[1]欧阳耀,李军.模糊数值模糊可测函数定义的注记[J].东南大学学报(自然科学版),2003,33(6):801-803.[doi:10.3969/j.issn.1001-0505.2003.06.028]
 Ouyang Yao,Li Jun.Note on the definition of fuzzy number-valued fuzzy measurable functions[J].Journal of Southeast University (Natural Science Edition),2003,33(6):801-803.[doi:10.3969/j.issn.1001-0505.2003.06.028]
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模糊数值模糊可测函数定义的注记()
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《东南大学学报(自然科学版)》[ISSN:1001-0505/CN:32-1178/N]

卷:
33
期数:
2003年第6期
页码:
801-803
栏目:
数学、物理学、力学
出版日期:
2003-11-20

文章信息/Info

Title:
Note on the definition of fuzzy number-valued fuzzy measurable functions
作者:
欧阳耀 李军
东南大学数学系, 南京 210096
Author(s):
Ouyang Yao Li Jun
Department of Mathematics, Southeast University, Nanjing 210096, China
关键词:
模糊σ-代数 模糊可测空间 模糊数值模糊可测函数
Keywords:
fuzzy σ-algebra fuzzy measurable space fuzzy number-valued measurable function
分类号:
O159
DOI:
10.3969/j.issn.1001-0505.2003.06.028
摘要:
本文指出了《模糊数值测度论》(张广全,清华大学出版社,1998)一书中关于模糊数值模糊可测函数的定义的几个充要条件不成立,原因在于该书中给出的模糊可测函数的定义存在缺陷.本文将对该定义加以修订并且在此基础上证明相应的结论,从而使实值模糊可测函数和模糊数值模糊可测函数的定义更加合理.
Abstract:
The note points out that the definition of fuzzy measurable function, which was presented by Zhang Guangquan [Fuzzy-valued measure theory, Tsinghua University Press, 1998], is defective, and that the several equivalent conditions for measurability of fuzzy number-valued functions in the book are not valid. We modify the definition into a reasonable form and show correct results.

参考文献/References:

[1] 张广全.模糊值测度论[M].北京:清华大学出版社,1998.256-336.
[2] 吴从炘,方锦喧.模糊分析学的结构理论[M].贵阳:贵州科技出版社,1994.34-72.
[3] Wang Z,Klir G J.Fuzzy measure theory [M].New York:Plenum Press,1992.39-128.
[4] Zhang G.Fuzzy number-valued fuzzy measure and fuzzy number-valued fuzzy integral on the fuzzy set [J]. Fuzzy Sets and Systems, 1992,49:357-376.
[5] Zhang G.The structural characteristics of the fuzzy number-valued fuzzy measure on the fuzzy σ-algebra and their applications [J]. Fuzzy Sets and Systems,1992,52:69-81.

备注/Memo

备注/Memo:
作者简介: 欧阳耀(1973—),男,硕士生; 李军(联系人),男,教授, lijun@seu.edu.cn.
更新日期/Last Update: 2003-11-20