## 3 Results and Discussion
### Subsumption Checking
This example of Table 5 implies that rather than to support the diagnosis of abnormal MRI result for a middle age patient with normal fasting glucose level all together, someone with a high cholesterol level and normal systolic blood pressure is more likely to support several possible subsets of items in consequent part from its proper rule (rule 846), e.g., sub-consequent rule 315: a middle age patient with abnormal MRI result. This means that the proper rule is still insufficient to replace the knowledge contained in its sub-consequent rules into a single rule. Although its CF value is only slightly higher than its proper rule, around 17.7%, the antecedent part of rule 315 still has better representation of positive dependency toward its consequent part. Moreover, by keeping sub-consequent rule 315, it might still contribute to be a consideration of another proper rules as sub-antecedence or sub-consequence or even become the proper rule of another set of sub-antecedence or sub-consequence rules in the next iteration. On the other hand, another example scenario that can occur during subsumption checking is presented in Table 6. In this case, one can see that among all of the obtained sub-antecedent rules of the proper rule (rule 837) only two sub-antecedent rules (rules 46 and 307) have a higher CF value compared to the proper rule. Since the proper rule still has sub-antecedent rules which are more interesting, we cannot imply that the proper rule can express the same meaning in the presence of rules 46 and 307 (i.e., some of the sub-antecedent rules). Hence, in this case, the proper rule is considered to be the redundant rule and should be discarded from the rule database while all of the sub-antecedent rule group is retained for further checking. A similar condition to Table 6 can also be seen in Table 7, where, among all of the obtained sub-consequent rules of the proper rule (rule 1044), there is one sub-consequent rule (rule 680) that has a higher CF value compared to the proper rule. In this condition, we also cannot imply that the proper rule represents the same meaning as its sub-consequent rules because at least one sub-consequent rule occurs that is more interesting than the proper rule. Therefore, we should keep the sub-consequent rule group for further evaluation and eliminate the redundant rule (i.e., the proper rule). \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Rule ID** & **Antecedent** & **Consequent** & **CF** \\ \hline
**45** & **[TC: High Cholesterol \(\Lambda\) SBP:Normal]** & **A: Middle Aged** & **0.453** & **sub-consequent** \\ \hline
**46** & **[TC: High Cholesterol \(\Lambda\) SBP:Normal]** & **FG: Normal** & **0.484** & **sub-consequent** \\ \hline
**315** & **[TC: High Cholesterol \(\Lambda\) SBP:Normal]** & **[A: Middle Aged** \(\Lambda\) MRI: Abnormal]** & **0.177** & **sub-consequent** \\ \hline
**319** & **[TC: High Cholesterol \(\Lambda\) SBP:Normal]** & **[FG: Normal \(\Lambda\) MRI: Abnormal]** & **0.168** & **sub-consequent** \\ \hline
**321** & **[TC: High Cholesterol \(\Lambda\) SBP:Normal]** & **[A: Middle Aged** \(\Lambda\)**FG: Normal]** & **0.375** & **sub-consequent** \\ \hline
846 & **[TC: High Cholesterol \(\Lambda\) SBP:Normal]** & **[A: Middle Aged** \(\Lambda\) FG: Normal \(\Lambda\) MRI: Abnormal]** & 0.164 & proper rule \\ \hline Notes: & & & \\ A & : Age & & \\ SBP & : Systolic Blood Pressure & & \\ TC & : Total Cholesterol & & \\ FG & : Fasting Glucose & & \\ MRI & : Magnetic Resonance Imaging & & \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Example of subsumption rules (proper rule and its sub-consequences). Towards this end, as shown in Figure 5, the result from our proposed algorithm shows that it can detect 1026 subsumption rules from an initial set of 1295 extracted rules. The proposed method reduced a greater number of redundant rules because the total number of extracted rules grew and led to a greater number of redundant rules when the support threshold was low.