集值测度和非可加集值测度的f-散度  

On the f-divergence for set-valued measures and non-additive set-valued measures

作　　者：巩增泰 申诚诚 GONG Zeng-tai;SHEN Cheng-cheng(College of Mathematics and Statistics,Northwest Normal University,Lanzhou 730070,China)

机构地区：[1]西北师范大学数学与统计学院,甘肃兰州730070

出　　处：《云南大学学报（自然科学版）》2020年第4期599-608,共10页Journal of Yunnan University(Natural Sciences Edition)

基　　金：国家自然科学基金(61763044).

摘　　要：散度作为信息之间的一种度量,在分类问题中因表示信息之间的差异程度而得到广泛应用.集值测度和非可加集值测度作为测度的推广,定义和讨论了集值测度和非可加集值测度的f-散度,H-散度和δ-散度,并利用集值的运算和偏序关系,证明了H-散度和δ-散度满足三角不等式性质和对称性,同时给出了集值测度和非可加集值测度Radon-Nikodym导数存在的充分必要条件.最后给出了算例.Divergence as a degree of the difference between two data is widely used in the classification problems.In this paper,f-divergence,H-divergence and δ-divergence of the set-valued measures and non-additive set-valued measures are defined and discussed respectively.It is proved that H-divergence and δ-divergence satisfy the triangle inequality and symmetry by means of the set operations and partial ordering relations.Meanwhile,the necessary and sufficient conditions of Radon-Nikodym derivatives of the set-valued measures and non-additive setvalued measures are investigated respectively.Finally,some examples are given to illustrate the effectiveness of the definitions and results proposed in the article.

关 键 词：f-散度 Hellinger距离 δ-距离 CHOQUET积分 RADON-NIKODYM导数 

分 类 号：O159[理学—数学]