| Fuzzy蕴涵代数的滤子理论刘春辉1,2 |
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| 引用本文： | 刘春辉.Fuzzy蕴涵代数的滤子理论刘春辉1,2[J].山东大学学报(理学版),2013,48(9):73-77. |
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| 作者姓名： | 刘春辉 |
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| 作者单位： | 1.赤峰学院教务处, 内蒙古 赤峰 024001; 2.赤峰学院数学与统计学院, 内蒙古 赤峰 024001 |
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| 基金项目： | 国家自然科学基金资助项目(10371106, 60774073) |
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| 摘 要： | 在Fuzzy蕴涵代数中引入对合滤子和结合滤子的概念并研究它们的性质, 获得了这两类滤子的几个等价刻画; 讨论了Fuzzy蕴涵代数的对合滤子、结合滤子、关联MP滤子、正关联MP滤子和交换MP滤子间的关系, 证明了一个非空集合为正关联MP滤子当且仅当它既是对合滤子又是交换MP滤子。
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| 关 键 词： | 模糊逻辑 Fuzzy蕴涵代数 对合滤子 结合滤子 (正)关联MP滤子 交换MP滤子 |
| 收稿时间： | 2012-08-09 |
Theory of filters in Fuzzy implication algebras |
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| LIU Chun-hui.Theory of filters in Fuzzy implication algebras[J].Journal of Shandong University,2013,48(9):73-77. |
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| Authors: | LIU Chun-hui |
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| Institution: | 1. Office of Academic Affairs, Chifeng University, Chifeng 024001, Inner Mongolia, China;
2. Department of Mathematics and Statistics, Chifeng University, Chifeng 024001, Inner Mongolia, China |
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| Abstract: | The notions of involution filters and associative filters in Fuzzy implication algebras are introduced and their properties are studied ulteriorly. Some characterizations of this two types of filters are obtained. The relations among involution, associative, implicative MP, positive implicative MP and commutative MP-filters are discussed. It is proved that a non-empty set is a positive implicative MP filter if and only if it is a implicative MP filters and a involution filters. |
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| Keywords: | fuzzy logic fuzzy implication algebra involution filter associative filter (positive)implicative MP-filter commutative MP-filter |
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