Entropy Measure Of Incomplete Information Systems

Uncertainty measure is one of the important issues in rough set theory.Among them,entropy measure has been widely concerned by scholars at home and abroad.This paper puts forward a method of partition derived from covering on the incomplete information systems.On this basis,the paper studied the entropy measure of incomplete information systems and their information structures.The specific contents are as follows:In view of the entropy measure of incomplete information systems,first we can define a relation by using the covering determined by the attribute set.Then we can prove that it is an equivalence relation,and put forward a method of partition derived from the covering.At the same time,we can prove that the finer the covering,the finer the partition derived from it.Second,according to the entropy measure which is based on partition,we can structure multiple methods to measure the uncertainty,such as information entropy,complementary entropy,joint entropy and conditional entropy,we also studied their property.At last,combining the concept of partition derived from covering and neighborhood,we can come to a conclusion about entropy measure which is based on its neighbourhood and studies its related properties.Aiming at the problem of entropy measurement of information structure in incom-plete information systems],the paper generalizes the above entropy measurement of in-complete information systems to the situation of information structure,defines informa-tion entropy,complementary entropy,joint entropy and conditional entropy respectively according to partition information structure and neighborhood information structure,and studies their properties.