| 模糊集收敛的等价性 |
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| 引用本文： | 边梦柯,樊太和.模糊集收敛的等价性[J].浙江工程学院学报,2014(1):79-82. |
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| 作者姓名： | 边梦柯 樊太和 |
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| 作者单位： | 浙江理工大学理学院,杭州310018 |
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| 基金项目： | 国家自然科学基金项目（11171308） |
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| 摘 要： | 基于前人在对特殊模糊集上关于确界收敛，L-收敛，Endograph-收敛，Sendograph-收敛之间的等价性的分析，证明了一般模糊数序列上确界度量收敛等价于同时层次收敛和强截集收敛，并对关于截集连续的模糊数集合上的收敛的等价性给出了一种简洁的几何证明方法。
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| 关 键 词： | 模糊数 上确界度量 截集收敛 强截集收敛 |
Equivalence Property of Convergence of Fuzzy Sets |
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| BIAN Meng-ke,FAN Tai-he.Equivalence Property of Convergence of Fuzzy Sets[J].Journal of Zhejiang Institute of Science and Technology,2014(1):79-82. |
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| Authors: | BIAN Meng-ke FAN Tai-he |
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| Affiliation: | (School of Sciences, Zhejiang Sci-Tech university, Hangzhou 310018, China) |
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| Abstract: | Base on the previous analysis of equivalency among clear boundary convergence, L-conver- gence, Endograph-convergence and Sendograph-convergence in special fuzzy sets, This paper proves that supremum metric convergence is equivalent to simultaneous level convergence and strong cut set conver- gence for general fuzzy number sequences and meanwhile gives a geometric method to prove the equivalence property of convergence on continuous fuzzy number set about cut set. |
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| Keywords: | fuzzy number supremum metric cut set convergence strong cut set convergence |
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