Abstract
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.
Highlights
Granular computing (GrC) is an emerging computing paradigm of intelligence information processing [1,2,3]
Tri-level thinking [41] provides a general tri-level framework; similar to tri-level thinking, our three-layer approach provides three-layer perspectives to measure uncertainty in different granularities and focused levels: a top level, a middle level, and a bottom level; that is, fuzzy neighborhood granule distance (FNGD), fuzzy neighborhood granular space distance (FNGSD), and fuzzy neighborhood boundary region distance (FNBRD) are hierarchically established from fine to coarse according to the semantics of granularity
neighborhood granule distance (NGD) only can measure the difference of grain size between neighborhood granules, while FNGD focuses on reflecting the difference between neighborhood granules for constructing lower/upper approximation of target concept. erefore, combining with NGD and FNGD, we further propose a method to discover the relation among neighborhood granules when describing a target concept in a granular space based on Algorithm 1
Summary
Granular computing (GrC) is an emerging computing paradigm of intelligence information processing [1,2,3]. If the uncertainty measure is not accurate enough, two different rough approximation spaces of a target concept may have the same uncertainty, and the difference between them for describing a target concept cannot be reflected In this case, attribute reduction, granularity selection, and multigranularity measure cannot be conducted effectively. In neighborhood rough set, current uncertainty measures focus on computing the knowledge granulation of single granular space. To characterize the difference between granular spaces for approximating a target concept, the fuzzy neighborhood granule distance (FNGD), fuzzy neighborhood granular space distance (FNGSD), and fuzzy neighborhood boundary region distance (FNBRD) are proposed, which are hierarchically organized from fineness to coarseness according to the semantics of granularity and provide three-layer perspectives in neighborhood system.
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