# Fuzzy Fireworks Algorithm Based on a Sparks Dispersion Measure
## 11 Results and Discussion
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Number** & **IFWA** & **IFWA** & **IFFWA** & **DPIFFWA-I** & **DPIFFWA-I** & **DPIFFWA-I** \\ \hline
**Function** & **Mean** & **STD** & **Z-Value** & **Mean** & **STD** & **Z-Value** \\ \hline
1 & \(8.40\) & \(1.67\) & \(-1.645\) & \(4.87\) & \(1.07\) & \(-9.7483\) \\
2 & \(9.82\times 10^{-1}\) & \(1.93\times 10^{-1}\) & \(-1.645\) & \(7.17\times 10^{-1}\) & \(2.53\times 10^{-1}\) & \(-4.5613\) \\
3 & \(3.89\times 10^{2}\) & \(9.38\times 10^{1}\) & \(-1.645\) & \(2.72\times 10^{2}\) & \(6.96\times 10^{1}\) & \(-5.4865\) \\
4 & \(2.15\times 10^{5}\) & \(1.96\times 10^{5}\) & \(-1.645\) & \(3.50\times 10^{4}\) & \(3.29\times 10^{4}\) & \(-4.9607\) \\
5 & \(1.26\times 10^{-1}\) & \(2.83\times 10^{-1}\) & \(-1.645\) & \(1.54\times 10^{2}\) & \(2.39\times 10^{2}\) & \(-2.1330\) \\
6 & \(1.61\times 10^{2}\) & \(7.72\times 10^{1}\) & \(-1.645\) & \(4.18\times 10^{1}\) & \(2.47\times 10^{1}\) & \(-8.0548\) \\
7 & \(-9.96\times 10^{2}\) & \(5.98\times 10^{1}\) & \(-1.645\) & \(-9.16\times 10^{2}\) & \(2.21\times 10^{1}\) & \(-6.8731\) \\
8 & \(-1.80\) & \(8.48\times 10^{-5}\) & \(-1.645\) & \(-1.80\) & \(7.63\times 10^{-4}\) & 0 \\
9 & \(-7.86\) & \(5.98\times 10^{-1}\) & \(-1.645\) & \(-7.27\) & \(2.32\times 10^{-1}\) & \(-5.0381\) \\
10 & \(-1.00\) & \(6.29\times 10^{-4}\) & \(-1.645\) & \(-9.95\times 10^{-1}\) & \(5.88\times 10^{-3}\) & \(-4.6311\) \\
11 & \(3.01\) & \(1.21\times 10^{-2}\) & \(-1.645\) & \(3.05\) & \(5.56\times 10^{-2}\) & \(3.8503\) \\
12 & \(7.15\) & \(6.27\) & \(-1.645\) & \(6.39\) & \(2.15\) & \(-0.6280\) \\
13 & \(-1.03\) & \(4.00\times 10^{-4}\) & \(-1.645\) & \(-1.03\) & \(8.94\times 10^{-4}\) & 0 \\
14 & \(-1.86\times 10^{2}\) & \(1.98\times 10^{1}\) & \(-1.645\) & \(-2.01\times 10^{2}\) & \(6.51\) & \(3.9418\) \\ \hline \hline \end{tabular}
\end{table} 
Table 13: Hypothesis test between IFWA and DPIFFWA-I with SI = 2. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Number** & **IFWA** & **IFWA** & **IFFWA** & **DPIFFWA-II** & **DPIFFWA-II** \\ \hline
**Function** & **Mean** & **STD** & **Z-Value** & **Mean** & **STD** & **Z-Value** \\ \hline
1 & \(8.40\) & \(1.67\) & \(-1.645\) & \(5.20\) & \(1.48\) & \(-7.8546\) \\
2 & \(9.82\times 10^{-1}\) & \(1.93\times 10^{-1}\) & \(-1.645\) & \(5.90\times 10^{-1}\) & \(3.12\times 10^{-1}\) & \(-5.8524\) \\
3 & \(3.89\times 10^{2}\) & \(9.38\times 10^{1}\) & \(-1.645\) & \(2.31\times 10^{2}\) & \(1.27\times 10^{2}\) & \(-5.4812\) \\
4 & \(2.15\times 10^{5}\) & \(1.96\times 10^{5}\) & \(-1.645\) & \(4.30\times 10^{4}\) & \(6.14\times 10^{4}\) & \(-4.5868\) \\
5 & \(1.26\times 10^{-1}\) & \(2.83\times 10^{-1}\) & \(-1.645\) & \(6.06\times 10^{-2}\) & \(1.78\times 10^{1}\) & \(-1.0714\) \\
6 & \(1.61\times 10^{2}\) & \(7.72\times 10^{1}\) & \(-1.645\) & \(4.17\times 10^{1}\) & \(3.43\times 10^{1}\) & \(-7.7351\) \\
7 & \(-9.96\times 10^{2}\) & \(5.98\times 10^{1}\) & \(-1.645\) & \(-1.07\times 10^{3}\) & \(7.97\times 10^{1}\) & \(4.0678\) \\
8 & \(-1.80\) & \(8.48\times 10^{-5}\) & \(-1.645\) & \(-1.80\) & \(6.25\times 10^{-4}\) & 0 \\
9 & \(-7.86\) & \(5.98\times 10^{-1}\) & \(-1.645\) & \(-8.85\) & \(6.56\times 10^{-1}\) & \(6.1087\) \\
10 & \(-1.00\) & \(6.29\times 10^{-4}\) & \(-1.645\) & \(-9.97\times 10^{-1}\) & \(7.49\times 10^{-3}\) & \(-2.1861\) \\
11 & \(3.01\) & \(1.21\times 10^{-2}\) & \(-1.645\) & \(3.00\) & \(7.55\times 10^{-3}\) & \(-3.8404\) \\
12 & \(7.15\) & \(6.27\) & \(-1.645\) & \(2.72\) & \(1.92\) & \(-3.7003\) \\
13 & \(-1.03\) & \(4.00\times 10^{-4}\) & \(-1.645\) & \(-1.03\) & \(5.10\times 10^{-4}\) & 0 \\
14 & \(-1.86\times 10^{2}\) & \(1.98\times 10^{1}\) & \(-1.645\) & \(-2.08\times 10^{2}\) & \(2.38\) & \(6.0423\) \\ \hline \hline \end{tabular}
\end{table} 
Table 14: Hypothesis test between IFWA and DPIFFWA-II with SI = 2.