| 可交换的s代数与格蕴涵代数 |
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| 引用本文： | 许格妮,关晓红.可交换的s代数与格蕴涵代数[J].西北纺织工学院学报,2010(2):254-256. |
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| 作者姓名： | 许格妮 关晓红 |
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| 作者单位： | [1]西安财经学院统计学院,陕西西安710061 [2]河南师范大学数学与信息科学学院,河南新乡453007 |
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| 基金项目： | 陕西省教育厅自然科学研究计划项目（09JK439） |
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| 摘 要： | 研究了一类模糊逻辑代数系统——交换s代数.给出了交换s代数一系列基本性质,证明了交换s代数关于其上的偏序关系≤构成格.最后,证明了在交换s代数中定义xy=x′→y,则X是一个格蕴涵代数,在格蕴涵代数L中,定义y=x′→y,则L是一个交换s代数.
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| 关 键 词： | 偏序集 交换s代数 格蕴涵代数 |
Commutative s-algebra and lattice implication algebra |
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| XU Ge-ni,GUAN Xiao-hong.Commutative s-algebra and lattice implication algebra[J].Journal of Northwest Institute of Textile Science and Technology,2010(2):254-256. |
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| Authors: | XU Ge-ni GUAN Xiao-hong |
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| Affiliation: | 1.School of Statistics,Xi′an University of Finance and Economics,Xi′an 710061,China;2.Department of Mathematics and Information Science,Henan Normal University,Xinxiang,Henan 453007,China) |
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| Abstract: | A ＂commutative law＂in the s-algebra is put forward,the commutative s-algebra is discussed and it is a lattice on the partial ordered set.Finally,the relations are given out between the commutative s-algebra and lattice implication algebra.A commutative s-algebra is a lattice implication algebra if xy=x′→y,a lattice implication algebra is a commutative s-algebra if xy=x′→y. |
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| Keywords: | partial ordered set commutative s-algebra lattice implication algebra |
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