(ANTI) FUZZY IDEALS OF SHEFFER STROKE BCK-ALGEBRAS | ||
| Journal of Algebraic Systems | ||
| دوره 11، شماره 1، آذر 2023، صفحه 105-135 اصل مقاله (214.2 K) | ||
| نوع مقاله: Original Manuscript | ||
| شناسه دیجیتال (DOI): 10.22044/jas.2022.11512.1582 | ||
| نویسندگان | ||
| Tahsin Oner1؛ T Kalkan1؛ Arsham Borumand Saeid* 2 | ||
| 1Department of Mathematics, Ege University, Bornova, Izmir, Turkey. | ||
| 2Department of Pure Mathematics, Faculty of Mathematics and Computer, Shahid Bahonar University of Kerman, Kerman, Iran. | ||
| چکیده | ||
| 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. | ||
| کلیدواژهها | ||
| (Sheffer stroke) BCK-algebra؛ (anti) fuzzy ideal؛ (anti) fuzzy ideal of Sheffer stroke BCK-algebra | ||
| مراجع | ||
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