一种基于相近关系的粗集理论扩展方法及属性约简

针对经典粗集理论中的不可分辨关系对连续属性值中噪声数据缺乏容错性的情况，提出一种相近关系代替不可分辨关系，并用不同的δ值调节相近关系中可接受的相近程度，限制可冗余的范围。给出相近度的计算方法，通过给定闲值定义真实相近类，用以减少一般相近类集合中对象的个数。另外，定义在相近关系下的粗集的一些基本概念，并提出相应的知识属性约简的方法。最后通过歼击机故障信息决策分类验证本文约简方法的正确性和对噪声数据的冗余性。

An Extending Method and Attributes Reduction of Rough Set Theory Based on Nearness Relation

This paper can be viewed as a generalization of the theory concerning rough set defined by tolerance relation. In this paper, a relation of nearness instead of indiscernibility is proposed for increasing the robustness of decision system which consists of noise pollution data. A real nearness class is presented by a given threshold that can decrease the number of the general nearness class. Some definitions and properties of this tolerance rough set are given and a new definition of degree of nearness is formulated.Particularly,the reduction of attributes under the nearness relation is proposed.Finally,an illustration of aircraft actuator failure classification is given, the method of attributes reduction is proved to be feasible and the decision under the noising data to be tolerant.