中文摘要：

首先将悲观多粒度的概念引入不完备粗糙集，给出了容差关系下不完备悲观多粒度粗糙集模型．其次，针对缺席型未知属性值，将非对称相似关系引入多粒度空间，提出了一种新的不完备多粒度粗糙集模型．该模型包括非对称相似关系下的乐观多粒度和悲观多粒度这一对不完备多粒度粗糙集模型．随后分析了这对新模型的具体性质，并将其与基于容差关系的不完备多粒度粗糙集进行了对比分析，发现使用基于非对称相似关系的不完备多粒度粗糙集，可以获得更高的近似精度．

英文摘要：

Granular computing is a new field of research. Its ideas, principles and strategies have appeared in many branches of science and different fields of computer science. As one of the basic mathematical models of granular computing, rough set theory is a useful tool to deal with partition related uncertainty, granularity, and incompleteness of knowledge. Classical rough set model is constructed on the basis of an indiscernibility relation. In the view of granular computing, an equivalence relation on the universe can be regarded as a granulation, and a partition can be regarded as a granulation space. Hence, the classical rough set theory is based on a single granulation. However, in some circumstances, we often need to describe concurrently a target concept through multi-binary relations on the universe according to different users~ requirements or targets of problem solving. Therefore,an incomplete multigranulation model which is based on multi tolerance relations is presented by Qian. It is applicable to deal with the incomplete decision system which has the＂ missing＂ unknown attribute values. However,there is another explain of the unknown attribute values, such is all the unknown attribute values are lostand they cannot be compared. Under this explanation, in order to apply granular computing in solving problems, one key issue needed to be addressed is to construct new relations to incomplete multigranulation spaces. In this paper, firstly, the pessimistic multigranulation is introduced to the incomplete decision systems firstly, and the tolerance relation based incomplete pessimistic multigranulation rough set is proposed. Secondly, the incomplete decision systems, in which all unknown values are considered as lost, are firstly explored by the multigranulation approach. The non-symmetric similarity relations are introduced into the multigranulation rough set, and then the similarity based incomplete optimistic multigranulation rough set and the similarity based incomplete pessimistic multigranulation roug