基于信息熵的不完备模糊信息系统属性约简

现实世界中广泛存在的信息不完备和模糊现象，限制了粗糙集理论在实际问题中的典型应用，目前在不完备模糊领域中基于分辨矩阵的算法时间复杂度较高，无法满足大规模数据的快速属性约简。针对这个原因，将完备信息系统中基于信息熵的快速属性约简算法推广到不完备模糊信息系统，通过相容关系及基于相容关系的近似集，给出计算条件信息熵的方法；在此基础上，设计出基于信息熵的不完备模糊信息系统的属性约筒算法。理论分析和实例结果表明了该算法的可行性和较好的时间优越性。

Attribute Reduction Based on Information Entropy in Incomplete and Fuzzy Information System

The incompleteness of information and fuzziness of objective exist widely in real life that confines the application of clas- sical rough set theory. However, the algorithm based on discernable matrix has a higher time complexity in the field of incomplete and fuzzy at present, which cannot meet the needs of the rapid reduction in mass data. For this reason, the rapid attribute reduction algorithm based on information entropy in complete information system is extended to the incomplete and fuzzy information system. The method for computing conditional information entropy is proposed by tolerance relation and the approximation of it. On this basis, the attribute re- duction algorithm of incomplete and fuzzy information system based on information entropy is designed. The theoretical analysis and ex- ample illustrate the feasibility of the algorithm and a better time for superiority.