数学学报 2011, 54(4) 633-642 DOI:      ISSN: 0583-1431 CN: 11-2038/O1

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本文关键词相关文章
模糊数
模糊数值函数
距离导数
本文作者相关文章
模糊有界变差函数全变差的积分表示与距离导数
巩增泰, 白玉娟
西北师范大学数学与信息科学学院 兰州 730070
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.  
关键词 模糊数   模糊数值函数   距离导数  
MSC2000 O159.2
The Representation of the Total Variation and the Metric Derivative for Fuzzy Bounded Variation Functions
Zeng Tai GONG, Yu Juan BAI
College of Mathematics and Information Science, Northwest Normal University, Lanzhou 730070, P. R. China
Abstract: 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.  
Keywords: fuzzy numbers   fuzzy-number-valued functions   metric derivative  
收稿日期 2009-02-25 修回日期 2011-03-23 网络版发布日期  
DOI:
基金项目:

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)

通讯作者:
作者简介:
作者Email: gongzt@nwnu.edu.cn

参考文献:
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[8] Feng Y. H., A note on indefinite integrals and absolute continuity for fuzzy-valued mappings, Fuzzy Sets and Systems, 2004, 147(3): 405-415.

[9] Gong Z. T., On the problem of characterizing derivatives for the fuzzy-valued functions (II), Fuzzy Sets and Systems, 2004, 145(3): 381-393.

[10] Kirchheim B., Retifiable metric spaces:local structure and regularity of the Hausdorff measure, Proceedings of the American Mathematical Society, 1994, 121(1): 113-123.

[11] Federer H., Geometric Measure Theory, Grundlehren Math. Wiss. 153, New York: Springer, 1969.

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[13] Gong Z. T., Nonabsolute fuzzy integrals, absolute integrability and its absolute-value inequality, Journal of Mathematical Reseach and Exposition, 2008, 28(3): 479-488.
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