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The Relationship of Filters in Lattice Implication Algebra

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Foundations of Intelligent Systems

Part of the book series: Advances in Intelligent and Soft Computing ((AINSC,volume 122))

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Abstract

In this paper, we focus on the properties of filters in lattice implication algebra. We study the relationship of associative filter and implicative filter, n-fold associative filter and n-fold implicative filter in detail. And a sufficient condition of involution filter in lattice implication algebra is proved. Then the relationship of some filters is given in Figure 4, and the transformation conditions among these filters are analyzed and obtained in Figure 5. Last, some properties of filter lattice are discussed.

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References

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Author information

Authors and Affiliations

  1. Intelligent Control Development Center, Southwest Jiaotong University, Chengdu, 610031, China

    Ruijuan Lv & Yang Xu

Authors
  1. Ruijuan Lv
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  2. Yang Xu
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Editor information

Editors and Affiliations

  1. Department of Computer Science and Engineering, Shanghai Jiao Tong University, 800 Dongchuan Road, 200240, Shanghai, China

    Yinglin Wang

  2. School of Information Science and Technology, Southwest Jiaotong University, 610031, Chengdu, Sichuan Province, China

    Tianrui Li

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© 2011 Springer-Verlag Berlin Heidelberg

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Lv, R., Xu, Y. (2011). The Relationship of Filters in Lattice Implication Algebra. In: Wang, Y., Li, T. (eds) Foundations of Intelligent Systems. Advances in Intelligent and Soft Computing, vol 122. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-25664-6_25

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  • DOI: https://doi.org/10.1007/978-3-642-25664-6_25

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-25663-9

  • Online ISBN: 978-3-642-25664-6

  • eBook Packages: EngineeringEngineering (R0)

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