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

• We propose the concept of local rough approximation measures(LRAMs), which related theorems keep the property of RAMs in classical RS. • We introduce the concept of local knowledge distance(LKD), which takes into account the uncertainty induced by the discrepancy between provided lower and upper approximations. Besides, some related propositions, theorems, corollaries, and a novel GM are presented based on LKD. • The improved LRAMs are constructed by integrating LRAMs with the proposed GM. It demonstrates that the improved LRAMs maintain monotonic with the subdivision of the granularity. • The improved LRAMs is designed as a heuristic forward greedy algorithm, which is applied to the feature selection. The experiments validate that this algorithm is relatively reasonable from different sides. 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. [ABSTRACT FROM AUTHOR]