Abstract: Combination entropy and combination granulation are a new kind of methods for measuring the uncertainty of an information system.In this paper，the forms of the combination entropy and the combination granulation，based on the indiscernibility between elements，are first constructed for imperfect information systems，as well as some of their properties are discussed.Then，the relationship between the combination entropy and the combination granulation is established as well.It is proved that the combination entropy and the combination granulation of imperfect information systems will degenerate into those of complete information systems.An illustrative example shows that the method proposed by this paper can effectively measure the uncertainty of imperfect information systems and extend the application range of combination entropy and combination granulation.

Key words: rough set theory, imperfect information systems, indiscernibility, combination entropy, combination granulation

摘要： 组合熵与组合粒度是一种新的度量信息系统不确定性的有效方法。基于对象之间的不可区分度将组合熵与组合粒度的概念推广到非完备信息系统中，并给出二者的性质。经证明，非完备信息系统中的组合熵与组合粒度之间具有严格的互补关系，并可退化为完备信息系统中的组合熵与组合粒度。实例表明该方法能够对非完备信息系统中的不确定性进行有效的度量，拓展了组合熵与组合粒度的应用范围。

关键词: 粗糙集理论, 非完备信息系统, 不可区分度, 组合熵, 组合粒度