## 5 Decision Support Model for Group Decision Making with HPMPRs  
Now, the issues of consistency and consensus are addressed. Algorithms 1-3 will provide the consistent individual HPMPRs and the group HPMPR with agreement among decision-makers. To comprehend the final standing of the alternatives, first for the alternative \(x_{i}\) the \(i\)th row of group HPMPR is aggregated by the HPMG operator (Equation (29)), and the aggregated HPFEs are ordered according to their score and deviation. In the form of the Algorithm 4, a complete decision model is presented. Flowchart of the decision-making model is presented in Figure 7. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \(n\) & \(m\) & \(d\) & \(GCI_{r}\) & \multicolumn{5}{c}{\(\beta\)} \\ \cline{4-9}  & & & & **0.2** & **0.4** & **0.7** & **0.9** \\ \hline
7 & 7 & 7 & 1.01 & 1.891 & 2.21 & 5.123 & 16.213 \\  & & & 1.05 & 0.997 & 1.012 & 2.213 & 7.211 \\  & & & 1.1 & 0.995 & 0.985 & 1.213 & 3.456 \\  & 7 & 6 & 1.01 & 1.893 & 2.225 & 5.54 & 16.523 \\  & & & 1.05 & 0.995 & 1.12 & 2.241 & 7.543 \\  & & & 1.1 & 0.994 & 0.994 & 1.223 & 3.672 \\ \hline
8 & 8 & 4 & 1.01 & 1.674 & 2.123 & 5.112 & 16.254 \\  & & & 1.05 & 0.992 & 1.111 & 2.213 & 7.654 \\  & & & 1.1 & 0.992 & 0.991 & 1.211 & 3.254 \\ \hline
8 & 9 & 8 & 1.01 & 1.259 & 2.004 & 4.951 & 15.319 \\  & & & 1.05 & 0.991 & 1.101 & 2.121 & 7.545 \\  & & & 1.1 & 0.991 & 0.989 & 1.221 & 3.224 \\  & 8 & 7 & 1.01 & 1.261 & 2.112 & 4.998 & 15.119 \\  & & & 1.05 & 0.991 & 1.104 & 2.132 & 7.614 \\  & & & 1.1 & 0.992 & 0.992 & 1.225 & 3.514 \\  & 8 & 6 & 1.01 & 1.271 & 2.151 & 4.997 & 15.211 \\  & & & 1.05 & 0.993 & 1.112 & 2.135 & 7.664 \\  & & & 1.1 & 0.994 & 0.995 & 1.231 & 3.612 \\ \hline
9 & 10 & 9 & 1.01 & 1.101 & 1.121 & 4.121 & 10.123 \\  & & & 1.05 & 0.998 & 1 & 1.857 & 6.345 \\  & & & 1.1 & 0.992 & 0.995 & 1.235 & 2.986 \\  & 7 & 8 & 1.01 & 1.211 & 1.225 & 4.234 & 10.512 \\  & & & 1.05 & 0.999 & 1 & 1.978 & 6.546 \\  & & & 1.1 & 0.999 & 0.999 & 1.435 & 3.102 \\  & 9 & 7 & 1.01 & 1.112 & 1.235 & 4.225 & 10.562 \\  & & & 1.05 & 0.999 & 0.999 & 1.898 & 6.658 \\  & & & 1.1 & 0.999 & 1 & 1.452 & 3.21 \\ \hline
10 & 9 & 10 & 1.01 & 1 & 1 & 2.1 & 7.152 \\  & & & 1.05 & 1 & 1 & 1.21 & 4.231 \\  & & & 1.1 & 1 & 1 & 1.102 & 2.147 \\  & 8 & 9 & 1.01 & 1 & 1 & 2.211 & 7.236 \\  & & & 1.05 & 1 & 1 & 1.223 & 4.542 \\  & & & 1.1 & 1 & 1 & 1.113 & 2.231 \\  & 8 & 8 & 1.01 & 1 & 1 & 2.321 & 7.325 \\  & & & 1.05 & 1 & 1 & 1.341 & 4.653 \\  & & & 1.1 & 1 & 1 & 1.231 & 2.251 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: _Cont._  
**Input:** The HPMPRs \(H_{k}=(h_{ij,k})_{n\times n}\)\((k=1,2,3,...,m)\) made by decision-makers, the weight vector \(\omega=(\omega_{1},\omega_{2},...,\omega_{m})\) of decision-makers in a normalized form, consistency tolerance value \(CI_{r}\), group consensus tolerance value \(GCI_{r}\), the maximum number of iterations allowed \(t_{\max}\), and the parameters \(0<\alpha\), \(\beta<1\) for modification. **Output:** The final standings of all the alternatives. **Step 1:** Compute NHPMPRs \(\overline{H}_{k}=(\overline{h}_{ij,k})_{n\times n}\) with optimized parameters \(\zeta_{k}\). Let \(t=0\) and \(H_{k}^{(0)}=(h_{ij,k}^{(0)})_{n\times n}=\overline{H}_{k}=(\overline{h}_{ij,k} )_{n\times n}\). **Step 2:** Calculate the consistent HPMPRs \(\widetilde{H}_{k}^{(t)}=\left(\widetilde{h}_{ij,k}^{(t)}\right)_{n\times n}\) by Algorithm 1 and consistency indexes \(CI\left(H_{k}^{(t)}\right),\) where  
\[CI\left(H_{k}^{(t)}\right)=\frac{1}{4n^{\pi}}\sum_{i=1}^{n}\sum_{j=1}^{n}\sum _{i=1}^{d}\left(\left(\widetilde{h}_{ij,k}^{(t)}\right)^{\sigma(s)}\times \left(\widetilde{h}_{ij,k}^{(t)}\right)^{\sigma(s)}\right)+\frac{2}{nd(n+1)} \sum_{i=1}^{n}\sum_{j\geq i}^{n}\sum_{i=1}^{d}\left|\left(\overline{p}_{ij,k}^ {(t)}\right)^{\sigma(s)}-\left(\widetilde{p}_{ij,k}^{(t)}\right)^{\sigma(s)} \right|. \tag{37}\]  
**Step 3:** If \(CI\left(H_{k}^{(t)}\right)\leq CI_{r}\) for all \(k=1,2,...,m\), then go to Step 5; otherwise, go to Step 4.