南京大学学报：自然科学版2012，Vol.48Issue(4)：436-444,9.
一种新的不完备多粒度粗糙集
A new incomplete multigranulation rough set
摘要
Abstract
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 rough set are proposed. Further, the properties of the two models are deeply studied. By comparing with the tolerance based incomplete multigranulation rough set, the higher accuracy of approximation can be generated by the similarity based incomplete multigranulation rough set.关键词
相似关系/不完备粗糙集/乐观多粒度粗糙集/悲观多粒度粗糙集Key words
similarity relation/incomplete rough set/optimistic multigranulation rough set/pessimisticmultigranulation rough set分类
计算机与自动化引用本文复制引用
王丽娟,杨习贝,杨静宇,吴陈..一种新的不完备多粒度粗糙集[J].南京大学学报：自然科学版,2012,48(4):436-444,9.基金项目
国家自然科学基金（61100116）,中国博士后科学基金（20100481149）,江苏省自然科学基金（BK2011492）,江苏省高校自然科学基金（11KJB520004）,江苏省博士后科学基金 （）
