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| 格蕴涵代数的素对偶理想 | |
| 引用本文： | 王学芳,刘培顺,徐扬.格蕴涵代数的素对偶理想[J].模糊系统与数学,2006,20(5):37-42. |
| 作者姓名： | 王学芳 刘培顺 徐扬 |
| 作者单位： | 1. 中国海洋大学,数学系,山东,青岛,266071 2. 中国海洋大学,计算机系,山东,青岛,266071 3. 西南交通大学,智能控制开发中心,四川,成都,610031 |
| 基金项目： | 国家自然科学基金资助项目(60474022) |
| 摘 要： | 在格蕴涵代数中定义了一类特殊的素对偶理想,讨论了它们的结构和性质,证明了该格蕴涵代数中的蕴涵运算可以由这些特殊的素对偶理想所确定,并且这些特殊的素对偶理想全体自然地构成一个格蕴涵代数,它和原格蕴涵代数具有格蕴涵代数同构关系。 |
| 关 键 词： | 非经典逻辑 格值逻辑 格蕴涵代数 对偶理想 素对偶理想 滤子 |
| 文章编号： | 1001-7402（2006）05-0037-06 |
| 收稿时间： | 2005-08-02 |
| 修稿时间： | 2005-10-23 |
Prime Dual Ideals of Lattice Implication Algebra |
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| WANG Xue-fang,LIU Pei-shun,XU Yang.Prime Dual Ideals of Lattice Implication Algebra[J].Fuzzy Systems and Mathematics,2006,20(5):37-42. | |
| Authors: | WANG Xue-fang LIU Pei-shun XU Yang |
| Institution: | 1. Department of Mathematics,Ocean University of China,Qingdao 266071,China; 2. Department of Computer Science,Ocean University of China,Qingdao 266071 ,China 3. Intelligent Control Development Center,Southwest Jiaotong University,Chengdu 610031 ,China |
| Abstract: | A special kind of prime dual ideals are defined in a lattice implication algebra, then their structures and properties are discussed. It is proved that the implication operation on this lattice implication algebra is determined by these prime dual ideals, and all of these prime dual ideals compose a lattice implication algebra which is lattice implication isomorphic to the former lattice implication algebra. |
| Keywords: | Non-classical Logic Lattice-valued Logic Lattice Implication Algebra Dual Ideal Prime Dual Ideal Filter |
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