| Logical Properties of Lattice Filter of Lattice Implication Algebra |
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| 作者姓名： | 赖家俊 徐扬 宋振明 |
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| 作者单位： | Intelligent Control Development Center Southwest Jiaotong University，School of Information Science and Technology Southwest Jiaotong University Chengdu 610031 China，Intelligent Control Development Center Southwest Jiaotong University，Intelligent Control Development Center Southwest Jiaotong University，Chengdu 610031 China，Chengdu 610031 China，Chengdu 610031 China |
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| 基金项目： | The National Natural Science Founda-tion of China (No.60474022)，the Specialized Research Fund for the Doctoral Program of Higher Education of China(No.20060613007) |
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| 摘 要： | Introduction The concept of lattice was first introduced andelaborated by Dedekind, and the abstract structure oflattice was proposed by Birkhoff in 19351]. Sincethen, the lattice theory has gradually developed to be acomplete theoretical system2], and extensively studiedby researchers3-6]. In 1990s, Xu7]proposed the con-cept of lattice implication algebras and investigatedsome of their properties. Then, Xu and Qin8]intro-duced the notion of filters in lattice implication algebraand dis…
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| 关 键 词： | 有序集合 晶格 滤波器 代数 |
| 文章编号： | 1005-2429（2007）04-0353-04 |
| 修稿时间： | 2005-12-21 |
Logical Properties of Lattice Filter of Lattice Implication Algebra |
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| LAI Jia-jun,XU Yang,SONG Zhen-ming.Logical Properties of Lattice Filter of Lattice Implication Algebra[J].Journal of Southwest Jiaotong University,2007,15(4):353-356. |
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| Authors: | LAI Jia-jun XU Yang SONG Zhen-ming |
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| Institution: | 1. Intelligent Control Development Center,Southwest Jiaotong University,Chengdu,610031,China;School of Information Science and Technology,Southwest Jiaotong University,Chengdu,610031,China
2. Intelligent Control Development Center,Southwest Jiaotong University,Chengdu,610031,China |
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| Abstract: | Some new properties of lattice filters are presented based on the order-preserving mapping and lattice homomorphism, and two necessary and sufficient conditions for lattice filters under the chain type are given. Then, the relations between lattice filter and lattice implication algebras (LIAs), i.e., the relations between lattice filter and LIA-filters, and the related properties are investigated. In addition, three necessary and sufficient conditions for LIA-filters are discussed. The obtained results may serve as some theoretical supports to lattice-valued logical system. |
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| Keywords: | Partially ordered set Lattice Lattice Filters Lattice implication algebra Filters |
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