# Granular Description of Uncertain Data for Classification Rules in Three-Way Decision
## 5 Experiment and Discussion
### Publicly-Available Real-World Datasets  
To further discuss performance of the proposed method in three-way decision-making, four public real-world datasets [35] are also studied, e.g., Iris data (ID), Seeds data (SD), Wine data (WD) and Thyroid Disease dataset (TDD). Detailed information about these four datasets is presented below:  
* Iris data is a typical dataset for clustering and classification. It has 150 samples and four attributes. The dataset is grouped into three classes. * Seeds data has a total of 210 samples of three different varieties of wheat, such as Kama, Rosa and Canadian. It has seven attributes for data analysis. * Wine data are from the chemical analysis of wines in Italy. There are 13 constituents detected in three different types of wines. In this paper, a number of 178 samples are used for experimental study. * The thyroid disease data includes 215 samples with five attributes. These samples are classified into three classes: normal, suffers from hyperhyperroidism and hypothyroidism. According to the information described above, the parameters of four datasets could be simply summarized in Table 4.  
According to the above description, to form classification rules in three-way decisions, the key factor is to construct granules for uncertainty descriptions. Based on the steps described in Section 3, uncertainty regions should be described aiming at each pair of two classes when orienting to multiple classes-based decision processes. While, considering data distributions of real-world datasets are arbitrary, suitable feature learning should be implemented first. For example, neural-network-based models are used first to learn features rid of structure information, then classification rules considering uncertain data descriptions are formed for three-way decision-making. Referring to the proposed method, the descriptors of uncertainty regions are realized by hypersphere granules which are affected by parameters of \(\rho\) and \(\beta\). Then, classification rules are formed based on these uncertain granules and the original two-way decision. Performances of the final three-way decision process are presented as follows. Tables 5-8 present the performance of three-way decisions on the given four real-world datasets. By setting different proportions of uncertain data in three-way decisions, the parameter \(\beta\) for controlling granule size is optimized and shown in these tables. Then, the metrics of _Acc_, \(R\), \(P\) and \(E_{mis}\) are given out. Here, considering fuzzy sets for describing the uncertain regions among multiple classes are not sure, they are not considered for comparison, but \(E_{ur}=0\%\) is still used to represent the traditional two-way decision. Then, based on the results in the above tables, it is also seen when more uncertain data is considered in three-way decisions, the value of \(\beta\) increases to guarantee suitable granules for uncertain data description. Moreover, the performance of three-way decision-making improves as more data is regarded as uncertain data, namely more data for \"clerical review\". In this way, the drawback is the manual cost that will increase under the condition of performance improvement. Therefore, a practical way is to trade off the manual cost and performance. Fortunately, based on results in Tables 5-8 it is found that the performance improvement becomes delayed when the proportion of uncertain data reaches a threshold. In this way, we can combine the results of the performance and the cost calculation in (28) to select the suitable parameters, and finally to realize a practical three-way decision-making. \begin{table}
\begin{tabular}{c c c c} \hline \hline  & **\# of Samples** & **\# of Attributes** & **\# of Classes** \\ \hline ID & 150 & 4 & 3 \\ SD & 210 & 7 & 3 \\ WD & 178 & 13 & 3 \\ TDD & 215 & 5 & 3 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Parameters of four real-world datasets. results. Overall, the feasibility of the proposed method on uncertainty data description is validated.