嵌套决策粒度约简关系的研究

在基于粗糙集理论的知识发现中,知识约简是核心内容。因此,本文从理论上分析了相容决策表中嵌套决策粒度约简的关系,得出并证明了粗决策粒度的相对 D 核一定是细决策粒度相对 D 核的子集,粗决策粒度的一个相对D约简在满足相容性的条件下一定可以扩张成细决策粒度的一个约简。反之,细决策粒度的一个约简一定可以缩减为粗决策粒度的一个约简。研究结果对基于决策表的知识约简和知识发现有一定的实际意义。

Research on Reduction Relationships of Nested Granularities

Knowledge Reduction plays an important role in knowledge discovery based on rough set theory.In this pa- per,therefore,the reduction relationships of nested granularities are theoretically analyzed in consistent information ta- bles.We educe and prove that relative core of coarser decision granularity must be a subset of relative core of finer deci- sion granularity.At the same time,a relative reduction of coarser decision granularity that satisfies consistency can be extended into a relative reduction of its finer decision granularity.Inversely,a relative reduction of finer decision granu- larity can also be cut back a relative reduction of its coarser decision granularity.The conclusions are helpful for knowl- edge reduction and knowledge discovery based on rough sets.