模糊有界变差函数全变差的积分表示与距离导数

The Representation of the Total Variation and the Metric Derivative for Fuzzy Bounded Variation Functions

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.