## 3 Results
### Street-Lighting System Assessment Using FSE  
The FSE method described in the methodology section provides an opportunity to capture the entire range of responses. The method gives higher weights to the response level (e.g., agree and disagree) towards which most of the respondents are inclined too. However, consideration is also given to the less selected response level (see Table 2). Equation (7) estimated the degree of association to the 5-level rating (\(S_{j}\) = 1, 2, 3, 4, 5) for each sub-criterion. The term \(X_{1}^{SC}\), representing the first sub-criterion, \"illumination brightness adequacy\" (refer to Table 1), was calculated as:  
\[\left(X_{i}^{SC}\right)_{1\times 5}=\left(x_{i1}^{SC},x_{i2}^{SC},x_{i3}^{SC},x_{ i4}^{SC},x_{i5}^{SC}\right)=\left(0.047,0.098,0.173,0.506,0.176\right)\] \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline
**Criterion** & **Statement to Assess** & **Strongly** & **Agree** & **Not** & **Disagree** & **Strongly** & **x2** & **Significance** & **Cramer’s V** & **Association** \\
**No.** & **Sub-Criteria** & **Aspect** & **Aspect** & **Aspect** & **Aspect** & **Disagree** & **Disagree** & **Aspect** & **Aspect** & **Cramer’s V** & **Association** \\ \hline \multirow{2}{*}{C\({}_{11}\)} & The illumination brightness of the city roads is considered adequate & 45 & 129 & 44 & 25 & 12 & 114 & Significant & 0.34 & Moderate \\ \hline \multirow{2}{*}{C\({}_{12}\)} & The level of lighting distribution on the roads is sufficient and regular & 47 & 104 & 60 & 33 & 11 & 128.1 & Significant & 0.36 & Moderate \\ \hline \multirow{2}{*}{C\({}_{13}\)} & Advertisement mobile screens and billboards beside the road do not adversely affect visibility & 48 & 90 & 39 & 47 & 31 & 29.4 & Significant & 0.17 & Weak \\ \hline \multirow{2}{*}{C\({}_{21}\)} & Current street-lighting design leads you to choose the right track & 56 & 123 & 40 & 23 & 13 & 121.4 & Significant & 0.35 & Moderate \\ \hline \multirow{2}{*}{C\({}_{22}\)} & The current night lighting in the city of Buraydah enables you to see the pavement, traffic signs, and the sides of the road & 45 & 116 & 48 & 35 & 11 & 168.2 & Significant & 0.41 & Moderate \\ \hline \multirow{2}{*}{C\({}_{23}\)} & Lights from incoming cars in the opposite direction do not adversely affect visibility & 42 & 79 & 48 & 59 & 28 & 106.2 & Significant & 0.33 & Moderate \\ \hline \multirow{2}{*}{C\({}_{31}\)} & The currently available street-lighting in your city is suitable for the eyes and does not cause glare & 54 & 109 & 41 & 39 & 12 & 138.0 & Significant & 0.37 & Moderate \\ \hline \multirow{2}{*}{C\({}_{32}\)} & During bad weather (dust or rain), the lighting is clear and adequate & 35 & 57 & 55 & 64 & 24 & 47.2 & Significant & 0.22 & Moderate \\ \hline \multirow{2}{*}{C\({}_{33}\)} & Road lighting level’s ambience is good in the city of Buraydah & 48 & 132 & 40 & 21 & 12 & 227.1 & Significant & 0.47 & Moderate \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Summary of responses, hypotheses, and the level of association between sub-criteria provided in Table 1 and overall performance. Similarly, \(SC_{ki}\), representing all the sub-criteria in Table 1, was calculated as:  
\[SC_{12}\ (sapcing\ appropriateness)=3.56\]  
and  
\[SC_{13}(Positioning\ of\ roadside\ advertisement\ billboards)=3.30.\]  
Relative importance weights of the sub-criteria, under each criterion, were estimated using Equation (9):  
\[w_{11}^{SC}=SC_{ki}/\sum_{i=1}^{n}SC_{ki}=3.67/(3.67+3.56+3.30)=3.67/10.53=0.348\]  
Likewise, the weight for \(w_{12}^{SC}\) was found to be 0.338, and 0.314 for \(w_{13}^{SC}\). Next, FSE applied Equation (11) to calculate the membership functions for each criterion:  
\[