| WBR0-代数的正则性及与其他逻辑代数的关系 |
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| 引用本文： | 周建仁,吴洪博.WBR0-代数的正则性及与其他逻辑代数的关系[J].山东大学学报(理学版),2012,47(2):86-92. |
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| 作者姓名： | 周建仁 吴洪博 |
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| 作者单位： | 陕西师范大学数学与信息科学学院,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(11171196) |
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| 摘 要： | 通过对正则剩余格和WBR0-代数的深入研究, 进一步明确了WBR0-代数与其他逻辑代数之间的关系。 主要结果有: (1)证明了正则剩余格与WBR0-代数是相同的代数结构;(2)通过联络图表列举了WBR0-代数与其他经典逻辑代数之间的联系,体现了WBR0-代数在逻辑代数中的地位与作用;(3)通过构造WBR0-代数的实例说明WBR0-代数与其他逻辑代数之间的区别。
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| 关 键 词： | 模糊逻辑 逻辑代数 正则剩余格 WBR0-代数 BL-代数 |
| 收稿时间： | 2011-09-23 |
The regularness of WBR0-algebras and relationship with other logic algebras |
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| ZHOU Jian-ren,WU Hong-bo.The regularness of WBR0-algebras and relationship with other logic algebras[J].Journal of Shandong University,2012,47(2):86-92. |
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| Authors: | ZHOU Jian-ren WU Hong-bo |
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| Institution: | (College of Mathematics and Information Sciences,Shaanxi Normal University,Xi’an 710062,Shaanxi,China) |
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| Abstract: | Regular residuated lattices and WBR0-algebras are investigated in depth.The relationship between WBR0-algebras and other logic algebras is made clearer and more definite than before.The main results of this paper are as follows:(1) It is proved that regular residuated lattices and WBR0-algebras are the same algebraic structure.(2) The connection among WBR0-algebras with other classical logic algebras is given by the network,through which the roles of WBR0-algebras are explained.(3) The difference between WBR0-algebras and other logic algebras is revealed by constructing a special WBR0-algebra. |
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| Keywords: | fuzzy logic logic algebra regular residuated lattice WBR0-algebra BL-algebra |
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