## 5 Results and Discussion
\begin{table}
\begin{tabular}{c c c c c} \hline \hline \multicolumn{1}{c}{**Criteria**} & \(\mathbf{K}\) & \(I\) & \(m\) & \(u\) \\ \hline Length & 4 & 0.05 & 0.1 & 0.17 \\ Number of junctions & 1 & 0.32 & 0.4 & 0.5 \\ Absence of footpath & 2 & 0.23 & 0.3 & 0.39 \\ Slope & 3 & 0.14 & 0.20 & 0.28 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Routes after being fuzzified and normalized between 0 and 10. Absence of footpath:  
\[(0.23\times 5,\ 0.30\times 7,\ 0.39\times 9)=(1.150,\ 2.100,\ 3.510)\]  
Slope:  
\[(0.14\times 1,\ 0.20\times 1,\ 0.28\times 3)=(0.140,\ 0.200,\ 0.840)\]  
All these calculations were carried out for only the first participant to obtain the weighted normalized decision matrix in Table 8.  
In Step 3, the fuzzy positive ideal condition (FPIC: the best condition, \(A^{+}\)) and the fuzzy negative ideal condition (FNIC: the worst condition, \(A^{-}\)) were defined by using Equations (6a) and (6b). In Formulas (6a) and (6b), the fuzzy positive \(A^{+}\) and negative \(A^{-}\) ideal solutions are defined; the values are computed by multiplying the fuzzy number of weight for each criterion (\(\widetilde{w}_{j}\)) by the fuzzy number of very high (VH) and very low (VL) ratings of the route, where VH corresponds to the fuzzy positive ideal solution (FPIS: the best condition, \(A^{+}\)) and VL corresponds to the fuzzy negative ideal solution (FNIS: the worst condition, \(A^{-}\)). The fuzzy numbers of the VH rating of the route are \((9,\ 10,\ 10)\) and the fuzzy numbers of VL \((1,\ 1,\ 3)\). The weight of the criteria for the first participant, as an example, are as follows: for length \((0.05,\ 0.10,\ 0.17)\), number of junctions \((0.32,\ 0.40,\ 0.50)\), absence of footpath \((0.23,\ 0.30,\ 0.39)\), and slope \((0.14,\ 0.20,\ 0.28)\). All these fuzzy numbers are multiplied by VH and VL numbers to obtain \(A^{+}\) and \(A^{-}\) as in the following calculations: \begin{table}
\begin{tabular}{c c c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Route**} & \multicolumn{4}{c}{**Length**} & \multicolumn{4}{c}{**No. of Junctions**} & \multicolumn{4}{c}{**Absence of Footpath**} & \multicolumn{4}{c}{**Slope**} \\ \cline{2-13}  & \(I\) & \(m\) & \(u\) & \(I\) & \(m\) & \(u\) & \(I\) & \(m\) & \(u\) & \(I\) & \(m\) & \(u\) \\ \hline R1 & 1 & 1 & 3 & 5 & 7 & 9 & 5 & 7 & 9 & 1 & 1 & 3 \\ R2 & 1 & 1 & 3 & 3 & 5 & 7 & 5 & 7 & 9 & 1 & 1 & 3 \\ R3 & 3 & 5 & 7 & 3 & 5 & 7 & 5 & 7 & 9 & 1 & 1 & 3 \\ R4 & 1 & 1 & 3 & 5 & 7 & 9 & 5 & 7 & 9 & 1 & 1 & 3 \\ R5 & 1 & 1 & 3 & 9 & 10 & 10 & 5 & 7 & 9 & 3 & 5 & 7 \\ R6 & 1 & 1 & 3 & 3 & 5 & 7 & 5 & 7 & 9 & 3 & 5 & 7 \\ R7 & 1 & 3 & 5 & 3 & 5 & 7 & 1 & 3 & 5 & 1 & 1 & 3 \\ R8 & 1 & 1 & 3 & 3 & 5 & 7 & 3 & 5 & 7 & 1 & 1 & 3 \\ R9 & 1 & 1 & 3 & 1 & 1 & 3 & 3 & 5 & 7 & 1 & 3 & 5 \\ R10 & 5 & 7 & 9 & 3 & 5 & 7 & 3 & 5 & 7 & 3 & 5 & 7 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: The importance of the weight of the criteria for the first participant. \begin{table}
\begin{tabular}{c c c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Route**} & \multicolumn{4}{c}{**Length**} & \multicolumn{4}{c}{**No of Junctions**} & \multicolumn{4}{c}{**Absence of Footpath**} & \multicolumn{4}{c}{**Slope**} \\ \cline{2-13}  & \(I\) & \(m\) & \(u\) & \(I\) & \(m\) & \(u\) & \(I\) & \(m\) & \(u\) & \(I\) & \(m\) & \(u\) \\ \hline R1 & 0.050 & 0.100 & 0.510 & 1.600 & 2.800 & 4.500 & 1.150 & 2.100 & 3.510 & 0.140 & 0.200 & 0.840 \\ R2 & 0.050 & 0.100 & 0.510 & 0.960 & 2.000 & 3.500 & 1.150 & 2.100 & 3.510 & 0.140 & 0.200 & 0.840 \\Step 5 estimated the relative closeness coefficient \(\widetilde{\widetilde{C}}_{i}\) of each alternative by Equation (8). Step 6 defuzzified the calculated fuzzy relative closeness coefficient \(\widetilde{\widetilde{C}}_{i}\) by Equation (9), and Step 7 calculated the \(ACI\) for each route by Equation (10). Table 10 presents the estimated \(ACI\) values for all routes. All these steps were repeated for all participants because each participant gives a different importance to the others based on their preferences.