| 模糊商空间理论两个定理的补充 |
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| 引用本文： | 吴明芬,沈挺,曹存根,吴贤维.模糊商空间理论两个定理的补充[J].北京交通大学学报(自然科学版),2009,33(6). |
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| 作者姓名： | 吴明芬 沈挺 曹存根 吴贤维 |
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| 作者单位： | 五邑大学,信息学院,广东,江门,529020;中国科学院,计算技术研究所,北京,100190;五邑大学,信息学院,广东,江门,529020;中国科学院,计算技术研究所,北京,100190 |
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| 基金项目： | 国家自然科学基金资助项目，广东省自然科学基金资助项目(0501332 |
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| 摘 要： | 张铃等在"模糊粒度计算方法"中,核心定理证明中构造的等价关系是循环定义的,且没有证明它的截关系与商空间所对应的等价关系是相等的;模糊等价关系的粗细定义与模糊集理论的意义不一致,容易引起歧义.本文用通用的模糊数学符号和序代数理论的方法和观点对其进行修正和补充,给出两个定理的完整证明,使得相关结果的表达更简洁和规范,完善了模糊商空间理论.
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| 关 键 词： | 粒度计算 模糊商空间 模糊等价关系 分层递阶结构 上确界 下确界 完备格 |
Two Theorems in Fuzzy Quotient Space Theory |
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| WU Mingfen,SHEN Ting,CAO Cungen,WU Xianwei.Two Theorems in Fuzzy Quotient Space Theory[J].JOURNAL OF BEIJING JIAOTONG UNIVERSITY,2009,33(6). |
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| Authors: | WU Mingfen SHEN Ting CAO Cungen WU Xianwei |
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| Institution: | WU Mingfen1,2,SHEN Ting1,CAO Cungen2,WU Xianwei1(1.School of Information Science,Wuyi University,Jiangmen Guangdong,529020 China,2.Institute of Computing Technology,Chinese Academy of Sciences,Beijing 100190,China) |
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| Abstract: | Zhang Bo and Zhang Ling,in their paper Theory of fuzzy quotient space,proposed a new method of granular computing which combine fuzzy sets and theory of quotient space.Unfortunately,the proof of two core theorems was not tight and complete enough,i.e.,the fuzzy equivalence relation constructed in the proof process of theorem,is cyclical definition,and its cut relations and quotient space corresponding to the equivalence relation are equal which isn't obvious.Moreover,the definition of inclusion for fuzzy eq... |
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| Keywords: | granular computing fuzzy quotient space fuzzy equivalence relation hierarchical structure supremum infimum complete lattice |
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