| MTL代数的特征定理 |
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| 引用本文： | 裴道武.MTL代数的特征定理[J].数学学报,2007,50(6):1201-120. |
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| 作者姓名： | 裴道武 |
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| 作者单位： | 浙江理工大学理学院 杭州 |
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| 基金项目： | 国家科技部973项目(2006CB708304)，国家自然科学基金(60475019) |
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| 摘 要： | 对于逻辑系统代数结构的研究,是一个十分重要的研究课题.近期提出的BL代数,R_0代数,MTL代数就是这个方向具有代表性的研究成果.本文讨论MTL代数的性质与结构,给出这种代数的几个特征定理,澄清这种代数与其它代数结构的关系.鉴于单位区间中由左连续t-范数诱导的剩余蕴涵与MTL代数的紧密联系,本文还考察了这种模糊蕴涵的特征性质.
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| 关 键 词： | 模糊逻辑 t-范基逻辑 MTL代数 |
| 文章编号： | 0583-1431（2007）06-1201-06 |
| 收稿时间： | 2006-4-26 |
| 修稿时间： | 2006-04-24 |
The Characterizations of MTL Algebras |
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| Dao Wu PEI.The Characterizations of MTL Algebras[J].Acta Mathematica Sinica,2007,50(6):1201-120. |
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| Authors: | Dao Wu PEI |
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| Institution: | Faculty of Science, Zhejiang Sci-Tech University, Hangzhou 310018, P. R. China |
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| Abstract: | In logic and algebra,the researches on some logical algebraic structures are important topics at all times.BL algebras,R0 algebras and MTL algebras which are proposed recently are representative results in this area.The present paper discusses properties and algebraic structures of MTL algebras.Several characteristic properties of MTL algebras are revealed,and relationships among MTL algebras and the related algebraic structures are clarified.Moreover,characteristic properties of residual impli- cations induced by left continuous t-norms are investisgated in this paper since they are closely related to MTL algebras. |
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| Keywords: | fuzzy logic t-norm based logic MTL algebra |
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