%0 Journal Article
%T (ANTI) FUZZY IDEALS OF SHEFFER STROKE BCK-ALGEBRAS
%J Journal of Algebraic Systems
%I Shahrood University of Technology
%Z 2345-5128
%A Oner, Tahsin
%A Kalkan, T
%A Borumand Saeid, Arsham
%D 2023
%\ 09/01/2023
%V 11
%N 1
%P 105-135
%! (ANTI) FUZZY IDEALS OF SHEFFER STROKE BCK-ALGEBRAS
%K (Sheffer stroke) BCK-algebra
%K (anti) fuzzy ideal
%K (anti) fuzzy ideal of Sheffer stroke BCK-algebra
%R 10.22044/jas.2022.11512.1582
%X The aim of this study is to introduce (anti) fuzzy ideals of a Sheffer stroke BCK-algebra. After describing an anti fuzzy subalgebra and an anti fuzzy (sub-implicative) ideal of a Sheffer stroke BCK-algebra, the relationships of these structures are demonstrated. Also, a t-level cut and a complement of a fuzzy subset are defined and some properties are investigated. An implicative Sheffer stroke BCK-algebra is defined and it is proved that a fuzzy subset of an implicative Sheffer stroke BCK-algebra is an anti fuzzy ideal if and only if it is an anti fuzzy sub-implicative ideal of this algebraic structure. A fuzzy congruence and a fuzzy quotient set of a Sheffer stroke BCK-algebra are studied in details and it is shown that there is a bijection between the set of fuzzy ideals and the set of fuzzy congruences on this algebraic structure. Finally, Cartesian product of fuzzy subsets of a Sheffer stroke BCK-algebra is determined and it is expressed that the Cartesian product of two anti fuzzy ideals of this algebraic structure is anti fuzzy ideal.
%U https://jas.shahroodut.ac.ir/article_2670_53a9cdb49aea8e7c6e3fc127fa3522c6.pdf