Fuzzy数测度的Radon-Nikodym导数

THE RADON-NIKODYM DERIVATIVE OF FUZZY NUMBER MEASURE

本文在推广[1]中R—Fuzzy值函数的积分的基础上,定义了Fuzzy数测度的R—N导数。并通过对Fuzzy数测度的研究,我们获得:①对有界凸Fuzzy值函数F,如果F(t)(x)关于x连续,则F必是某一Fuzzy数测度π的R—N导数。②如果Fuzzy数测度π关于有限非负测度γ绝对连续,则π存在R—N导数。

In this paper, We have extend the integralsof (?)—fuzzy valued function in[1]. On this basic, We have defined the Radon—Nikodym derivative of fuzzy number measure, and show that for bounded convex fuzzy valued functionF(t), if F(t)(x) is continuous with respect to x. then F(t) is the R—N derivative of a fuzzy number measure, that if fuzzy number measure (?) is obsolutely continuous with respect to finite nonnegative measure λ, then (?) exist the R—N derivative.