| 赋范Fuzzy蕴涵代数 |
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| 引用本文： | 刘春辉,徐罗山.赋范Fuzzy蕴涵代数[J].扬州大学学报(自然科学版),2009,12(3). |
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| 作者姓名： | 刘春辉 徐罗山 |
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| 作者单位： | 1. 扬州大学,数学科学学院,江苏,扬州,225002;赤峰学院初等教育学院,内蒙古,赤峰,024001
2. 扬州大学,数学科学学院,江苏,扬州,225002 |
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| 基金项目： | 国家自然科学基金资助项目 |
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| 摘 要： | 运用泛函分析的方法和技巧考虑非经典数理逻辑问题,首先引入赋范Fuzzy蕴涵代数及蕴涵距离的概念,并给出它们的若十性质;其次对赋范Fuzzy蕴涵代数中的序列和蕴涵开(闭)球进行研究.证明了:①每一半径不小于球心范数的蕴涵开(闭)球都是MP滤子;②每个收敛序列都有唯一的极限;③每个收敛序列都是Cauchy列;④如果一个Cauchy列{xn}的某个子列收敛于点x,则该Cauchy列本身也收敛于点x.
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| 关 键 词： | 赋范Fuzzy蕴涵代数 MP滤子 蕴涵距离 收敛序列 Cauchy列 |
Normed fuzzy implication algebras |
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| LIU Chun-hui,XU Luo-shan.Normed fuzzy implication algebras[J].Journal of Yangzhou University(Natural Science Edition),2009,12(3). |
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| Authors: | LIU Chun-hui XU Luo-shan |
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| Abstract: | This paper considers problems of non-classical mathematical logic using the methods and techniques in functional analysis. The notions of normed fuzzy implication algebras and implication distance are introduced and several properties of them are given. The properties of sequences and implication open (closed) balls in normed fuzzy implication algebras are studied. Main results are: ① every implication open (closed) ball with radius not less then the norm of the heart point is an MP-filter; ② every convergent sequence has unique limit; ③ every convergent sequence is a Cauchy sequence; ④ if a Cauchy sequence {x_n} has a subsequence which converges to a point x, then {x_n} converges to x too. |
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| Keywords: | normed fuzzy implication algebra MP-filter implication distance convergent sequence Cauchy sequence |
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