for each measure of severity (Se), occurrence (Oc), and detection (De). \begin{table}
\begin{tabular}{p{113.8 pt} p{113.8 pt} p{113.8 pt}} \hline \hline
**Level I Elements** & **Level II Elements** & **Interruption Mode** \\ \hline \multirow{4}{*}{Visibility (V)} & Collaboration (V1) & V1 II: Less transparency \\ \cline{2-3}  & & V1I2: Competitiveness among partners \\ \cline{2-3}  & & V2 II: Lack of consistent decision-making \\ \cline{2-3}  & & V2I2: Lack of trust and willingness \\ \cline{2-3}  & & V3 II: Shortages/lack of exchange information \\ \cline{2-3}  & & V3I2: Low employees confidence \\ \hline \multirow{4}{*}{Stability (S)} & Policies (S1) & S1 II: Lack of prioritization \\ \cline{2-3}  & & S1I2: Design change \\ \cline{2-3}  & Disaster recovery (S2) & S2 II: Mismatch between supply and demand \\ \cline{2-3}  & & S2I2: Long recovery time \\ \cline{2-3}  & Stable roles and regulations (S3) & S3 II: Difficulties of regulatory compliance \\ \cline{2-3}  & & S3I2: Changes in government policies \\ \hline \multirow{4}{*}{DSS (D)} & Expertise (D1) & D1 III: Variations in skills \\ \cline{2-3}  & & D1I2: Scarcity of special competencies \\ \cline{2-3}  & Powerful tools (D2) & D2 II: Selecting the right tool \\ \cline{2-3}  & & D2I2: Criteria, process mapping, and flow problems \\ \cline{2-3}  & Technology (D3) & D3 II: Technological constraints (implementation) \\ \cline{2-3}  & & D3I2: Digital transformation (SC transformation) \\ \hline \multirow{4}{*}{Flexibility (F)} & Awareness (L1) & L1 III: Lack of trends and situational awareness \\ \cline{2-3}  & & L1I2: Deficiencies in traceable and sustainable awareness \\ \cline{2-3}  & Resilience (L2) & L2 II: Lack of resistance, recovery, and redundancy systems (plans) \\ \cline{2-3}  & & L2I2: Unexpected changes (external changes) \\ \cline{2-3}  & Innovation (L3) & L3 II: Slow reaction to modern innovations \\ \cline{2-3}  & & L3I2: Adoption of significant changes \\ \hline \hline \end{tabular}
\end{table} 
Table 2: _Cont._Let \(u=\{EU,\,VL,\,UL,\,NE,\,LK,\,VL,\,EL\}\) be the set of the semantic elements and \(k^{u}_{e}=(a^{u}_{e},\,p^{u}_{e},\,c^{u}_{e})\) be the triangular fuzzy evaluation of the semantic value \(u\) given by expert \(e\). Then, \(k^{u}=(a^{u},b^{u},\,c^{u})\) represent the weighted fuzzy evaluations on semantic value \(u\). \(k^{u}\) can be obtained by means of the following equations:  
\(a^{u}=\sum_{e=1}^{n}\rho_{e}a^{u}_{e},\quad b^{u}=\sum_{e=1}^{n}\rho_{e}b^{u}_{ e},\quad c^{u}=\sum_{e=1}^{n}\rho_{e}c^{u}_{e},\)  
\(\sum_{e=1}^{n}\rho_{e}=1,\,0\leq\rho_{e}\leq 1,\,\,\) for each \(u=\{EU,\,VL,\,UL,\,NE,\,LK,\,VL,\,EL\}\),  
where \(\rho_{e}\) is a weight given to reflect the importance of evaluation made by expert \(e\), \(e\ =\ 1,\cdots,\,n\).