## 3 Performance Attributes and Scenarios
### MCDM Approach for Evaluating Thermal Gasification Techniques for MSW
#### 3.4.3 Normalization of the Decision Matrix  
Elimination of the effect of variation in criteria dimensions on the evaluation of the thermal gasification methods is necessary in order to normalize the matrix and in order to ensure equality among all the attributes in the same format. This requires the introduction of the normalized decision \(\mathrm{R_{ij}}\) obtained using Equation (10). \[\mathrm{R_{ij}}=\frac{\mathrm{C_{ij}}}{\sqrt{\sum\mathrm{C_{ij}^{2}}}} \tag{10}\]  
After normalization of the different evaluation criteria for all given thermal gasification techniques (refer to Equation (10)), the decision matrix is expressed for each scenario type as shown below in Tables 8 and 9. \begin{table}
\begin{tabular}{c c c c} \hline \hline  & \multicolumn{3}{c}{**E\({}_{\mathrm{j}}\) Entropy Weight**} \\ \hline
**Evaluation Criterion (C\({}_{\mathrm{j}}\)) \(\downarrow\)** & **Non-Recycling Scenario of MSW** & **Recycling Scenario of MSW** \\ \hline C\({}_{1}\) & 0.065 & 0.077 \\ \hline C\({}_{2}\) & 0.071 & 0.062 \\ \hline C\({}_{3}\) & 0.081 & 0.074 \\ \hline C\({}_{4}\) & 0.085 & 0.083 \\ \hline C\({}_{5}\) & 0.097 & 0.086 \\ \hline C\({}_{6}\) & 0.125 & 0.123 \\ \hline C\({}_{7}\) & 0.066 & 0.065 \\ \hline C\({}_{8}\) & 0.094 & 0.099 \\ \hline C\({}_{9}\) & 0.095 & 0.084 \\ \hline C\({}_{10}\) & 0.078 & 0.064 \\ \hline C\({}_{11}\) & 0.066 & 0.065 \\ \hline C\({}_{12}\) & 0.078 & 0.119 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: The entropy weight values for the different gasification methods. \begin{table}
\begin{tabular}{l l l l l l l} \hline \hline  & \multicolumn{3}{c}{**Alternative Thermal Gasification Techniques**} \\ \hline
**Evaluation Criterion (C\({}_{\mathrm{j}}\)) \(\downarrow\)** & **Updraft** & **Downdraft** & **Cross-Draft** & **Bubbling Bed** & **Circulating Fluidized Bed** & **Dual Fluidized Bed** \\ \hline C\({}_{1}\) & 0.399 & 0.451 & 0.296 & 0.574 & 0.443 & 0.154 \\ \hline C\({}_{2}\) & 0.381 & 0.352 & 0.415 & 0.421 & 0.447 & 0.426 \\ \hline C\({}_{3}\) & 0.279 & 0.254 & 0.216 & 0.261 & 0.289 & 0.812 \\ \hline C\({}_{4}\) & 0.283 & 0.425 & 0.312 & 0.453 & 0.453 & 0.481 \\ \hline C\({}_{5}\) & 0.987 & 0.017 & 0.006 & 0.137 & 0.077 & 0.002 \\ \hline C\({}_{6}\) & 0.471 & 0.236 & 0.236 & 0.471 & 0.471 & 0.471 \\ \hline C\({}_{7}\) & 0.629 & 0.419 & 0.524 & 0.314 & 0.210 & 0.105 \\ \hline C\({}_{8}\) & 0.341 & 0.327 & 0.313 & 0.429 & 0.368 & 0.600 \\ \hline C\({}_{9}\) & 0.154 & 0.193 & 0.193 & 0.386 & 0.309 & 0.811 \\ \hline C\({}_{10}\) & 0.645 & 0.737 & 0.154 & 0.074 & 0.111 & 0.006 \\ \hline C\({}_{11}\) & 0.798 & 0.332 & 0.199 & 0.193 & 0.399 & 0.133 \\ \hline C\({}_{12}\) & 0.277 & 0.066 & 0.830 & 0.277 & 0.277 & 0.277 \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Normalized decision matrix \(\mathrm{R_{ij}}\) for thermal gasification techniques for the non-recycling scenario. From Table 10, it is evident that in the case of a non-recycling scenario for criteria C3, C4, C5, and C7, the thermal gasification technique alternative 6: DUAL FB is the best strategy, and this technique is worst for criteria C1, C8, C9, C10, and C11. The gas produced by dual fluidized bed gasifiers has higher heating values and higher cold gas efficiency, as evident in the literature. Also, the tar content present in the gas is much lower [24]. This method is a poor performer in terms of emissions and fuel preparation requirements. In contrast, the thermal gasification technique alternative 4: BUBBLING BED is best for criterion C1, which is the gas production rate, and the alternative 5: CIRCULATING FB method is best for criterion C2, which is the carbon conversion efficiency. While the thermal gasification technique alternative 3: CROSS-DRAFT is the best strategy for criteria C6 and C8, it is the worst for criterion C3, and the alternative 2: DOWNDRAFT strategy is the best for criteria C10 and C12 but the worst for criterion C2. Similarly, one can make the observations regarding best and worst alternatives vs criteria to address the recycling scenario.