# Optimization of PFMEA Team Composition in the Automotive Industry Using the IPF-RADAR Approach
## 3 Methodology
### The Proposed IPF-RADAR Algorithm  
The process of candidate evaluation and selection of PFMEA team members, according to the proposed model, is carried out through the following steps:  
Step 1. After defining the criteria, \(k,k=1,\ldots,K\), based on the recommendations from the AIAG&VDA Handbook, the decision-makers, \(e,e=1,\ldots,E\), make their assessments of the importance of each criterion.  
Step 2. By applying the fuzzy addition mathematical operation, the assessments obtained at the level of each decision-maker, \(\widetilde{w}_{k}^{e}\), are aggregated, resulting in a unique unnormalized weight for each criterion, \(\widetilde{\omega}_{k}\). The fuzzy values are ultimately transformed into crisp values by applying the defuzzification procedure [46], and normalized by applying a linear normalization procedure to obtain crisp criteria weights, \(\omega_{k}\).  
Step 3. The candidates, \(i,\ i=1,\ldots,I\), are evaluated based on the considered criteria, \(k,k=1,\ldots,K\). The decision-makers assess the candidates by consensus. Based on these assessments, a fuzzy decision matrix is formed, \(\left[\widetilde{M}_{ik}\right]_{I\times K}\).  
The steps of the basic RADAR method were further extended using IVPFNs algebra rules [44; 45]. For the computational operation of subtraction, the distance between two IVPFNs was used.  
Step 4. The maximum proportion matrix, \(\alpha\), is generated:  
\[\left[\alpha_{ik}\right]_{I\times K} \tag{10}\]  
such that  
\[\alpha_{ik}=d\left(d\left(\underset{i}{\max}\widetilde{M}_{ik},\ \widetilde{M}_{ik}\right);\ \left(d\left(\underset{i}{\max}\widetilde{M}_{ik},\ \widetilde{M}_{ik}\right)+d\left(\widetilde{M}_{ik},\ \underset{i}{\min}\widetilde{M}_{ik}\right)\right)\right) \tag{11}\]  
Step 5. The minimum proportion matrix, \(\beta\), is generated:  
\[\left[\beta_{ik}\right]_{I\times K} \tag{12}\]such that  
\[\beta_{ik}=d\bigg{(}d\bigg{(}\overset{\sim}{M}_{ik},\ \underset{i}{\min} \overset{\sim}{M}_{ik}\bigg{)};\ \bigg{(}d\bigg{(}\underset{i}{\max} \overset{\sim}{M}_{ik},\ \overset{\sim}{M}_{ik}\bigg{)}+d\bigg{(}\overset{\sim}{M}_{ik}, \ \underset{i}{\min}\overset{\sim}{M}_{ik}\bigg{)}\bigg{)}\bigg{)} \tag{13}\]  
Considering the fact that all evaluated criteria are of the benefit type, the calculation formulas for cost-type criteria according to the RADAR method are not presented in this paper.  
The maximum and minimum values are taken as the highest and lowest assessments given by the decision-makers for each criterion, respectively.  
Step 6. The empty range matrix is generated:  
\[\left[E_{ik}\right]_{I\times K} \tag{14}\]  
such that  
\[E_{ik}=\left|\alpha_{ik}-\beta_{ik}\right| \tag{15}\]  
Step 7. The relative relationship matrix, \(\left[RR_{ik}\right]_{I\times K}\), is generated:  
\[RR_{ik}=\frac{\alpha_{ik}}{\beta_{ik}+E_{ik}} \tag{16}\]  
Step 8. The weighted relative relationship matrix, \(\left[WRR_{ik}\right]_{I\times K}\), is generated:  
\[WRR_{ik}=RR_{ik}\cdot\omega_{k} \tag{17}\]  
Step 9. The aggregated ranking index, \(RI_{i}\), is calculated:  
\[RI_{i}=\frac{\min\sum_{k=1}^{K}WRR_{i}}{\sum_{k=1}^{K}WRR_{i}} \tag{18}\]  
Step 10. The candidates are ranked using the RADAR method.  
The graphical representation of the proposed methodology is shown in Figure 1. The presented algorithm includes the main steps of the developed mathematical model.  
Figure 1: The proposed algorithm.