基于局部可调节多粒度粗糙集的属性约简

Attribute Reduction Based on Local Adjustable Multi-granulation Rough Set

经典的多粒度粗糙集模型采用多个等价关系(多粒度结构)来逼近目标集。根据乐观和悲观策略,常见的多粒度粗糙集分为两种类型:乐观多粒度粗糙集和悲观多粒度粗糙集。然而,这两个模型缺乏实用性,一个过于严格,另一个过于宽松。此外,多粒度粗糙集模型由于在逼近一个概念时需要遍历所有的对象,因此非常耗时。为了弥补这一缺点,进而扩大多粒度粗糙集模型的使用范围,首先在不完备信息系统中引入了可调节多粒度粗糙集模型,随后定义了局部可调节多粒度粗糙集模型。其次,证明了局部可调节多粒度粗糙集和可调节多粒度粗糙集具有相同的上下近似。通过定义下近似协调集、下近似约简、下近似质量、下近似质量约简、内外重要度等概念,提出了一种基于局部可调节多粒度粗糙集的属性约简方法。在此基础上,构造了基于粒度重要性的属性约简的启发式算法。最后,通过实例说明了该方法的有效性。实验结果表明,局部可调节多粒度粗糙集模型能够准确处理不完备信息系统的数据,降低了算法的复杂度。

In classical multi-granulation rough set models,multiple equivalent relations(multiple granular structures)are used to approximate a target set.According to optimistic and pessimistic strategies,there are two types of common multi-granulation called optimistic multi-granulation and pessimistic multi-granulation respectively.The two combination rules seem to lack of practicability since one is too restrictive and the other too relaxed.In addition,multi-granulation rough set model is highly time-consuming because it is necessary to scan all the objects when approximating a concept.To overcome this disadvantage and enlarge the using range of multi-granulation rough set model,this paper firstly introduced the adjustable multi-granulation rough set model in incomplete information system and defined the local adjustable multi-granulation rough set model.Secondly,this paper proved that local adjustable multi-granulation rough set and adjustable multi-granulation rough set have the same upper and lower approximations.By defining the concepts of lower approximation cosistent set,lower approximation reduction,lower approximation quality,lower approximation quality reduction,and importance of internal and external,a local adjustable multi-granulation rough set model for attribute reduction was proposed.Furthermore,a heuristic algorithm of attribute reduction was constructed based on granular significance.Finally,the effectiveness of the method was illustrated through examples.The experimental results show that local adjustable size rough set model can accurately process the data of incomplete information system,and it can reduce the complexity of the algorithm.