# Recognition Algorithm Based on Improved FCM and Rough Sets for Meibomian Gland Morphology
## 3. MGD Identification Based on Improved FCM and Rough Sets
### Classification Rule Extraction  
In this paper, the establishment of a knowledge expression system is based on Tamura features of meibomian gland image recognition. Table 2 lists the texture characteristic data of meibomian gland images obtained from the experiments. There were 96 image samples we took as the training data, and the condition attributes were coarseness, contrast, directionality, line-likeness, regularity, and roughness. The decision attributes were named I, II, III, IV, representing the normal, shortened, deletion, and serious deletion meibomian gland, respectively.  
Table 2 contains the textures of the meibomian glands, and the dependencies between morphological features. However, this information is not easy to understand, and is difficult to directly be used for identification. Therefore, the data first requires further processing. The improved FCM algorithm was used to cluster six consecutive conditional variables. According to the principle of maximum membership [29], the original continuous feature space was mapped to discrete feature space using the improved FCM, as shown in Table 3.  
A flow chart of attribute reduction using the rough sets algorithm is shown in Figure 8. The rough sets theory was used for attribute reduction of the data in Table 3. We then used the Johnson algorithm [29] to obtain the core of conditional attributes as [coarseness, contrast, line-likeness, regularity]. This showed that for decision attributes, these four attributes were sufficient to maintain the classification ability of the information system. By sorting the reduced decision table, the rules of precision >0.75 and coverage >0.05 were selected [30]. Finally, the typical diagnostic rule table is shown in Table 4. Using the rough sets theory effectively explored the potential laws of knowledge by simplifying unnecessary attributes, and we could extract the most concise and accurate classification rules in pattern recognition.  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**Sample**} & \multicolumn{6}{c}{**Condition Attribute**} & \multirow{2}{*}{**Decision Attribute**} \\ \cline{2-2} \cline{4-7}  & **crs** & **con** & **dir** & **lin** & **reg** & **rgh** \\ \hline
1 & 19.018 & 44.011 & 35.55 & 0.22 & 0.943 & 63.028 & I \\
2 & 20.416 & 57.585 & 28.821 & 0.248 & 0.9 & 78.001 & II \\
3 & 18.599 & 45.586 & 37.261 & 0.178 & 0.949 & 64.185 & III \\
4 & 22.711 & 44.708 & 34.895 & 0.205 & 0.905 & 67.418 & IV \\
5 & 18.848 & 37.956 & 35.943 & 0.194 & 0.965 & 56.804 & II \\
6 & 21.759 & 62.73 & 26.198 & 0.312 & 0.916 & 84.489 & I \\
7 & 19.374 & 57.7 & 35.622 & 0.283 & 0.958 & 77.074 & II \\
8 & 19.454 & 59.199 & 26.239 & 0.293 & 0.929 & 78.653 & II \\ \hline  & & & & & & & \\ \hline
89 & 19.166 & 45.466 & 38.209 & 0.251 & 0.963 & 64.632 & IV \\
90 & 20.924 & 58.651 & 38.423 & 0.291 & 0.878 & 79.575 & III \\
91 & 21.067 & 41.477 & 29.958 & 0.236 & 0.902 & 62.545 & III \\
92 & 21.397 & 60.464 & 32.286 & 0.192 & 0.941 & 81.861 & IV \\
93 & 20.774 & 53.858 & 29.261 & 0.235 & 0.943 & 74.632 & IV \\
94 & 19.844 & 49.788 & 28.553 & 0.216 & 0.94 & 69.632 & II \\
95 & 19.443 & 46.836 & 33.736 & 0.266 & 0.938 & 66.279 & I \\
96 & 17.613 & 46.098 & 17.812 & 0.282 & 0.901 & 63.711 & II \\ \hline \hline \end{tabular}
\end{table}
Table 2: Characteristic data of meibomian gland image.  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**Sample**} & \multicolumn{6}{c}{**Condition Attribute**} & \multirow{2}{*}{**Decision Attribute**} \\ \cline{2-2} \cline{4-7}  & **crs** & **con** & **dir** & **lin** & **reg** & **rgh** \\ \hline
1 & 1 & 2 & 3 & 2 & 3 & 2 & I \\
2 & 3 & 4 & 1 & 3 & 1 & 4 & II \\
3 & 1 & 2 & 4 & 1 & 4 & 2 & III \\
4 & 4 & 2 & 3 & 1 & 1 & 3 & IV \\
5 & 1 & 1 & 3 & 1 & 4 & 1 & II \\
6 & 4 & 5 & 1 & 4 & 2 & 5 & I \\
7 & 2 & 4 & 3 & 4 & 4