The MBJ-neutrosophic set is applied to the implicative ideal of BCK-algebra to introduce the concept of implicative MBJ-neutrosophic ideal. Several properties are investigated. The relationship between implicative MBJ-neutrosophic ideal and each MBJ-neutrosophic subalgebra, (positive implicative, commutative) MBJ-neutrosophic ideal is established. Conditions for MBJ-neutrosophic subalgebra (resp., MBJ-neutrosophic ideal, positive implicative MBJ-neutrosophic ideal and commutative MBJ-neutrosophic ideal) to be implicative MBJ-neutrosophic ideal are provided. Characterizations of implicative MBJ-neutrosophic ideal are discussed.
Citation: M. Mohseni Takallo, Rajab Ali Borzooei, Seok-Zun Song, Young Bae Jun. Implicative ideals of BCK-algebras based on MBJ-neutrosophic sets[J]. AIMS Mathematics, 2021, 6(10): 11029-11045. doi: 10.3934/math.2021640
The MBJ-neutrosophic set is applied to the implicative ideal of BCK-algebra to introduce the concept of implicative MBJ-neutrosophic ideal. Several properties are investigated. The relationship between implicative MBJ-neutrosophic ideal and each MBJ-neutrosophic subalgebra, (positive implicative, commutative) MBJ-neutrosophic ideal is established. Conditions for MBJ-neutrosophic subalgebra (resp., MBJ-neutrosophic ideal, positive implicative MBJ-neutrosophic ideal and commutative MBJ-neutrosophic ideal) to be implicative MBJ-neutrosophic ideal are provided. Characterizations of implicative MBJ-neutrosophic ideal are discussed.
| [1] | L. A. Zadeh, Fuzzy sets, Inf. Control, 8 (1965), 338–353. |
| [2] | F. Smarandache, Neutrosophic probability, set, and logic, Bull. Transilv. Univ. Braşov Ser. B (N.S.), 6 (1999), 41–48. |
| [3] | F. Smarandache, A unifying field in logics. Neutrosophy: Neutrosophic probability, set and logic, Rehoboth: American Research Press, 1999. |
| [4] | F. Smarandache, Neutrosophic set-a generalization of the intuionistic fuzzy set, Int. J. Pure Appl. Math., 24 (2005), 287–297. |
| [5] |
G. Muhiuddin, $p$-ideals of BCI-algebras based on neutrosophic ${\mathcal N}$-structures, J. Intell. Fuzzy Syst., 40 (2021), 1097–1105. doi: 10.3233/JIFS-201309
|
| [6] | G. Muhiuddin, Y. B. Jun, Further results of neutrosophic subalgebras in BCK/BCI-algebras based on neutrosophic point, TWMS J. Appl. Eng. Math., 10 (2020), 232–240. |
| [7] | G. Muhiuddin, F. Smarandache, Y. B. Jun, Neutrosophic quadruple ideals in neutrosophic quadruple BCI-algebras, Neutrosophic Sets Syst., 25 (2019), 161–173. |
| [8] | M. M. Takallo, R. A. Borzooei, Y. B. Jun, MBJ-neutrosophic structures and its applications in BCK/BCI-algebras, Neutrosophic Sets Syst., 23 (2018), 72–84. |
| [9] |
A. Alsubie, A. Al-Masarwah, MBJ-neutrosophic hyper BCK-ideals in hyper BCK-algebras, AIMS Math., 6 (2021), 6107–6121. doi: 10.3934/math.2021358
|
| [10] | K. Hur, J. G. Lee, Y. B. Jun, Positive implicative MBJ-neutrosophic ideals of BCK/BCI-algebras, Ann. Fuzzy Math. Inf., 17 (2019), 65–78. Available from: https://doi.org/10.30948/afmi.2019.17.1.65. |
| [11] |
Y. B. Jun, M. M. Takallo, Commutative MBJ-neutrosophic ideals of BCK-algebras, J. Algebraic Hyperstructures Logical Algebras, 2 (2021), 69–81. doi: 10.52547/HATEF.JAHLA.2.1.5
|
| [12] | Y. B. Jun, E. H. Roh, MBJ-neutrosophic ideals of BCK/BCI-algebras, Open Math., 17 (2019), 588–601. Available from: http://dx.doi.org/10.1515/math-2019-0106. |
| [13] | J. Meng, Y. B. Jun, BCK-algebras, Seoul: Kyung Moon Sa Co., 1994. |
M. Mohseni Takallo, Rajab Ali Borzooei, Seok-Zun Song, Young Bae Jun. Implicative ideals of BCK-algebras based on MBJ-neutrosophic sets[J]. AIMS Mathematics, 2021, 6(10): 11029-11045. doi: 10.3934/math.2021640
DownLoad: