Abstract

After ($\alpha$, $\beta$)-fuzzy congruence relation, ($\overline{\alpha}$, $\overline{\beta}$)-fuzzy congruence relation on lattice implication algebras is further investigated and it's properties is discussed, where $\overline{\alpha},\overline{\beta}\in\{\overline{\in_{h}},\overline{q_{\delta}},\overline{\in_{h}}\vee \overline{q_{\delta}},\overline{\in_{h}}\wedge \overline{q_{\delta}}\}$ but $\overline{\alpha}\neq \overline{\in_{h}}\wedge \overline{q_{\delta}}$. Specially, $(\overline{\in_{h}},\overline{\in_{h}}\vee \overline{q_{\delta}})$-fuzzy congruence relation is mainly investigate,which is generalization of $(\overline{\in},\overline{\in}\vee \overline{q})$-fuzzy congruence relation. Some characterizations for an ($\overline{\alpha}$, $\overline{\beta}$)-fuzzy congruence relation on $\mathscr{L}$ to be a congruence and a fuzzy congruence on $\mathscr{L}$ are derived.

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