Pseudo permutation-BCK-algebras with their ideals

This paper provides new ideas like pseudo permutation BCK-algebra, pseudo permutation subalgebra, pseudo permutation ideal, and portion permutation. Moreover,their qualities are discussed. In this work, we show that if λβ po is a portion permutation of M = (X,⊛,⊚,T), then λβ po ⊛ λiβ = λβ po ⊚ λi β for any λi β ∈ X. Next, some interesting results in pseudo permutation BCK-algebra are given and shown. Furthermore, some instances are provided to support our findings in this paper.