Evidence Theory and Rough Set Theory

DOI：

 作者 单位 苏运霖 暨南大学计算机科学系,广州,510632 管纪文 乌斯特大学约旦镇分校信息软件工程学院,英国 David A.Bell 乌斯特大学约旦镇分校信息软件工程学院,英国

约集论用于处理模糊性与不确定性.在某些方面,它同Dempster-Shafer的证据论相重迭,但约集论使用分划来描述约集、下界近似及上界近似,从而获取知识表示中的不确定性,而证据论使用证据函数来实现同一目的.该文针对两个理论表述上的差异,揭示出其内在的关系,以有助于人们对两者的理解,从而为开拓它们的应用铺平道路.此外,在证据论中,组合证据的基本操作是正交和,而在约集论中,基本操作是分划的交,因而存在“证据组合是否对应于分划的交”的问题.通过一个例子来说明回答是否定的.

The rough set theory is introduced to deal with vagueness and uncertainty. In some aspects, the rough set theory overlaps with the Dempster-Shafer theory of evidence, but the rough set theory uses partitions to specify rough sets, lower and upper approximations, and then to capture uncertainty in knowledge representation. In this paper, directing against the discrepancy in the specification between the two theories, the authors explore their relationship in order for ones to understand them and open the way of applying them. In addition, in evidence theory, the basic aperation to combine evidences is the orthogonal sum, while in the rough set theory, the basic operation is the intersection of partition. Therefore, “Does the evidence combination correspond to the partition?” is the question which may be naturally raised. An example is presented to show that the answer is “no”.
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