@article {
author = {Oner, Tahsin and Kalkan, T and Borumand Saeid, Arsham},
title = {(ANTI) FUZZY IDEALS OF SHEFFER STROKE BCK-ALGEBRAS},
journal = {Journal of Algebraic Systems},
volume = {11},
number = {1},
pages = {105-135},
year = {2023},
publisher = {Shahrood University of Technology},
issn = {2345-5128},
eissn = {2345-511X},
doi = {10.22044/jas.2022.11512.1582},
abstract = {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.},
keywords = {(Sheffer stroke) BCK-algebra,(anti) fuzzy ideal,(anti) fuzzy ideal of Sheffer stroke BCK-algebra},
url = {https://jas.shahroodut.ac.ir/article_2670.html},
eprint = {https://jas.shahroodut.ac.ir/article_2670_53a9cdb49aea8e7c6e3fc127fa3522c6.pdf}
}