| MV代数定义的蕴涵简化形式 |
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| 引用本文： | 刘敏,吴洪博.MV代数定义的蕴涵简化形式[J].模糊系统与数学,2006,20(6):44-50. |
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| 作者姓名： | 刘敏 吴洪博 |
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| 作者单位： | 陕西师范大学,数学研究所,陕西,西安,710062 |
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| 基金项目： | 国家自然科学基金资助项目(10471083)，陕西师范大学重点科研基金资助项目(995130)，陕西师范大学研究生培养创新基金资助项目(2006CXS017) |
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| 摘 要： | 通过对MV代数和Lukasiewicz命题演算系统的研究,我们对MV代数的定义进行了简化,并讨论了MV代数和其它代数之间的关系。主要结果是:(1)从蕴涵角度出发,给出了MV代数的两种简化定义;(2)提出了弱格蕴涵代数的概念,并证明了它与BR0代数等价;(3)证明了弱格蕴涵代数是正则Fuzzy蕴涵代数。
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| 关 键 词： | 模糊逻辑 MV代数 弱格蕴涵代数 BR0代数 正则Fuzzy蕴涵代数 |
| 文章编号： | 1001-7402（2006）06-0044-07 |
| 收稿时间： | 2005-11-23 |
| 修稿时间： | 2006-03-21 |
The Simplified Forms of Definition of MV-algebra |
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| LIU Min,WU Hong-bo.The Simplified Forms of Definition of MV-algebra[J].Fuzzy Systems and Mathematics,2006,20(6):44-50. |
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| Authors: | LIU Min WU Hong-bo |
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| Abstract: | Through study of MV-algebra and the Lukasiewicz propositional calculus system, we have simplified the definition of MV-algebra and investigated the relation among some logic algebras.the main results of the paper are: (1) Two equlvalent simplifies forms of MV-algebra are obtained; (2) The concept of Weak Lattice Implication-Algebra is proposed, and the equivalence between BR_0-algebra and Weak Lattice Implication-Algebra is proved; (3) It is proved that Weak Lattice Implication-Algebra is Regular Fuzzy Implication-Algebra. |
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| Keywords: | Fuzzy Logic MV-algebra Weak Lattic Implication-Algebra Basic R_0-algebra Regular Fuzzy Implication-algebra |
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