属性约简准则与约简信息损失的研究

Study on Criteria of Attribute Reduction and Information Loss of Attribute Reduction

属性约简是粗糙集的重要研究内容,信息熵是度量信息量的方法.在研究绝对约简和几种相对约简的基础上,归纳出属性约简的一般准则.定义了基于条件属性信息熵的属性约简和基于联合熵的属性约简,研究了几种属性约简与绝对约简之间的关系.定义了基于条件属性信息熵的约简信息损失,澄清了属性约简不损失信息的含糊观念,指出了属性约简只是在约简准则意义下不损失信息,在信息熵意义下可能损失信息.为进一步研究粗糙集、粒计算中属性约简与分类夯实了信息论基础.

Attribute reduction is one of important topics in rough set theory,and information entropy is an index of measuring the amount of information.After investigating absolute attribute reduct and several kinds of relatively attribute reducts,a general criterion of reducts is induced in rough set theory.With this criterion of reducts,attribute reduct based on information entropy and attribute reduct based on joint entropy are defined.The relationships among attribute reducts and absolute attribute reduct are investigated.Moreover,information loss based on information entropy for attribute reducts is defined,which can measure information loss after attribute reduction has been conducted.The old concepts that attribute reduction can not lose information are improved,and attribute reduction and classification can be further investigated from information loss and information entropy.