扩展优势关系下的变精度粗糙集模型

基于优势关系的变精度粗糙集模型将传统粗糙集中的等价关系扩展为优势关系,并结合变精度的思想来定义相关概念,从而可以处理具有偏好关系的信息并具有一定的容错能力。然而,传统优势关系的定义仍然过于严格,只有当一个对象x的每个属性值都优于另一个对象y时,该对象x才优于y。当属性个数较多时,这种优势关系的定义会导致对象的优势集偏小,影响到规则的提取和决策结果。为了解决这一问题,通过引入参数的方法扩展了传统优势关系的定义,并在此基础上进一步给出了扩展后的优势集和近似集的概念,建立了扩展优势关系下的变精度粗糙集模型,采用覆盖率和测试精度作为模型的评估指标。最后给出算例,并在UCI数据集上进行大量的实验将所提模型与传统优势关系下的变精度粗糙集模型进行比较。

Variable Precision Rough Set Model Based on Extended Dominance Relations

The variable precision rough set (VPRS) model based on dominance relations extends equivalence relations in traditional rough sets to dominance relations,and combines with the idea of variable precision to define the relevant concepts.Therefore,it can deal with preference-ordered information with certain fault tolerance degree.However,the definition of traditional dominance relation is still too strict,in which object x is superior to object y only when all attribute values of x are superior to that of y.This definition is difficult to be satisfied especially when the number of attributes is large.This will lead to smaller dominance,and even worse,it will affect the extraction of decision rules and then the process of decision making.To address this problem,the concept of dominance relation was extended by introducing a parameter and then the dominance set and approximation sets were correspondingly defined based on this extended do-minance relation.The extended VPRS model was also developed,and the coverage rate and the test accuracy were used as evaluation criteria to for model.Finally,an illustrative example was given and the experimens on UCI data were conducted to compare the proposed extended model with the traditional VPRS model.