Study of the Pseudo-Valuation Functions on Hyper BCK-Algebras

In this paper, the notions of some kinds of pseudo valuations such as positive implicative pseudo valuation, (weak) implicative pseudo valuation, and commutative pseudo valuation in different types, are examined. Several examples, properties and characterizations of them are given as well. The relationships between them and the substructures of hyper BCK-algebras are investigated, too. Finally, by giving various examples and theorems, the relationships among the proposed pseudo valuations are investigated and characterized, especially in hyper BCK-algebras with three elements.