On Permutation Distributive BI-Algebras

The purpose of this work is to introduce permutation BI-algebras as a new class of algebras in order to understand how it interacts to existing classes and how they may be used to form various types of superstructures. Their fundamental characteristics have been studied in this work. We looked at permutation BI-ideal, permutation BI-algebra, and permutation right (left) distributive BI-algebra. For the first time, we looked at some novel ideas in permutation theory. We also looked at the permutation right compatible relation, permutation left compatible relation, and permutation compatible relation in permutation BI-algebra.