On Permutation Upper and Transitive Permutation BE-Algebras

We present permutation BE-algebras as a new class of BE-algebras and examine their basic features in this work. The goal of this paper is to look into and discuss some new notions in permutation BE-algebras, like permutation upper and permutation ideals, as well as some new algebras of permutation BE-algebras, such as permutation IBE-energetic algebras, transitive permutation BE-algebras, and self-distributive permutation BE-algebras are introduced. In addition, we look into their relationships in permutation BE-algebras. Filters are also described in terms of permutation filters. It is demonstrated that for all
$\lambda_{i}^{\beta},\lambda_{j}^{\beta}\in X$
, the permutation upper set
$A(\lambda_{i}^{\beta},\lambda_{j}^{\beta})$
is a permutation filter of
$X$
if
$X$
is a self - distributive permutation BE-algebra.