A more general form of interval valued fuzzy filters in ordered semigroups

In this paper, we generalize the concept of interval valued $$(\in ,\in \vee q_{\widetilde{k}})$$ -fuzzy left (right) filters in ordered semigroups introducing and studying the notion of an interval valued $$(\in ,\in \vee q_{\widetilde{ k}}^{_{\widetilde{\delta }}})$$ -fuzzy left (right) filter. Several properties and characterizations are investigated and obtained on ordered semigroups by an interval valued $$ (\in ,\in \vee q_{\widetilde{k}}^{_{\widetilde{\delta }}})$$ -fuzzy left (right) filter. Characterizations of interval valued fuzzy left (resp. right) filters and interval valued $$(\in ,\in \vee q_{\widetilde{k} }^{_{\widetilde{\delta }}})$$ -fuzzy left (resp. right) filters are considered by using implication operators and the notion of implication-based interval valued fuzzy left (resp. right) filters.