Material implications in lattice effect algebras

In this paper we show that it is not acceptable using the minimal conditions of implication introduced for orthomodular lattices as minimal conditions of a good implication for lattice effect algebras. Hence, we first define the concept of a partial t-norm on bounded lattices. Then we obtain the concept of a pt-implication on bounded involutive lattices by introducing some conditions using partial t-norms. Furthermore, we conclude that the Sasaki arrow which is a very important implication in lattice effect algebras is the best pt-implication on them. Finally, applying the Sasaki arrow, we construct a fuzzy implication on a lattice effect algebra and also we prove that it is a weak pt-implication as well.