Local knowledge distance for rough approximation measure in multi-granularity spaces

Abstract

As the significant expansion of classical rough sets, local rough sets(LRS) is an effective model for processing large-scale datasets with finite labels. However, the process of establishing a category of monotonic uncertainty measure with strong distinguishing ability for LRS remains ambiguous. To construct this model, both the monotonicity of local lower approximation set and the local structure of granularity should be considered. First, the monotonicity of local rough approximation measure(LRAM) is established by the local lower and upper approximation sets. Subsequently, the local knowledge distance(LKD) is proposed to measure the uncertainty derived from the disparities between local upper and lower approximation sets. The more rational uncertainty measure associated LRAM with LKD is designed as a feature selection algorithm. Eventually, the experiments reflect the feasibility of the developed uncertainty measure.