Abstract

In [2], Jun discussed implication-based subalgebras in BCK/BCI-algebras. In this article, more general forms than Jun’s results are discussed. We provide an example to show that a fuzzy subalgebra with thresholds 0 and 0.5 is not an implication-based subalgebra under the Łuckasiewicz implication operator, and then conditions for a fuzzy subalgebra with thresholds 0 and 0.5 to be an implication-based subalgebra under the Łuckasiewicz implication operator are provided.