摘要
定义和讨论了模糊数值函数的距离导数,给出了模糊有界变差函数全变差的积分表示.发现模糊绝对连续函数是几乎处处距离可导的,距离导数的积分等于其原函数的总变差,从而给出了模糊有界变差函数全变差的积分表示.
The metric derivative of the fuzzy-number-valued functions and the representation of the total variation for the fuzzy-number-valued function which is of bounded variation are defined and discussed. It is proved that the fuzzy absolutely continuous functions are metrically differentiable almost everywhere, and the integration of its metric derivative equals to the total variation of the primitive. Finally, the representation of the total variation for the fuzzy-number-valued functions which is of bounded variation is given.
出处
《数学学报(中文版)》
SCIE
CSCD
北大核心
2011年第4期633-642,共10页
Acta Mathematica Sinica:Chinese Series
基金
国家自然科学基金(71061013
10771171)
西北师范大学知识创新工程(NWNU-KJCXGC-03-61)
关键词
模糊数
模糊数值函数
距离导数
fuzzy numbers
fuzzy-number-valued functions
metric derivative