Interval-valued \(m\)-polar fuzzy positive implicative ideals in BCK-algebras. (English) Zbl 1512.06008
Summary: In this paper, the notion of interval-valued \(m\)-polar fuzzy positive implicative ideals in BCK-algebras is presented. Then, the relationships between interval-valued \(m\)-polar fuzzy positive implicative ideals and interval-valued \(m\)-polar fuzzy ideals are investigated. After that, the concepts of interval-valued \(m\)-polar \(( \in , \in \vee q_{\widetilde{\kappa}})\)-fuzzy positive implicative ideals and interval-valued \(m\)-polar \(( \in , \in \vee q_{\widetilde{\kappa}})\)-fuzzy ideals are defined and some equivalent conditions are provided. Furthermore, we show that interval-valued \(m\)-polar \(( \in , \in \vee q_{\widetilde{\kappa}})\)-fuzzy positive implicative ideals are interval-valued \(m\)-polar \(( \in , \in \vee q_{\widetilde{\kappa}})\)-fuzzy ideals, but the converse need not be true in general and an example is given in this aim.
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