New Type of Soft (Prime) Ideals in Commutative BCK-Algebras
The soft set theory is an important mathematical tool for dealing with uncertainty. By endowing a par-ameter set as a commutative BCK-algebra (that is commutative weak-BCI-algebra), the notions of a new type of soft prime ideals, annihilators of soft sets and new type of involutory soft ideals in co...
| Main Author: | |
|---|---|
| Format: | Article |
| Language: | zho |
| Published: |
Journal of Computer Engineering and Applications Beijing Co., Ltd., Science Press
2022-07-01
|
| Series: | Jisuanji kexue yu tansuo |
| Subjects: | |
| Online Access: | http://fcst.ceaj.org/fileup/1673-9418/PDF/2012083.pdf |
| _version_ | 1818017419172511744 |
|---|---|
| author | HUANG Yu, LIAO Zuhua |
| author_facet | HUANG Yu, LIAO Zuhua |
| author_sort | HUANG Yu, LIAO Zuhua |
| collection | DOAJ |
| description | The soft set theory is an important mathematical tool for dealing with uncertainty. By endowing a par-ameter set as a commutative BCK-algebra (that is commutative weak-BCI-algebra), the notions of a new type of soft prime ideals, annihilators of soft sets and new type of involutory soft ideals in commutative BCK-algebras are introduced. Two new compositional operations are defined and used to characterize the new type of soft ideals in commutative BCK-algebras. By using partial ordering on commutative BCK-algebras, some properties of the new type of soft ideals are studied. Properties of annihilators of soft sets and new type of involutory soft ideals are obtained. The existence of a new type of soft prime ideals in commutative BCK-algebras and its difference from the standard soft prime ideals are illustrated with examples. It is shown that a soft set is a new type of soft prime ideals in commutative BCK-algebras and its level set is a prime ideal is not a necessary and sufficient condition, which is different from the results of the usual fuzzy algebra. Some equivalent characterizations of the new type of soft prime ideals in commutative BCK-algebras are given. Furthermore, the properties of its homomorphism image and inverse image are discussed. |
| first_indexed | 2024-04-14T07:26:52Z |
| format | Article |
| id | doaj.art-e0705b72f91c4d49a1e10153a590a6b8 |
| institution | Directory Open Access Journal |
| issn | 1673-9418 |
| language | zho |
| last_indexed | 2024-04-14T07:26:52Z |
| publishDate | 2022-07-01 |
| publisher | Journal of Computer Engineering and Applications Beijing Co., Ltd., Science Press |
| record_format | Article |
| series | Jisuanji kexue yu tansuo |
| spelling | doaj.art-e0705b72f91c4d49a1e10153a590a6b82022-12-22T02:05:59ZzhoJournal of Computer Engineering and Applications Beijing Co., Ltd., Science PressJisuanji kexue yu tansuo1673-94182022-07-011671673168010.3778/j.issn.1673-9418.2012083New Type of Soft (Prime) Ideals in Commutative BCK-AlgebrasHUANG Yu, LIAO Zuhua01. Department of Basic Course Teaching, Wuxi Taihu University, Wuxi, Jiangsu 214064, China;2. School of Science, Jiangnan University, Wuxi, Jiangsu 214122, ChinaThe soft set theory is an important mathematical tool for dealing with uncertainty. By endowing a par-ameter set as a commutative BCK-algebra (that is commutative weak-BCI-algebra), the notions of a new type of soft prime ideals, annihilators of soft sets and new type of involutory soft ideals in commutative BCK-algebras are introduced. Two new compositional operations are defined and used to characterize the new type of soft ideals in commutative BCK-algebras. By using partial ordering on commutative BCK-algebras, some properties of the new type of soft ideals are studied. Properties of annihilators of soft sets and new type of involutory soft ideals are obtained. The existence of a new type of soft prime ideals in commutative BCK-algebras and its difference from the standard soft prime ideals are illustrated with examples. It is shown that a soft set is a new type of soft prime ideals in commutative BCK-algebras and its level set is a prime ideal is not a necessary and sufficient condition, which is different from the results of the usual fuzzy algebra. Some equivalent characterizations of the new type of soft prime ideals in commutative BCK-algebras are given. Furthermore, the properties of its homomorphism image and inverse image are discussed.http://fcst.ceaj.org/fileup/1673-9418/PDF/2012083.pdf|bck-algebras|soft sets|prime ideals|annihilators|compositional operation |
| spellingShingle | HUANG Yu, LIAO Zuhua New Type of Soft (Prime) Ideals in Commutative BCK-Algebras Jisuanji kexue yu tansuo |bck-algebras|soft sets|prime ideals|annihilators|compositional operation |
| title | New Type of Soft (Prime) Ideals in Commutative BCK-Algebras |
| title_full | New Type of Soft (Prime) Ideals in Commutative BCK-Algebras |
| title_fullStr | New Type of Soft (Prime) Ideals in Commutative BCK-Algebras |
| title_full_unstemmed | New Type of Soft (Prime) Ideals in Commutative BCK-Algebras |
| title_short | New Type of Soft (Prime) Ideals in Commutative BCK-Algebras |
| title_sort | new type of soft prime ideals in commutative bck algebras |
| topic | |bck-algebras|soft sets|prime ideals|annihilators|compositional operation |
| url | http://fcst.ceaj.org/fileup/1673-9418/PDF/2012083.pdf |
| work_keys_str_mv | AT huangyuliaozuhua newtypeofsoftprimeidealsincommutativebckalgebras |