A novel measure of knowledge granularity in rough sets

Knowledge granularity, an average measure of the size of knowledge granules, is a type of uncertainty arises from the indiscernibility relation. Consequently, granularity and indiscernibility are closely connected. In our opinion, knowledge granularity is a measure of uncertainty in an intragranule. In this paper, a new measure of knowledge granularity for information system is proposed, which is characterised by mathematical expectation of lengths of granules in a partition. Based on the definition of knowledge granularity, relative knowledge granularity for decision table is also defined. The most advantage of relative knowledge granularity in this paper is that it can reveal the fact that granules belong to positive region have no contribution to the value of this measure. With this observation and the monotonicity of positive region, relative knowledge granularity can be computed recursively by adopting the strategy of separate-and-conquer, which is effective, especially for large scale data.