TY - JOUR
ID - 2670
TI - (ANTI) FUZZY IDEALS OF SHEFFER STROKE BCK-ALGEBRAS
JO - Journal of Algebraic Systems
JA - JAS
LA - en
SN - 2345-5128
AU - Oner, Tahsin
AU - Kalkan, T
AU - Borumand Saeid, Arsham
AD - Department of Mathematics, Ege University, Bornova, Izmir, Turkey.
AD - Department of Pure Mathematics, Faculty of Mathematics and Computer, Shahid
Bahonar University of Kerman, Kerman, Iran.
Y1 - 2023
PY - 2023
VL - 11
IS - 1
SP - 105
EP - 135
KW - (Sheffer stroke) BCK-algebra
KW - (anti) fuzzy ideal
KW - (anti) fuzzy ideal of Sheffer stroke BCK-algebra
DO - 10.22044/jas.2022.11512.1582
N2 - 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.
UR - https://jas.shahroodut.ac.ir/article_2670.html
L1 - https://jas.shahroodut.ac.ir/article_2670_53a9cdb49aea8e7c6e3fc127fa3522c6.pdf
ER -