## 3 The GIS-Based UGC Classification Processes: An Experimental Case
### Fuzzy Rule Set Creation: Construction of the Fuzzy Rule Set  
The seven indicators selected by the domain expert identify the input variables of the fuzzy rule set to be built. In order to create the fuzzy rules, a fuzzy partition of the domain of each indicator is constructed by the domain expert using triangular, S-shape and Z-shape fuzzy numbers. Figure 3 shows the fuzzy numbers used and their membership functions. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Indicator** & **Label** & **Inf** & **Mean** & **Sup** & **Type of Fuzzy Set** \\ \hline \multirow{4}{*}{I\({}_{1}\)} & Scanty & 0 & 10 & 20 & ZS \\  & Mean & 10 & 20 & 50 & TR \\  & Discrete & 20 & 50 & 100 & TR \\  & High & 50 & 100 & \(\infty\) & SS \\ \hline \multirow{4}{*}{I\({}_{2}\)} & Null & 0 & 2 & 5 & ZS \\  & Low & 2 & 5 & 10 & TR \\ \cline{1-1}  & Adequate & 5 & 10 & 30 & TR \\ \cline{1-1}  & High & 10 & 30 & 50 & TR \\ \cline{1-1}  & Very High & 30 & 50 & 100 & SS \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Fuzzy partitions of the indicators (SS = S-Shape, ZS = Z-Shape, TR = Triangular). Figure 3: Fuzzy numbers used to create the fuzzy sets. In order to extract the fuzzy rules, the expert defines the taxonomy of the UGA class. In our experiment, the following set of urban area classes is considered, in which each class characterizes a type of urban area characterized by the presence of urban green space with specific characteristics. The domain expert defined five UGA classes and they are described in Table 3.  
To each UGA class is assigned a fuzzy set defined in the domain [0, 1]; the five fuzzy sets are shown in Table 4. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Urban Green Area Class** & **Inf** & **Mean** & **Sup** & **Type of Fuzzy Set** \\ \hline
1 & 0 & 0.1 & 0.2 & SS \\
2 & 0.1 & 0.2 & 0.4 & TR \\
3 & 0.2 & 0.4 & 0.6 & TR \\
4 & 0.4 & 0.6 & 0.8 & TR \\
5 & 0.6 & 0.8 & 1 & ZS \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Fuzzy partition of the urban green area classes (UGA class). \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Indicator** & **Label** & **Inf** & **Mean** & **Sup** & **Type of Fuzzy Set** \\ \hline \multirow{4}{*}{I\({}_{3}\)} & Scanty & 0 & 5 & 10 & ZS \\  & Mean & 5 & 10 & 30 & TR \\  & Discrete & 10 & 30 & 50 & TR \\  & High & 30 & 50 & \(\infty\) & SS \\ \hline \multirow{4}{*}{I\({}_{4}\)} & Scanty & 0 & 10 & 20 & ZS \\  & Mean & 10 & 20 & 50 & TR \\  & Discrete & 20 & 50 & 100 & TR \\  & High & 50 & 100 & \(\infty\) & SS \\ \hline \multirow{4}{*}{I\({}_{5}\)} & Scanty & 0 & 10 & 20 & ZS \\  & Mean & 10 & 20 & 50 & TR \\  & Discrete & 20 & 50 & 100 & TR \\  & High & 50 & 100 & \(\infty\) & SS \\ \hline \multirow{4}{*}{I\({}_{6}\)} & Null & 0 & 2 & 5 & ZS \\  & Low & 2 & 5 & 10 & TR \\  & Adequate & 5 & 10 & 30 & TR \\  & High & 10 & 30 & 50 & TR \\  & Very High & 30 & 50 & 100 & SS \\ \hline \multirow{4}{*}{I\({}_{7}\)} & Null & 0 & 2 & 5 & ZS \\  & Low & 2 & 5 & 10 & TR \\  & Low & 2 & 5 & 10 & TR \\  & Low & 2 & 5 & 10 & TR \\  & Low & 2 & 5 & 10 & TR \\  & Low & 2 & 5 & 10 & TR \\  & Low & 2 & 5 & 10 & TR \\  & Low & 2 & 5 & 10 & TR \\  & 2 & 5 & 10 & 30 & TR \\  & 2 & 5 & 10 & 30 & TR \\  & High & 10 & 30 & 50 & TR \\  & Very High & 30 & 50 & 100 & SS \\ \hline \hline \end{tabular}
\end{table} 
Table 2: _Cuts._ \begin{table}
\begin{tabular}{c c} \hline \hline
**Urban Green Area Class** & **Description** \\ \hline \multirow{4}{*}{1} & Densely urbanized or industrial area with no urban \\  & greenery and high presence of built surfaces and \\  & waterproof open spaces \\  & Densely urbanized or industrial area with a low presence \\  & of urban greenery \\  & Urbanized area with minimal presence of urban greenery \\  & Urbanized area with urban greenery \\  & Tourist residential area or area with natural parks with \\  & high presence of urban greenery \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Urban green area classes (UGA class). Based on their knowledge, the expert extracts the set of fuzzy rules needed to classify the microzones.