Fuzzy Knowledge Distance with Three-Layer Perspectives in Neighborhood System

Information granule is the basic element in granular computing (GrC), and it can be obtained according to the granulation criterion. In neighborhood rough sets, current uncertainty measures focus on computing the knowledge granulation of single granular space and have two main limitations: (i) neglecting the structural information of boundary regions and (ii) the inability to reflect the difference between neighborhood granular spaces with the same uncertainty for approximating a target concept. Firstly, a fuzziness-based uncertainty measure for neighborhood rough sets is introduced to characterize the structural information of boundary regions. Moreover, from the perspective of distance, based on the idea of density peaks, we present a fuzzy-neighborhood-granule-distance- (FNGD-) based method to discover the relationship between granules in a granular space. Then, to characterize the difference between granular spaces for approximating a target concept, we present the fuzzy neighborhood granular space distance (FNGSD) and fuzzy neighborhood boundary region distance (FNBRD). FNGD, FNGSD, and FNBRD are hierarchically organized from fineness to coarseness according to the semantics of granularity, which provide three-layer perspectives in the neighborhood system.