## 3 Results
### Calculation of the Synthetic Importance Weights of Evaluation Criteria
#### 3.1.3 Determination of the Fuzzy Positive and Fuzzy Negative Ideal Reference Points  
As the positive TFN are in the range of [0, 1], so the fuzzy positive ideal reference point and fuzzy negative ideal reference point can be defined as  
\[\text{A}^{+} =[(1,1,1),\ (1,1,1),\ (1,1,1),\ (1,1,1)] \tag{14}\] \[\text{A}^{-} =[(0,0,0),\ (0,0,0),\ (0,0,0),\ (0,0,0),\ (0,0,0)] \tag{15}\]  
1.4 Calculation for the Distance of Each Concrete Siliceous Material to FPIRP and FNIRP and Determining the Closeness Coefficient (CC) for Ranking of Concrete Siliceous Material  
The distance of each concrete siliceous material to the FPIRP and FNIRP can be calculated using Equations (10) and (11). Once the distances of concrete siliceous material from FPIRP and FNIRP are determined, the closeness coefficient for the concrete siliceous material alternatives can be obtained with Equation (12). Closeness coefficients are calculated based on the obtained FPIRP and FNIRP. The distances of concrete siliceous material from FPIRP and FNIRP, the closeness coefficient and ranking of various concrete siliceous materials are shown in Table 6. Figure 2 depicts the graphical representation of concrete siliceous materials ranking as per the obtained Closeness Coefficients.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Indicator** & **Description of the Indicator** & **Fuzzy Importance Weight** & **BNP Values** & **Rank** \\ \hline \(SC_{1}\) & Concrete curing system & (0.460,0.660,0.860) & 0.6600 & 13 \\ \(SC_{2}\) & Concrete compaction system & (0.540,0.740,0.880) & 0.7200 & 9 \\ \(SC_{3}\) & Consetiveness of concrete mix & (0.500,0.700,0.900) & 0.7000 & 11 \\ \(SC_{4}\) & Consistency of concrete mix & (0.540,0.740,0.900) & 0.7267 & 8 \\ \(SC_{5}\) & Comply strength requirement of concrete mix & (0.580,0.780,0.920) & 0.7600 & 6 \\ \(SC_{6}\) & Comply durability requirements of concrete mix & (0.5400,740,0.880) & 0.7200 & 9 \\ \(SC_{7}\) & Relative proportion of concrete components & (0.500,0.700,0.860) & 0.6867 & 12 \\ \(SC_{8}\) & Siliceous material availability & (0.220,0.420,0.620) & 0.4200 & 16 \\ \(SC_{9}\) & Energy conservation & (0.580,0.780,0.940) & 0.7667 & 3 \\ \(SC_{10}\) & Concrete material conservation & (0.700,0.900,1.000) & 0.8667 & 1 \\ \(SC_{11}\) & Waste material utilization & (0.620,0.820,0.960) & 0.8000 & 2 \\ \(SC_{12}\) & Conformation to environmental standards & (0.580,0.780,0.940) & 0.7667 & 5 \\ \(SC_{13}\) & Reduction in carbon foot print & (0.540,0.740,0.920) & 0.7333 & 7 \\ \(SC_{14}\) & Resistance to extreme exposure conditions & (0.580,0.780,0.940) & 0.7667 & 3 \\ \(SC_{15}\) & Waste material cleaning & (0.220,0.420,0.600) & 0.4133 & 17 \\ \(SC_{16}\) & Public welfare and safety & (0.240,0.380,0.560) & 0.3933 & 19 \\ \(SC_{17}\) & Increased employment & (0.220,0.420,0.500) & 0.3800 & 20 \\ \(SC_{18}\) & Concrete production cost & (0.240,0.420,0.6200) & 0.4267 & 15 \\ \(SC_{19}\) & Siliceous material transportation cost & (0.240,0.400,0.560) & 0.4000 & 18 \\ \(SC_{20}\) & Lifelong maintenance cost & (0.260,0.460,0.660) & 0.4600 & 14 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Fuzzy importance weight, best non-fuzzy performance (BNP), and rank of each indicator.