Abstract
Some kinds of pseudo valuations such as positive implicative pseudo valuation, (weak) implicative pseudo valuation, and commutative pseudo valuation of various types are introduced. 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.
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