## 4 Application in Circular Model Selection with Significant Challenges
### Stage 3: Sensitivity Analysis for Validation  
A sensitivity analysis is presented to examine the robustness of the proposed model ZF-DEMATEL-TOPSIS. In MCDM techniques particularly, weights exchange (i.e., 25%, 50%, 75% and 100%) does the sensitivity analysis. Evaluating the influence of the sub-criteria w.r.t criteria global weights on the order of the findings is the main goal of the sensitivity analysis assessment. The tests are then run with each initial sub-criteria w.r.t criteria weight increased by 25%, 50%, 75% and 100%. The values of the other sub-criteria w.r.t criteria are reduced by a set amount while one sub-criterion is raised, bringing the total number  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**CMs** & **C1 (Min)** & **C2 (Min)** & **C3 (Min)** & **C4 (Min)** & **C5 (Max)** & **C6 (Max)** & **C7 (Max)** & **C8 (Max)** \\ \hline CM1 & 0.057 & 0.071 & 0.059 & 0.057 & 0.053 & 0.048 & 0.033 & 0.036 \\ CM2 & 0.057 & 0.065 & 0.055 & 0.045 & 0.056 & 0.060 & 0.036 & 0.038 \\ CM3 & 0.046 & 0.037 & 0.060 & 0.046 & 0.057 & 0.060 & 0.043 & 0.041 \\ A\({}^{+}\) & 0.046 & 0.037 & 0.055 & 0.045 & 0.057 & 0.060 & 0.043 & 0.041 \\ A\({}^{-}\) & 0.057 & 0.071 & 0.060 & 0.057 & 0.053 & 0.048 & 0.033 & 0.036 \\ \hline
**CMs** & **C9 (Max)** & **C10 (Max)** & **C11 (Min)** & **C12 (Max)** & **C13 (Min)** & **C14 (Min)** & **C15 (Min)** & \\ \hline CM1 & 0.045 & 0.066 & 0.056 & 0.067 & 0.046 & 0.049 & 0.055 \\ CM2 & 0.046 & 0.071 & 0.053 & 0.068 & 0.057 & 0.060 & 0.058 & \\ CM3 & 0.041 & 0.071 & 0.045 & 0.066 & 0.034 & 0.035 & 0.042 & \\ A\({}^{+}\) & 0.046 & 0.071 & 0.045 & 0.068 & 0.034 & 0.035 & 0.042 & \\ A\({}^{-}\) & 0.041 & 0.066 & 0.056 & 0.066 & 0.057 & 0.060 & 0.058 & \\ \hline \hline \end{tabular}
\end{table}
Table 17: Calculate the A\({}^{+}\) and A\({}^{-}\).  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Circular Models** & **Si\({}^{+}\)** & **Si\({}^{-}\)** & **CC\({}_{i}\)** & **Rank** \\ \hline CM1 & 0.048 & 0.016 & 0.247 & 3 \\ CM2 & 0.048 & 0.020 & 0.292 & 2 \\ CM3 & 0.007 & 0.056 & 0.888 & 1 \\ \hline \hline \end{tabular}
\end{table}
Table 18: Compute closeness co-efficient.  
of sub-criteria to one using Equations (18) and (19). The global weight of each criterion is changed by 25%, 50%, 75% and 100% throughout a series of assessment runs and then follow the stage 2 to determine the circular models ranking. Totally, 60 assessment runs make up the scenario for this proposed model ZF-DEMATEL-TOPSIS.  
Increase the weight of the sub-criteria by 25% with respect to the main criteria, and a new set of weights for the sub-criteria w.r.t criteria would be generated. The new global weight of the sub-criteria relative to the criteria would alter as follows using Equations (18) and (19) would then be used to normalize the global weight of other sub-criteria w.r.t criteria. There is no change in the analysis of weight increased by 25% are shown in Figure 6.  
Increase the weight of the sub-criteria by 50% with respect to the main criteria, and a new set of weights for the sub-criteria w.r.t criteria would be generated. Similarly, there is a change in the analysis of weight increased by 50%, 75%, and 100% in the C13 and C14 the rank order changed into CM3 \(>\) CM1 \(>\) CM2 are shown in Figures 7-9.  
According to the Figure 6 is stable and resilient since adjustments to the global weights by 25% of the sub-criteria w.r.t criteria. With regard to the criterion, the closeness coefficient differs noticeably for each and every sub-criterion, but the high impact priority remains unchanged from the order in Table 18. The order of the circular models is consistent compared with stage 2 outcomes. However, in Figures 7-9 there are certain circumstances where they have some changes on the ultimate priority order of the circular models. Out of 60 experiments 6 experiments ranks are change so the consistency ratio is 90% for the sensitivity analysis.  
Figure 6: Sensitivity analysis for 25%.  
Figure 8: Sensitivity analysis for 75%.  
Figure 7: Sensitivity analysis for 50%.