## 2 Materials and Methods
### Fuzzy TOPSIS Methodology  
[PERSON] [25] implemented the concept of fuzzy sets theory to express the linguistic terms used in decision-making to alleviate the difficulty of operational management. [PERSON] and [PERSON] [26] first suggested the TOPSIS method, a linear weighting technique. The weights can be assigned to the criteria using various methods such as mean weight (MW), entropy analysis, eigenvector method, standard deviation (SD), analytical network process (ANP), and analytical hierarchy process (AHP). The proposed MCDM based Fuzzy TOPSIS approach is implemented to the problem of ranking the sustainable concrete siliceous material. Based on an in-depth literature review, eleven of the most common siliceous concrete materials were identified. It includes Nano-Cement, Nano-Particles of Siliceous Material, Natural Pozzolana, Metakaolin, Silica Fume, Fly Ash, Rice Husk Ash, Lime Stone, Blast Furnace Slag, Recycled Aggregate, and Waste Glass. Figure 1 illustrates the fuzzy-TOPSIS based framework for the ranking of sustainable siliceous concrete materials management. The experts with commendable experience in concrete technology were asked to judge and rank the selected sustainable criteria and sustainable indicators. A questionnaire (Sample Questionnaire-1, Appendix A) based on linguistics terms and triangular fuzzy number (TFN) was offered for  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Title** & **Sustainability Criteria** & **Principal Issues** \\ \hline \multirow{6}{*}{technical sustainability} & \(\bullet\) & silicous material availability \\  & \(\bullet\) & relative proportion of \\  & \(\bullet\) & concrete components \\  & \(\bullet\) & consistency of concrete mix \\  & \(\bullet\) & concrete compaction system \\  & \(\bullet\) & Cohesiveness of concrete mix \\  & \(\bullet\) & Concrete curing system \\  & \(\bullet\) & Comply strength \\  & \(\bullet\) & requirement of concrete mix \\  & \(\bullet\) & Comply durability \\  & \(\bullet\) & requirements of concrete mix \\ \hline \multirow{6}{*}{Environment sustainability} & \(\bullet\) & Waste material utilization \\  & \(\bullet\) & Concrete \\  & \(\bullet\) & material conservation \\  & Environmental & \(\bullet\) & Reduction in carbon \\  & \(\bullet\) & foot print \\  & \(\bullet\) & Resistance to extreme \\  & \(\bullet\) & exposure conditions \\  & \(\bullet\) & Energy conservation \\  & \(\bullet\) & Conformation to \\  & \(\bullet\) & environmental standards \\ \hline \multirow{6}{*}{Social sustainability} & \(\bullet\) & Public welfare and safety \\  & \(\bullet\) & Waste material cleaning \\  & \(\bullet\) & Increased employment \\ \cline{1-1}  & \(\bullet\) & \\ \cline{1-1}  & \(\bullet\) & \\ \cline{1-1}  & \(\bullet\) & \\ \cline{1-1}  & \(\bullet\) & \\ \hline \multirow{6}{*}{Economic sustainability} & \(\bullet\) & Life-long maintenance cost \\ \cline{1-1}  & \(\bullet\) & Concrete production cost \\ \cline{1-1}  & \(\bullet\) & Silicous material \\ \cline{1-1}  & \(\bullet\) & transportation cost \\ \cline{1-1} \cline{1  
establishing the importance of the criteria and role of siliceous concrete material towards sustainability. Questionnaire-1 used five linguistic terms [27], namely, Very Low, Low, Medium, High, and Very High, along with corresponding triangular fuzzy numbers (TFN) of (0,0.1,0.3), (0.1,0.3,0.5), (0.3,0.5,0.7), (0.5,0.7,0.9), and (0.7,0.9,1), respectively, reflecting the importance weights of each performance criteria in providing sustainability in siliceous concrete material. Later, on Questionnaire-2 (Appendix B) was administered which used five linguistic terms [28], namely, Very Poor, Poor, Fair, Good and Very Good, along with corresponding triangular fuzzy numbers (TFN) of (0,1,3), (1,3,5), (3,5,7), (5,7,9), and (7,9,10) to ascertain the role of each concrete siliceous material to provide the much needed sustainability on the selected set of twenty criteria. The overall performance of each concrete siliceous material was documented.