变精度粗糙集的逻辑解释及其约简

Reduction in variable precision rough set and its interpretation with logic

针对Ziarko提出的变精度粗糙集缺乏相应的逻辑解释,且约简方法不合理,对经典粗糙集的逻辑解释进行了扩展,提出了变精度粗糙集决策算法应满足的四个条件,证明了变精度粗糙集决策算法与β近似的关系并得到变精度粗糙集决策算法的性质;其次,在变精度粗糙集的逻辑解释下,提出基于β下近似分布和β上近似分布变精度粗糙集的约简方法,从而保证了约简前后分类能力大小不发生改变且符合变精度粗糙集的逻辑解释;最后,通过实例说明基于β下近似分布和β上近似分布约简方法的合理性。

Ziarko＇ s variable precision rough set model lacks for logic interpretation and its reduction method has many defec- tions. In order to solve these problems, this paper extended the interpretation of rough set model, proposed four conditions which decision algorithms in variable precision rough set need satisfy, and proved the relations of decision algorithms and ap- proximations. Moreover, in order to keep the ability of classification unchanged during the course of reduction, it put forward a reduction method which based on fl-lower approximation distribution and fl-npper approximation distribution in variable preci- sion rough set. Finally, a case shows the validitv of the oronosed method_