## 5 Discussion  
As can be seen from Tables 1 to 5, the overall accuracies as well as Kappa coefficient in the presented fuzzy method stand higher than those of crisp method; in addition, the majority of the User's Accuracies and Producer's Accuracies in the presented method results show up higher than the crisp check method. It means that, using fuzzy rule-based system improved the accuracy of the classification.  
Considering the User's/Producer's accuracies of the presented method (Tables 1 and 3), one comes to the understanding that almost all segments are properly classified (with accuracies better than 80%) except those belonging to building and bare land classes. High level of User's Accuracy for buildings shows that the criteria for building extraction are adequate; meanwhile, low amount of Producer's Accuracy for building class indicates that there are some buildings that are not covered by this rule and are mistakenly labeled as another class. On the other hand, the User's Accuracy for bare land class is around 70% for both datasets, which means there are plenty of segments mistakenly committed to the bare land class. Comparing the related numbers, it is inferred that some buildings are not properly extracted; therefore, they remained unclassified and in the last step of classification (3.6.2), in which the unclassified segments are assigned to the bare land class, they are falsely classified as bare land, reducing both building and bare land classes' accuracies. The same contamination has happened for road segments. Those segments, which are missed in road classification, are transferred to the bare land class. In this study, also building detection is dependent on shadow detection. Therefore, if for some reason the method fails to detect a shadow, the associated building will be also missed. If ancillary data for building extraction, such as a building map or road map, is added to this process, the accuracy of the classification will be remarkably improved.  
The presented method performed quite well in vegetation detection, however, the crisp method missed to classify a huge number of segments related to vegetation.  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline  & **Building** & **Road** & **Shadow** & **Vegetation** & **Bare Land** & **Sum** & **User’s Accuracy** \\ \hline Building & 10,043 & 0 & 936 & 0 & 3,542 & 14,521 & **0.69** \\ Road & 1,856 & 20,303 & 1,347 & 0 & 3,906 & 27,411 & **0.74** \\ Shadow & 0 & 209 & 4,798 & 182 & 2,137 & 7,326 & **0.65** \\ Vegetation & 0 & 0 & 47 & 68,535 & 186 & 68,768 & **1** \\ Bare Land & 3,333 & 7,148 & 821 & 56,896 & 13,775 & 81,974 & **0.17** \\ Sum & 15,232 & 27,660 & 7,950 & 125,613 & 23,545 & 200,000 & \\ Producer’s Accuracy & **0.66** & **0.73** & **0.6** & **0.55** & **0.59** & \\ \hline \end{tabular}  
* The overall accuracies and Kappa coefficients for both of the methods are also presented in Table 5.  
\end{table}
Table 4: Confusion Matrix for the check project (QB data).  
\begin{table}
\begin{tabular}{c c c c c} \hline  & **Fuzzy Method** & **Crisp Method** & **Fuzzy Method** & **Crisp Method** \\  & **(for GeoEye)** & **(for GeoEye)** & **(for QB)** & **(for QB)** \\ \hline Overall Accuracy & 0.82 & 0.68 & 0.9 & 0.42 \\ Kappa Coefficient & 0.76 & 0.58 & 0.82 & 0.59 \\ \hline \end{tabular}  
* \end{table}
Table 5: Overall Accuracy and Kappa Coefficient of the presented method and the check project.  
Fredericton is a very green town, therefore the most of the QB image is vegetated and since this method is very good at detecting vegetation, the overall accuracy and kappa coefficient for QB image classification are affected by this classification accuracy and show up higher than that of GeoEye image.