Set Pair-Information Entropy And Its Application

Information entropy is a theory tool that deals effectively with uncertainty in information system. It measures mainly the importance of attributes and the uncertainty of information system in rough set theory. Set pair-information entropy is given when set pair analysis method is integrated into entropy theory of information system. The contact state both systems and the certainty and uncertainty in system are measured uniformly by set pair-information entropy.First, Set pair-information entropy is given based on set pair analysis method and combination entropy. The basic properties and the forms based on the data distribution are discussed. Set pair-information entropy degenerates in system when two systems can be combined. It is proved that the laws hidden in systems are found with set pairinformation entropy through a case study.Secondly, the set pair-information entropy is given based on the correlation function of set pair, The basic properties, the change laws of the set pair-information entropy and the relationship between the set pair of information entropy and set pair correlation function, information entropy, combination entropy and negentropy are discussed.What's more, the original data is divided into multiple independent subset by equivalence partition. The significance of attribute was defined and the algorithm for attribute reduction is proposed based on set pair-information entropy in subset. The feasible and efficient of the algorithm was illustrated through a case study.Finally, three-way decision model based on set pair-information entropy is established in three-way decision theory. The risk evaluation of three-way decision reliability was discussed. It is given that three-way decision changed into two-way decision when the value of different entropy is zero.