Communications of the
Korean Mathematical Society CKMS

As a generalization of the concept of a fuzzy implicative filter which is introduced by Liu and Li [3], the notion of $(\in,$ $\in\! \vee \, {\rm q}_k)$-fuzzy implicative filters is introduced, and related properties are investigated. The relationship between $(\in,$ $\in\! \vee \, {\rm q}_k)$-fuzzy filters and $(\in,$ $\in\! \vee \, {\rm q}_k)$-fuzzy implicative filters is established. Conditions for an $(\in,$ $\in\! \vee \, {\rm q}_k)$-fuzzy filter to be an $(\in,$ $\in\! \vee \, {\rm q}_k)$-fuzzy implicative filter are considered. Characterizations of an $(\in,$ $\in\! \vee \, {\rm q}_k)$-fuzzy implicative filter are provided, and the implication-based fuzzy implicative filters of an $R_0$-algebra is discussed.

Keywords: fuzzy filter, fuzzy implicative filter, fuzzifying implicative filter, $t$-implication-based fuzzy implicative filter

MSC numbers: 03G10, 03G25, 08A72