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(\(\in , \in \vee {\,q}\))-Fuzzy Filter Theory in FI-algebras

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Fuzzy Systems & Operations Research and Management

Part of the book series: Advances in Intelligent Systems and Computing ((AISC,volume 367))

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Abstract

The notions of (\(\in , \in \vee {\,q}\))-fuzzy filters and (\(\in , \in \vee {\,q}\))-fuzzy implicative (positive implicative, commutative, involution) filters in FI-algebras are introduced and their properties are investigated. Equivalent characterizations of various (\(\in , \in \vee {\,q}\))-fuzzy filters are obtained. Relations among various (\(\in , \in \vee {\,q}\))-fuzzy filters are discussed and it is proved that a fuzzy set is (\(\in , \in \vee {\,q}\))-fuzzy positive implicative filter iff it is both (\(\in , \in \vee {\,q}\))-fuzzy implicative and (\(\in , \in \vee {\,q}\))-fuzzy commutative (or involution) filter.

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Acknowledgments

Thanks to the support by National Natural Science Foundation of China (No. 60774073 and No. 10371106).

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Authors and Affiliations

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

    Chun-hui Liu

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

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Editors and Affiliations

  1. Guangzhou University, Guangzhou, China

    Bing-Yuan Cao

  2. Foreign Affairs Office, National Defense University, Beijing, China

    Zeng-Liang Liu

  3. Higher Education Mega Center, Guangzhou University, Guangzhou, China

    Yu-Bin Zhong

  4. Zhuhai Campus, Beijing Normal University, Zhuhai, China

    Hong-Hai Mi

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Liu, Ch. (2016). (\(\in , \in \vee {\,q}\))-Fuzzy Filter Theory in FI-algebras. In: Cao, BY., Liu, ZL., Zhong, YB., Mi, HH. (eds) Fuzzy Systems & Operations Research and Management. Advances in Intelligent Systems and Computing, vol 367. Springer, Cham. https://doi.org/10.1007/978-3-319-19105-8_20

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  • DOI: https://doi.org/10.1007/978-3-319-19105-8_20

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-19104-1

  • Online ISBN: 978-3-319-19105-8

  • eBook Packages: EngineeringEngineering (R0)

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