Cross entropy of mass function and its application in similarity measure

Abstract

Dempster-Shafer (D-S) evidence theory needs the weaker conditions than Bayesian probability theory by assigning the probability into power sets. Hence it has the more stronger ability to express imprecise and unknown information which can be used in many fields. In D-S evidence theory, how to measure the cross entropy between different mass functions is also an open issue. Hence, the paper proposed the new cross entropy by considering the cardinality of mass function which is compatible with classical cross entropy. In addition, there are some numerical examples to explain the reasonableness of proposed cross entropy. Cross entropy can describe the difference of information. Similarity is also an effective method to measure the non-difference of information. It is an interesting question to set the relationship between cross entropy and similarity. Hence, the paper proposed similarity measure based on the entropy and cross entropy. Besides, the paper also discussed some measurement axioms of proposed similarity measure to verify its reasonableness. Finally, based on the new similarity measure, the paper proposed new classification method under D-S evidence theory. The IRIS data set is used to the classification method to verify the effectiveness of its by setting different the number of training data and comparing with other methods.