| BR0-分配性及其推广 |
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| 引用本文： | 李玲玲,吴洪博.BR0-分配性及其推广[J].山东大学学报(理学版),2012,47(2):93-97. |
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| 作者姓名： | 李玲玲 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(10871121) |
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| 摘 要： | 在BR0- 代数结构中,BR0-分配性a→b∨c=(a→b)∨(a→c)具有十分重要的地位。本文证明了具有BR0-分配性的剩余格同样具备十分良好的性质。首先将BR0-分配性引入到剩余格中,并给出了BR0-分配性的等价形式。其次,在完备剩余格中将BR0-分配性进行了推广,提出了BR0-第一无限分配性和BR0-第二无限分配性。最后,分别在正则完备剩余格,单位区间［0,1］中讨论了两种BR0-无限分配性的关系及性质。
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| 关 键 词： | 模糊逻辑 剩余格 BR0-代数 BR0-分配性 无限分配性 |
| 收稿时间： | 2011-04-07 |
BR0-distributivity and its generalization |
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| LI Ling-ling,WU Hong-bo.BR0-distributivity and its generalization[J].Journal of Shandong University,2012,47(2):93-97. |
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| Authors: | LI Ling-ling 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: | BR0-distributivity has an important position in the structure of BR0-algebras which says a→b∨c=(a→b)∨(a→c).It is proved that residuated lattices with BR0-distributivity also have good properties.BR0-distributivity is introduced in residuated lattices,and its equivalent form is given.Then the BR0-distributivity is generalized in complete residuated lattices,and BR0-first infinite distributivity and BR0-second infinite distributivity are obtained.Finally,the properties and relationship between two kinds of BR0-infinite distributivity are discussed in regular complete residuated lattices and the unite interval ,respectively. |
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| Keywords: | fuzzy logic residuated lattice BR0-algebras BR0-distributivity infinite distributivity |
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