feature rule reducts are redundant. MRG algorithm eliminates all redundant rule reducts then it attains the minimal set of rule reducts as shown in Table 4.7.

| F I                  | F2   | F3   | F4   |     |
|----------------------|------|------|------|-----|
| One feature r-reduct | NaN  | NaN  | NaN  | 3   |
| NaN                  | NaN  | NaN  |      |     |
| NaN                  |      |      |      |     |
| NaN                  | 2    | NaN  |      |     |
| NaN                  |      |      |      |     |
| NaN                  | 2    | NaN  |      |     |
| NaN                  | NaN  | NaN  | 0    |     |
| NaN                  | NaN  | 0    | NaN  |     |
| NaN                  | NaN  | NaN  | 2    |     |
| Two feature r-reduct | NaN  | 0    | 1    | NaN |
| NaN                  | 1    | 1    | NaN  |     |
| NaN                  | 1    | NaN  | 1    |     |
| NaN                  | NaN  | 1    | l    |     |
| NaN                  | 0    | NaN  | 1    |     |

| d   |
|-----|
| o   |
| 1   |
| 1   |
| 1   |
| 1   |
| 2   |
| 2   |
| 0   |
| 1   |
| i   |
| l   |

| obj   |
|-------|
| 1     |
| 3     |
| 3     |
| 3     |
| 3     |
| 4     |
| 4     |
| 1     |
| 2     |
| 2     |
| 2     |
| S     |

Table 4.7: Minimal set of r-reducts (MRG)
Pruning Rule Reduction (PRG) algorithm also eliminates redundant rule reducts. It finds minimal rule reducts for an information system. The difference between MRG and PRG is the elimination method. MRG needs to revise the decision table but PRG uses a tree structured data type. This tree acts as a map for searching rule reducts. While processing the method, some branches of the tree is pruned, hence it means there is a redundant rule reduct. The branches that are declared as redundant, are not searched for rule reduction. Therefore, processing time is shortened. Finally, minimal set of rule reduction is reached by PRG in a less time than MRG.

The fourth object is marked in Table 4.8. The PRG algorithm is tried to find the rule reducts for that object. The searching methodology is indicated step by step.

| Object   | F1   | F2   | F3   | F4   | Decision   |
|----------|------|------|------|------|------------|
| 0        | 0    | 0    |      |      |            |
| x        | l    | 3    |      |      |            |
| 0        | l    | l    | 1    | l    |            |
| x        | 2    | 2    |      |      |            |
| x x 3    | 1    | 0    | 1    |      |            |
| x a      | 0    | l    | 0    | 2    | 2          |
| xs       | 0    | 0    | 0    | 1    | 2          |

Table 4.8: Searching the fourth object for rule reduction