## 6 A Practical Example for GDM with IVIFPRs
### Comparative Analyses
#### 6.2.1 Comparison with [PERSON]'s Method  
We adopt [PERSON]'s method [12] to solve the practical example in 6.1. Similar to [PERSON]'s method, set the consistent threshold value \(\mathrm{MCI}_{0}=0.1\) and group's opinions \(l=0.5\), different DMs' weight vectors \(\eta_{i}(i=1,2,3)\) can be obtained when taking different values of parameter \(\tau\), which denotes three particular principles of minority, majority and compromise principle if \(\tau=0\), \(1\) and \(0.5\), respectively. The calculation results are shown in Table 3. Additionally, when \(\mathrm{MCI}_{0}=0.1\), the ranking orders of alternatives for different values of parameters (\(\varphi\) in the proposed algorithm and \(\tau\) in [PERSON]'s method [12]) are depicted in Figure 2. \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline \(\varphi\) & \(S(w_{1})\) & \(H(w_{1})\) & \(S(w_{2})\) & \(H(w_{2})\) & \(S(w_{3})\) & \(H(w_{3})\) & \(S(w_{4})\) & \(H(w_{4})\) & **Ranking Order** \\ \hline
0 & 0.2449 & 0.9393 & 0.3092 & 0.9461 & 0.2752 & 0.9442 & 0.2122 & 0.9338 & \(x_{2}>x_{3}>x_{1}>x_{4}\) \\
0.1 & 0.2451 & 0.9393 & 0.3091 & 0.9461 & 0.2751 & 0.9443 & 0.2122 & 0.9339 & \(x_{2}>x_{3}>x_{1}>x_{4}\) \\
0.2 & 0.2451 & 0.9395 & 0.3090 & 0.9463 & 0.2750 & 0.9445 & 0.2123 & 0.9341 & \(x_{2}>x_{3}>x_{1}>x_{4}\) \\
0.3 & 0.2451 & 0.9395 & 0.3091 & 0.9464 & 0.2749 & 0.9445 & 0.2123 & 0.9341 & \(x_{2}>x_{3}>x_{1}>x_{4}\) \\
0.4 & 0.2450 & 0.9396 & 0.3093 & 0.9466 & 0.2749 & 0.9446 & 0.2121 & 0.9343 & \(x_{2}>x_{3}>x_{1}>x_{4}\) \\
0.5 & 0.2454 & 0.9394 & 0.3092 & 0.9466 & 0.2747 & 0.9444 & 0.2122 & 0.9344 & \(x_{2}>x_{3}>x_{1}>x_{4}\) \\
0.6 & 0.2454 & 0.9394 & 0.3094 & 0.9466 & 0.2745 & 0.9445 & 0.2121 & 0.9345 & \(x_{2}>x_{3}>x_{1}>x_{4}\) \\
0.7 & 0.2453 & 0.9389 & 0.3090 & 0.9461 & 0.2754 & 0.9440 & 0.2124 & 0.9342 & \(x_{2}>x_{3}>x_{1}>x_{4}\) \\
0.8 & 0.2452 & 0.9389 & 0.3089 & 0.9461 & 0.2755 & 0.9441 & 0.2125 & 0.9341 & \(x_{2}>x_{3}>x_{1}>x_{4}\) \\
0.9 & 0.2472 & 0.9370 & 0.3116 & 0.9456 & 0.2715 & 0.9421 & 0.2108 & 0.9348 & \(x_{2}>x_{3}>x_{1}>x_{4}\) \\
1 & 0.2460 & 0.9370 & 0.3101 & 0.9463 & 0.2722 & 0.9418 & 0.2110 & 0.9371 & \(x_{2}>x_{3}>x_{1}>x_{4}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Computation results and ranking orders for different values of parameters \(\varphi\) with \(\mathrm{MCI}_{0}=0.1\)  
\begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline
**Parameter** & \(S(w_{1})\) & \(H(w_{1})\) & \(S(w_{2})\) & \(H(w_{2})\) & \(S(w_{3})\) & \(H(w_{3})\) & \(S(w_{4})\) & \(H(w_{4})\) & **Ranking Order** \\ \hline \(\mathrm{MCI}_{0}=0.1\) & 0.2454 & 0.9394 & 0.3092 & 0.9466 & 0.2747 & 0.9444 & 0.2122 & 0.9344 & \(x_{2}>x_{3}>x_{1}>x_{4}\) \\ \(\mathrm{MCI}_{0}=0\) & 0.2489 & 0.9348 & 0.3092 & 0.9423 & 0.2732 & 0.9400 & 0.2112 & 0.931 Table 3 and Figure 2 reveal that the ranking order results are different, but the best alternative is \(x_{2}\), which is the same as the proposed algorithm. Compared with [PERSON]'s method [12], the proposed algorithm has the following advantages. 1. When measuring the consistency degree of an IVIFPR, the proposed algorithm is more straightforward than [PERSON]'s method [12]. [PERSON]'s method [12] needs resort to two particular IFPR matrices from original IVIFPR. In contrast, the proposed algorithm directly performs the measurement work only depending on original IVIFPR, which can avoid losing original information via [PERSON]'s method [12]. 2. In terms of repairing and improving the unacceptable multiplicative consistent IVIFPR, different from the iterative algorithms proposed in [PERSON]'s method [12], this paper directly built an optimization model through considering various decision-making principles, which can quickly obtain the acceptable consistent IVIFPR and flexibly reflect the principles of decision making. 3. For determining priority weights of alternatives, [PERSON]'s method [12] constructed a goal optimization model which needs numerous computations.