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.