# Combining Fuzzy C-Means Clustering with Fuzzy Rough Feature Selection
## 6 Discussion and Conclusions  
A new method named C-FRFS based on fuzzy rough feature selection has been presented in this paper. The first development based on the fuzzy c-means clustering uses a new kind of membership function which automatically forms the membership matrix only with the knowledge contained in the dataset itself. The second development employs the setting up of the fuzzy relation--different to methods used in many articles which use a single equation--we have combined fuzzy equivalence mentioned in other research and the membership function generated through the above way to set  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Method** & **Rank** \\ \hline C-FRFS & 1.0556 \\ T-FRFS & 1.9444 \\ FRFS & 3.3333 \\ Unred. & 3.6667 \\ \hline \hline \end{tabular}
\end{table}
Table 6: Average ranks of methods.  
\begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline
**Datasets** & **Glass** & **Iris** & **Cleveland** & **Wine** & **User** & **Vertebral** & **Sonar** & **Yeast** & **Hillvalley** & **Mean** \\ \hline C-FRFS & 63.66 & 94.52 & **55.01** & **95.51** & **91.01** & 80.90 & 72.44 & 56.36 & 50.59 & 73.33 \\ T-FRFS & 64.85 & 94.52 & 54.46 & 94.82 & 90.99 & 71.11 & 72.49 & 56.55 & 50.84 & 72.29 \\ FRFS & **66.46** & **94.82** & 54.61 & 95.38 & 90.65 & **81.11** & 70.04 & **56.99** & **51.03** & 73.45 \\ Unred. & **66.46** & **94.82** & 54.42 & 95.13 & 90.65 & **81.11** & **76.07** & **56.99** & **51.03** & **74.08** \\ \hline \hline \end{tabular}
\end{table}
Table 4: Resulting classification accuracies. Unred.: unreduced.  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Method** & **Rank** \\ \hline C-FRFS & 1.0556 \\ T-FRFS & 1.9444 \\ FRFS & 3.3333 \\ Unred. & 3.6667 \\ \hline \hline \end{tabular}
\end{table}
Table 5: Division of accuracies and number of selected features.  
up the fuzzy relation. An example is given to illustrate how reduction may be achieved. Note that no user-defined thresholds are required for the method, although a choice must be made regarding fuzzy connections and the priori coefficient of fuzzy equivalence. Experimental results over nine datasets taken from UCI showed the applicability and effectiveness of our proposed new method. In order to measure the performance of every method, we considered the number of selected features, classification accuracies, and the division of classification accuracies by the number of selected features. We compared the results operated on different methods, such as T-FRFS, FRFS, unreduced, and our new method C-FRFS. The comparisons indicated that our method was outperformed. We also compared the time taking of three methods on different sizes of datasets. The results demonstrated that our new method did not influence the efficiency remarkably. That was to say, we improved the accuracy and validity of feature selection with nearly no time loss.  
Further research in this area will include a more in-depth experimental investigation of the prior coefficient with its evaluation and a more efficient fuzzy clustering method to raise up the accuracies of our feature selection method.  
Conceptualization, R.Z. and L.G.; Data curation, X.Z.; Funding acquisition, L.G.; Investigation, R.Z.; Methodology, R.Z. and X.Z.; Project administration, L.G. and X.Z.; Resources, L.G.; Software, R.Z.; Supervision, L.G.; Validation, R.Z., L.G., and X.Z.; Visualization, R.Z.; Writing--original draft, R.Z.  
This research was funded by the National Key R&D Program of China (Grant No. 2017 YFB080301). The APC was funded by L.G.  
The authors would like to thank the reviewers for their helpful advice.  
The authors declare no conflict of interest.