## 3 Results and Discussion
### Circularity Checking  
After performing subsumption checking, the current rules are subjected to circularity checking. Basically, there are two type of circularity in this study, as previously mentioned in Definition 9. In the case of direct-circular rules, the program detected 54 conditions of direct-circular rules, which basically contained 27 pairs of direct-circular rule conditions. The following table contains examples of direct-circular rules that were detected. In KBSs when there is a circular redundancy in the rule base, then the last rule of the cycle can simply be eliminated. In the direct-circular type I scenario, even though the order of the circular rules is swapped, they maintain their circularity. For instance, in Table 8, one can see that rules 357 and 359 are a pair of direct-circular rules. Without considering any interestingness measure, then rule 359 is supposed to be discarded from the rule database due to its position as the last rule which closes the rule-chain (i.e., create a circular rule). However, if during the rule inference, rule 359 is found first followed by rule 357 as the last rule that closes the cycle, those rules will retain their direct-circular relationship, but this time, rule 357 is discarded due to its position as the last rule of the cycle. Hence, it can be confusing to decide which rule should be discarded. Since our proposed algorithm takes certainty factor values as the interestingness measure, then this value can be the parameter to retain the more interesting rule and discard the least one regardless of its position in the cycle as the first or last rule. Therefore, in the case of rules 357 and 359, one can see that without considering any interestingness measure, then rule 359 is supposed to be discarded from the rule database due to its position as the last rule which closes the cycle. Fortunately, it has a lower certainty factor value as well. However, suppose we found a pair of direct-circular rules, such as rules 1191 and 1230. Without considering any interestingness measure, then rule 1230 is supposed to be discarded from the rule database due to its position as the last rule which closes the cycle. However, if we take the certainty factor value to determine which rule is more likely to occur compared to the other rule, then rule 1230 turns out to be more interesting than rule 1191. Therefore, we no longer discard the last rule, but we instead discard the least interesting rule in terms of its certainty factor value. This implies that by keeping rule 1230, it could allow to improve the diagnosis of an adult patient to have normal MRI result when a patient has a normal systolic blood pressure, acceptable BMI, and normal conditions of both blood sugar and cholesterol, rather than the reverse presented conditions (i.e., rule 1191), which are indicated by higher value of CF of 22.2% than rule 1191 (CF = 17.6%). In addition, another example result of direct-circular type II that was found during the circularity checking can be seen in Table 9. According to the table, rules 375, 410, 415, and 414 successfully create a rule-chain. However, the conclusion of the last rule in the chain (rule 414) closes the chain with rule 415; hence, the rule chain satisfies direct-circular type II. This condition might be found during rule inference, which leads to an endless loop for which it is difficult to derive a final conclusion. Therefore, in order to break the circularity, we delete rule 415 with the least CF among the rules, which are direct-circular (i.e., rules 415 and 414), as previously mentioned in Property 3. Henceforth, the example results no longer contained circularity.