%0 Journal Article
%T Commutative pseudo BE-algebras
%J Iranian Journal of Fuzzy Systems
%I University of Sistan and Baluchestan
%Z 1735-0654
%A Ciungu, L. C.
%D 2016
%\ 02/28/2016
%V 13
%N 1
%P 131-144
%! Commutative pseudo BE-algebras
%K Pseudo BE-algebra
%K Pseudo BCK-algebra
%K Commutative pseudo BCK-algebra
%K Commutative pseudo BE-algebra
%K Pointed pseudo BE-algebra
%K Relative involutive pseudo BE-algebra
%K Relative Glivenko property
%R 10.22111/ijfs.2016.2293
%X The aim of this paper is to introduce the notion of commutative pseudo BE-algebras and investigate their properties.We generalize some results proved by A. Walendziak for the case of commutative BE-algebras.We prove that the class of commutative pseudo BE-algebras is equivalent to the class of commutative pseudo BCK-algebras. Based on this result, all results holding for commutative pseudo BCK-algebras also hold for commutative pseudo BE-algebras. For example, any finite commutative pseudo BE-algebra is a BE-algebra, and any commutative pseudo BE-algebra is a join-semilattice. Moreover, if a commutative pseudo BE-algebra is a meet-semilattice, then it is a distributive lattice. We define the pointed pseudo-BE algebras, and introduce and study the relative negations on pointed pseudo BE-algebras. Based on the relative negations we construct two closure operators on a pseudo BE-algebra.We also define relative involutive pseudo BE-algebras, we investigate their properties and prove equivalent conditions for a relative involutive pseudo BE-algebra.We define the relative Glivenko property for a relative good pseudo BE-algebra and show that any relativeinvolutive pseudo BE-algebra has the relative Glivenko property.
%U https://ijfs.usb.ac.ir/article_2293_89fc397124e86bd8d36d0f72b59437ba.pdf