Knowledge granularity representation and efficient algorithm of algebraic reduction

Firstly, a modified relative knowledge granularity is proposed. Its monotonicity is proved, and the necessary and sufficient conditions for equality are given. It is demonstrated that remaining the modified relative knowledge granularity and positive region unchanged is a necessary and sufficient condition for each other. Then the main concepts of algebraic reduction are described by knowledge granularity. The relation between existing relative knowledge granularity and its improvement is discussed. By modified relative knowledge granularity, an attribute relative significance is defined, and its recursive computing formula is presented. Then a heuristic attribute reduction algorithm based on this significance is designed, whose equivalence is computed by radix sort. The experimental results show that the algorithm is feasible and efficient.