# An IVTIFN-TOPSIS Based Computational Approach for Pipe Materials Selection
## 4 Results and Discussion  
### Evaluation Results  
Table 4 shows that the ranking result from the IVTIFN-TOPSIS (E) model is M3 \(>\) M4 \(>\) M1 \(>\) M2. It is clear that two optional plastic materials, i.e., PVC (M3) and HDPE (M4), are the optimal and near-optimal materials. Figure 3 shows that they have excellent performances in most criteria. For instance, PVC and HDPE show better capacities in corrosive resistance (C4) and scaling resistance (C5), which are the key functional premises to ensure the liability of the piping system. In contrast to M3 and M4, they have their own advantages and disadvantages. PVC shows superiorities in mechanical properties (C1 and C2), marketing price (C6) and roughness (C8). Nevertheless, HDPE is more environmentally-friendly and capable of anti-corrosion. By taking the relative importance of criteria into consideration, the most appropriate material for waste-water piping is PVC (M3). M1 performs better than M2 in most of the evaluation criteria, excepting C4 and C5. \begin{table}
\begin{tabular}{c c c c c c c c c c c c} \hline \hline  & & **C1** & **C2** & **C3** & **C4** & **C5** & **C6** & **C7** & **C8** & **C9** & **C10** & **C11** \\ \hline \multirow{4}{*}{Engineer 1} & M1 & E & E & VP & VP & VP & G & G & F & G & G \\  & M2 & E & E & VP & P & P & E & G & F & E & E & E \\  & M3 & F & F & F & G & G & P & P & E & P & P & P \\  & M4 & P & P & E & E & E & F & VP & G & P & VP & VP \\ \hline \multirow{4}{*}{Engineer 2} & M1 & E & E & F & P & P & E & E & F & E & E & G \\  & M2 & E & E & F & P & P & E & E & F & E & E & G \\  & M3 & F & F & G & G & G & P & P & E & P & P & F \\  & M4 & VP & VP & E & E & E & F & VP & G & P & P & P \\ \hline \multirow{4}{*}{Engineer 3} & M1 & E & E & P & P & VP & F & G & F & G & G & G \\  & M2 & P & VP & G & G & G & P & P & G & P & F & P \\  & M3 & F & F & E & E & E & F & P & G & VP & P & VP \\  & M4 & E & E & VP & VP & VP & G & G & F & G & G & G \\ \hline \multirow{4}{*}{Engineer 4} & M1 & E & E & VP & P & P & E & G & F & E & E & E \\  & M2 & F & F & F & G & G & P & P & E & P & P & P \\  & M3 & P & P & E & E & E & F & VP & G & P & VP & VP \\  & M4 & E & E & F & P & P & E & E & F & E & E & G \\ \hline \multirow{4}{*}{Engineer 5} & M1 & E & E & F & P & P & E & E & F & E & E & G \\  & M2 & F & F & G & G & G & P & P & E & P & P & F \\  & M3 & VP & VP & E & E & E & F & VP & G & P & P & P \\  & M4 & E & E & P & P & VP & F & G & F & G & G & G \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Subjective judgments on performances of the alternative materials. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multicolumn{2}{c}{**Criteria**} & \multicolumn{2}{c}{**Engineer 1**} & \multicolumn{2}{c}{**Engineer 2**} & \multicolumn{2}{c}{**Engineer 3**} & \multicolumn{2}{c}{**Engineer 4**} & \multicolumn{2}{c}{**Engineer 5**} \\ \hline \multirow{4}{*}{Functional} & C1 & EL & L & L & L & L & EL \\  & C2 & EL & L & EL & L & EL & EL \\  & C3 & EL & EL & EL & EL & EL \\  & C4 & EH & H & H & H & EH \\  & C5 & EH & EH & H & H & H \\ \hline \multirow{4}{*}{Economic} & C6 & EH & EH & EH & EH & EH \\  & C7 & L & M & L & L & L \\ \cline{1-1}  & C8 & L & M & M & L & L \\ \hline \multirow{4}{*}{Environmental} & C9 & EL & EL & EL & EL & EL \\  & C10 & EL & EL & L & L & L \\ \cline{1-1}  & C11 & EL & EL & L & L & L \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Subjective judgments on the importance of the proposed criteria. A correlation test is conducted to examine the correlation among criteria by using Pearson analysis, through which Table 5 shows that a number of criteria are significantly correlated to each other, highlighted by the functional attributes, i.e., among C1 to C5. The major purpose of the materials selection is to ensure reliable piping of waste water, by which anticorrosion and anticlogging are the prerequisites. The criteria C4 and C5 have directly reflected such functional performances.