Neutrosophic Quadruple BCK/BCI-Algebras

被引：15

作者：

Jun, Young Bae ^{[1
]}

Song, Seok-Zun ^{[2
]}

Smarandache, Florentin ^{[3
]}

Bordbar, Hashem ^{[4
]}

机构：

[1] Gyeongsang Natl Univ, Dept Math Educ, Jinju 52828, South Korea

[2] Jeju Natl Univ, Dept Math, Jeju 63243, South Korea

[3] Univ New Mexico, Math & Sci Dept, 705 Gurley Ave, Gallup, NM 87301 USA

[4] Shahid Beheshti Univ, Dept Math, Tehran 1983963113, Iran

来源：

AXIOMS | 2018年 / 7卷 / 02期

基金：

新加坡国家研究基金会;

关键词：

neutrosophic quadruple BCK/BCI-number; neutrosophic quadruple BCK/BCI-algebra; neutrosophic quadruple subalgebra; (positive implicative) neutrosophic quadruple ideal;

D O I：

10.3390/axioms7020041

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The notion of a neutrosophic quadruple BCK/BCI-number is considered, and a neutrosophic quadruple BCK/BCI-algebra, which consists of neutrosophic quadruple BCK/BCI-numbers, is constructed. Several properties are investigated, and a (positive implicative) ideal in a neutrosophic quadruple BCK-algebra and a closed ideal in a neutrosophic quadruple BCI-algebra are studied. Given subsets A and B of a BCK/BCI-algebra, the set NQ(A,B), which consists of neutrosophic quadruple BCK/BCI-numbers with a condition, is established. Conditions for the set NQ(A,B) to be a (positive implicative) ideal of a neutrosophic quadruple BCK-algebra are provided, and conditions for the set NQ(A,B) to be a (closed) ideal of a neutrosophic quadruple BCI-algebra are given. An example to show that the set {0} is not a positive implicative ideal in a neutrosophic quadruple BCK-algebra is provided, and conditions for the set {0} to be a positive implicative ideal in a neutrosophic quadruple BCK-algebra are then discussed.

引用

页数：16

共 50 条

[1] Neutrosophic quadruple ideals in neutrosophic quadruple BCI-algebras
Muhiuddin, G.
Smarandache, Florentin
Jun, Young Bae
[J]. NEUTROSOPHIC SETS AND SYSTEMS, 2019, 25 : 161 - 173
[2] Polarity of generalized neutrosophic subalgebras in BCK/BCI-algebras
Borzooei, Rajab Ali
Smarandache, Florentin
Jun, Young Bae
[J]. Neutrosophic Sets and Systems, 2020, 32 : 123 - 145
[3] Polarity of generalized neutrosophic subalgebras in BCK/BCI-algebras
Borzooei, Rajab Ali
Smarandache, Florentin
Jun, Young Bae
[J]. NEUTROSOPHIC SETS AND SYSTEMS, 2020, 32 : 123 - 145
[4] BS-Neutrosophic Structures in BCK/BCI-Algebras
Satyanarayana, B.
Baji, Shake
Madhavi, U. Bindu
[J]. Neutrosophic Sets and Systems, 2023, 58 : 93 - 108
[5] MBJ-neutrosophic ideals of BCK/BCI-algebras
Jun, Young Bae
Roh, Eun Hwan
[J]. OPEN MATHEMATICS, 2019, 17 : 588 - 601
[6] Generalizations of Neutrosophic Subalgebras in BCK/BCI-Algebras Based on Neutrosophic Points
Kim, Seon Jeong
Song, Seok-Zun
Jun, Young Bae
[J]. NEUTROSOPHIC SETS AND SYSTEMS, 2018, 20 : 26 - 35
[7] Neutrosophic N-structures applied to BCK/BCI-algebras
[J]. Bordbar, Hashem (bordbar.amirh@gmail.com), 1600, MDPI AG (08):
[8] FURTHER RESULTS OF NEUTROSOPHIC SUBALGEBRAS IN BCK/BCI-ALGEBRAS BASED ON NEUTROSOPHIC POINTS
Muhiuddin, G.
Jun, Young Bae
[J]. TWMS JOURNAL OF APPLIED AND ENGINEERING MATHEMATICS, 2020, 10 (01): : 232 - 240
[9] Interior BCK/BCI-Algebras
Ahn, Sun Shin
Bordbar, Hashem
Jun, Young Bae
[J]. INTERNATIONAL JOURNAL OF COMPUTATIONAL INTELLIGENCE SYSTEMS, 2021, 14 (01) : 1923 - 1933
[10] On Vague BCK/BCI-algebras
Saeid, Arsham Borumand
[J]. 2009 IEEE INTERNATIONAL CONFERENCE ON FUZZY SYSTEMS, VOLS 1-3, 2009, : 1669 - 1671

← 1 2 3 4 5 →