Abstract: The incomplete ordered information system extends the model of classic rough set theory. Instead of applying equivalence relationship, it has better performance on the data with unknown attribute values or preferred relationship by applying the dominance relationship. Based on the research on the features of incomplete ordered information system, a pair of upper and lower operators are given, while their relationship with likelihood function and belief function are also elaborated. Moreover, the definitions of[R]reduction, belief reduction and plausible reduction are given on the incomplete ordered information system respectively. This paper proves that a [R] reduction is equivalent with the belief reduction, which are both the minimum attribute set to keep the belief function, and the conclusion is that a plausibility consistent set must be a [R] consistent set.

Key words: incomplete ordered information system, evidence characteristic, attribute reduction, belief reduction, plausible reduction

摘要： 不完备有序信息系统粗糙集模型是经典粗糙集的扩展，利用优势关系代替等价关系能很好地处理含未知属性值和带有偏好关系的数据。研究了不完备序信息系统的证据特征，给出了不完备序上、下近似算子，并证明了二者分别与证据理论中的似然函数、信任函数相对应。进而提出了不完备序信息系统的[R]约简、信任约简以及似然约简的概念，探讨了它们之间的一致性，证明了[R]约简与信任约简是等价的，均是保持信任函数和的最小属性集合，得出了似然约简协调集必为[R]约简协调集的结论。

关键词: 不完备序信息系统, 证据特征, 属性约简, 信任约简, 似然约简