The concept of a neutrosophic set, which is a generalization of an intuitionistic fuzzy set and a para consistent set etc., was introduced by F. Smarandache. Since then, it has been studied in various applications. In considering a generalization of the neutrosophic set, Mohseni Takallo et al. used the interval valued fuzzy set as the indeterminate membership function because interval valued fuzzy set is a generalization of a fuzzy set, and introduced the notion of MBJ-neutrosophic sets, and then they applied it to BCK/BCI-algebras. The aim of this paper is to apply the concept of MBJ-neutrosophic sets to a $ BE $-algebra, which is a generalization of a BCK-algebra. The notions of MBJ-neutrosophic subalgebras and MBJ-neutrosophic filters of $ BE $-algebras are introduced and related properties are investigated. The conditions under which the MBJ-neutrosophic set can be a MBJ-neutrosophic subalgebra/filter are searched. Characterizations of MBJ-neutrosophic subalgebras and MBJ-neutrosophic filters are considered. The relationship between an MBJ-neutrosophic subalgebra and an MBJ-neutrosophic filter is established.
Citation: Rajab Ali Borzooei, Hee Sik Kim, Young Bae Jun, Sun Shin Ahn. MBJ-neutrosophic subalgebras and filters in $ BE $-algebras[J]. AIMS Mathematics, 2022, 7(4): 6016-6033. doi: 10.3934/math.2022335
The concept of a neutrosophic set, which is a generalization of an intuitionistic fuzzy set and a para consistent set etc., was introduced by F. Smarandache. Since then, it has been studied in various applications. In considering a generalization of the neutrosophic set, Mohseni Takallo et al. used the interval valued fuzzy set as the indeterminate membership function because interval valued fuzzy set is a generalization of a fuzzy set, and introduced the notion of MBJ-neutrosophic sets, and then they applied it to BCK/BCI-algebras. The aim of this paper is to apply the concept of MBJ-neutrosophic sets to a $ BE $-algebra, which is a generalization of a BCK-algebra. The notions of MBJ-neutrosophic subalgebras and MBJ-neutrosophic filters of $ BE $-algebras are introduced and related properties are investigated. The conditions under which the MBJ-neutrosophic set can be a MBJ-neutrosophic subalgebra/filter are searched. Characterizations of MBJ-neutrosophic subalgebras and MBJ-neutrosophic filters are considered. The relationship between an MBJ-neutrosophic subalgebra and an MBJ-neutrosophic filter is established.
| [1] |
S. S. Ahn, K. S. So, On ideals and upper sets in $BE$-algerbas, Sci. Math. Jpn., 68 (2008), 279–285. https://doi.org/10.32219/isms.68.2_279 doi: 10.32219/isms.68.2_279
|
| [2] |
K. T. Atanassov, Intuitionistic fuzzy sets, Fuzzy sets Syst., 20 (1986), 87–96. https://doi.org/10.1016/S0165-0114(86)80034-3 doi: 10.1016/S0165-0114(86)80034-3
|
| [3] | Y. B. Jun, S. S. Ahn, On hesitant fuzzy filters in $BE$-algebras, J. Comput. Anal. Appl., 22 (2017), 346–358. |
| [4] |
Y. H. Kim, H. S. Kim, On $BE$-algerbas, Sci. Math. Jpn., 66 (2007), 113–116. https://doi.org/10.32219/isms.66.1_113 doi: 10.32219/isms.66.1_113
|
| [5] |
A. Rezei, A. B. Saeid, F. Smarnadache, Neutrosophic filters in $BE$-algebras, Ratio Math., 29 (2015), 65–79. https://doi.org/10.23755/rm.v29i1.23 doi: 10.23755/rm.v29i1.23
|
| [6] | F. Smarandache, Neutrosophy: Neutrosophic probability, set, and logic: analytic synthesis & synthetic analysis, American Research Press, 1998. |
| [7] |
P. Singh, A type-2 neutrosophic-entropy-fusion based multiple thresholding method for the brain tumor tissue structures segmentation, Appl. Soft Comput., 103 (2021), 107119. https://doi.org/10.1016/j.asoc.2021.107119 doi: 10.1016/j.asoc.2021.107119
|
| [8] |
P. Singh, Y. P. Huang, A high-order neutrosophic-neuro-gradient descent algorithm-based expert system for time series forecasting, Int. J. Fuzzy Syst., 21 (2019), 2245–2257. https://doi.org/10.1007/s40815-019-00690-2 doi: 10.1007/s40815-019-00690-2
|
| [9] | 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. |
| [10] | L. A. Zadeh, Fuzzy sets, Inform. Control, 8 (1965), 338–353. |
Rajab Ali Borzooei, Hee Sik Kim, Young Bae Jun, Sun Shin Ahn. MBJ-neutrosophic subalgebras and filters in $ BE $-algebras[J]. AIMS Mathematics, 2022, 7(4): 6016-6033. doi: 10.3934/math.2022335
DownLoad: