Shahrood University of TechnologyJournal of Algebraic Systems2345-512811120230901(ANTI) FUZZY IDEALS OF SHEFFER STROKE BCK-ALGEBRAS105135267010.22044/jas.2022.11512.1582ENTahsin OnerDepartment of Mathematics, Ege University, Bornova, Izmir, Turkey.T KalkanDepartment of Mathematics, Ege University, Bornova, Izmir, Turkey.Arsham Borumand SaeidDepartment of Pure Mathematics, Faculty of Mathematics and Computer, Shahid
Bahonar University of Kerman, Kerman, Iran.0000-0001-9495-6027Journal Article20211224The 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.https://jas.shahroodut.ac.ir/article_2670_53a9cdb49aea8e7c6e3fc127fa3522c6.pdf