Abstract
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.
Original language | English |
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Pages (from-to) | 6016-6033 |
Number of pages | 18 |
Journal | AIMS Mathematics |
Volume | 7 |
Issue number | 4 |
DOIs | |
State | Published - 2022 |
Keywords
- MBJ-neutrosophic filter
- MBJ-neutrosophic set
- MBJ-neutrosophic subalgebra