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International Conference on Fuzzy Information & Engineering

ICFIE 2017: Fuzzy Sets and Operations Research pp 119–129Cite as

On \((\in , {\in }{\vee }{q_{k}})\)-fuzzy Filters in \(R_{0}\)-algebras

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Part of the book series: Advances in Intelligent Systems and Computing ((AISC,volume 872))

Abstract

In the present paper, the \((\in , {\in }{\vee }{q_{k}})\)-fuzzy filter theory in \(R_0\)-algebras is further studied. Some new properties of \((\in , {\in }{\vee }{q_{k}})\)-fuzzy filters are given. Representation theorem of \((\in , {\in }{\vee }{q_{k}})\)-fuzzy filter which is generated by a fuzzy set is established. It is proved that the set consisting of all \((\in , {\in }{\vee }{q_{k}})\)-fuzzy filters on a given \(R_{0}\)-algebra, under the partial order \(\sqsubseteq \), forms a complete distributive lattice.

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Acknowledgements

Thanks to the support by Higher School Research Foundation of Inner Mongolia, China (No. NJSY14283, NJZY18206).

Recommender: Shu-hai Li, a professor of Chifeng University.

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Authors and Affiliations

  1. Department of Mathematics and Statistics, Chifeng University, Chifeng, 024000, China

    Chun-hui Liu

Authors
  1. Chun-hui Liu
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Correspondence to Chun-hui Liu .

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Editors and Affiliations

  1. Foshan University, Foshan, Guangdong, China

    Bing-Yuan Cao

  2. School of Mathematics and Information Science, Guangzhou University, Guangzhou, China

    Yu-Bin Zhong

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Liu, Ch. (2019). On \((\in , {\in }{\vee }{q_{k}})\)-fuzzy Filters in \(R_{0}\)-algebras. In: Cao, BY., Zhong, YB. (eds) Fuzzy Sets and Operations Research. ICFIE 2017. Advances in Intelligent Systems and Computing, vol 872. Springer, Cham. https://doi.org/10.1007/978-3-030-02777-3_11

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