• Title/Summary/Keyword: fuzzifying (implicative) filter

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IMPLICATIVE FILTERS OF R0-ALGEBRAS BASED ON FUZZY POINTS

  • Jun, Young-Bae;Song, Seok-Zun
    • Communications of the Korean Mathematical Society
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    • v.27 no.4
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    • pp.669-687
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    • 2012
  • As a generalization of the concept of a fuzzy implicative filter which is introduced by Liu and Li [3], the notion of (${\in}$, ${\in}{\vee}q_k$)-fuzzy implicative filters is introduced, and related properties are investigated. The relationship between (${\in}$, ${\in}{\vee}q_k$)-fuzzy filters and (${\in}$, ${\in}{\vee}q_k$)-fuzzy implicative filters is established. Conditions for an (${\in}$, ${\in}{\vee}q_k$)-fuzzy filter to be an (${\in}$, ${\in}{\vee}q_k$)-fuzzy implicative filter are considered. Characterizations of an (${\in}$, ${\in}{\vee}q_k$)-fuzzy implicative filter are provided, and the implication-based fuzzy implicative filters of an $R_0$-algebra is discussed.