On The F-divergence For Set-valued Measures And Non-additive Set-valued Measures

Divergence as a degree of the difference between two data is widely used in the classification problems.In this paper,f-divergence,Hellinger diver-gence and δ-divergence of the set-valued measures and non-additive set-valued mea-sures are defined and discussed respectively.It prove that Hellinger divergence andδ-divergence satisfy the triangle inequality and symmetry by means of the set oper-ations and partial ordering relations.Meanwhile,the necessary and sufficient condi-tions of Radon-Nikodym derivatives of the set-valued measures and non-additive set-valued measures are investigated respectively.In addition,based on the definition of the conjugate measure of non-additive set-valued measure,a new f-divergence is proposed and the non-negative property of the new f-divergence is proved.Finally,by means of the generalized Radon-Nikodym derivative of the proposed non-additive set-valued measure,the generalized f-divergence is characterized and an example is given.