Tahsin Oner - Department of Mathematics, Ege University, Bornova, Izmir, Turkey.
T Kalkan - Department of Mathematics, Ege University, Bornova, Izmir, Turkey.
Arsham Borumand Saeid - Department of Pure Mathematics, Faculty of Mathematics and Computer, Shahid Bahonar University of Kerman, Kerman, Iran.

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.

(Sheffer stroke) BCK-algebra, (anti) fuzzy ideal, (anti) fuzzy ideal of Sheffer stroke BCK-algebra