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

  • Chun-hui Liu
Conference paper
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 367)


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.


Fuzzy logic FI-algebra (Open image in new window)-fuzzy filter (Open image in new window)-fuzzy 



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


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Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  1. 1.College of Mathematics and StatisticsChifeng UniversityChifengChina

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