In this paper, we introduce the concept of quasi-coincidences in MBJ-neutrosophic sets and obtain some of its properties. Also by defining the pre-image and the image of an MBJ-neutrosophic set under ...a mapping, we confirm that their properties are naturally extensions of the classical case. Next, we define two types of MBJ-neutrosophic neighborhood system and discuss their various properties and introduce the notion of ◦-resp. ∗-MBJ-neutrosophic bases and deal with some of their properties. Finally, we define ◦-CI , ∗-CI , ◦-CII and ∗-CII corresponding to the first countability and the second countability in classical topological spaces, and we obtain the relationships between them.
The neutrosophic set consists of three fuzzy sets called true membership function, false membership function and indeterminate membership function. MBJ-neutrosophic structure is a structure ...constructed using interval-valued fuzzy set instead of indeterminate membership function in the neutrosophic set. In general, the indeterminate part appears in a wide range. So instead of treating the indeterminate part as a single value, it is treated as an interval value, allowing a much more comprehensive processing. In an attempt to apply the MBJ-neutrosophic structure to ordered BCI-algebras, the notion of MBJ-neutrosophic (ordered) subalgebras is introduced and their properties are studied. The relationship between MBJ-neutrosophic subalgebra and MBJ-neutrosophic ordered subalgebra is established, and MBJ-neutrosophic ordered subalgebra is formed using (intuitionistic) fuzzy ordered subalgebra. Given an MBJ-neutrosophic set, its (q, c, p)-translative MBJ-neutrosophic set is introduced and its characterization is considered. An MBJ-neutrosophic ordered subalgebra is created using (q, c, p)-translative MBJ-neutrosophic set. Keywords: Ordered BCI-algebra, ordered subalgebra, MBJ-neutrosophic ordered subalgebra, MBJ-ordered subalgebras, (q, c, p)-translative MBJ-neutrosophic set. 2020 Mathematics Subject Classification. 06F35, 03G25, 08A72.
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.
In this paper, the idea of T-MBJ neutrosophic set is introduced in which MBJ-neutrosophic set is used to present this new set called T-MBJ neutrosophic set. furthermore the notion of T-MBJ ...neutrosophic M-subalgebra on G-algebra is also introduced and provide the conditions for T-MBJ neutrosophic M-subalgebra. The word M in the term M-subalgebra, represents the initial of author's first name Mohsin. We study the T-MBJ neutrosophic set through different characteristics and also prove some results for better understanding of newly define T-MBJ neutrosophic set. Keywords: G-algebra; T-MBJ neutrosophic set; T-MBJ neutrosophic M-subalgebra.
The notion of MBJ-neutrosophic ideal is introduced, and its properties are investigated. Conditions for an MBJ-neutrosophic set to be an MBJ-neutrosophic ideal are provided. In a
-algebra, a ...condition for an MBJ-neutrosophic set to be an MBJ-neutrosophic ideal is given. In a
-algebra, a condition for an MBJ-neutrosophic subalgebra to be an MBJ-neutrosophic ideal is given. In a
-algebra, conditions for an MBJ-neutrosophic ideal to be an MBJ-neutrosophic subalgebra are considered. In an (
)-
-algebra, we show that every MBJ-neutrosophic ideal is an MBJ-neutrosophic ∘-subalgebra, and a characterization of an MBJ-neutrosophic ideal is established.
As a generalization of a neutrosophic set, the notion of MBJ-neutrosophic sets is introduced by Mohseni Takallo, Borzooei and Jun, and it is applied to BCK/BCI-algebras. In this article, ...MBJ-neutrosophic set is used to study commutative ideal in BCI-algebras. The concept of closed MBJ-neutrosophic ideal and commutative MBJ-neutrosophic ideal is introduced and their properties and relationships are studied. The conditions for an MBJ-neutrosophic ideal to be a commutative MBJ-neutrosophic ideal are given. The conditions for an MBJ-neutrosophic ideal to be a closed MBJ-neutrosophic ideal are provided. Characterization of a commutative MBJ-neutrosophic ideal is established. Finally, the extension property for a commutative MBJ-neutrosophic ideal is founded.
This paper extends the concept of ideal of a beta - algebra to MBJ - Neutrosophic beta - Ideal of a beta - algebra. Further discusses about the homomorphic image, inverse image, cartesian product and ...related results. Keywords: Neutrosophic Set, MBJ - Neutrosophic Set, MBJ - Neutrosophic beta - Ideals, Cartesian Product of MBJ - Neutrosophic beta - algebra.
Smarandache (F. Smarandache. Neutrosophy, neutrosophic probability, set, and logic, ProQuest Information & Learning, Ann Arbor, Michigan, USA, 105 p., 1998) initiated neutrosophic sets which can be ...used as a mathematical tool for dealing with indeterminates and inconsistent information. As a generalization of a neutrosophic set, the notion of MBJ-neutrosophic sets is introduced, and it is applied to BCK/BCI-algebras. The concept of MBJ-neutrosophic subalgebras in BCK/BCI-algebras is introduced, and related properties are investigated. A characterization of MBJ-neutrosophic subalgebra is provided. Using an MBJ-neutrosophic subalgebra of a BCI-algebra, a new MBJ-neutrosophic subalgebra is established. Homomorphic inverse image of MBJ-neutrosophic subalgebra is considered. Translation of MBJ-neutrosophic subalgebra is discussed. Conditions for an MBJ-neutrosophic set to be an MBJ-neutrosophic subalgebra are provided. Keywords: MBJ-neutrosophic set; MBJ-neutrosophic subalgebra; MBJ-neutrosophic S-extension.
The concepts of a BMBJ-neutrosophic -subalgebra and a (closed) BMBJ-neutrosophic ideal are introduced, and several properties are investigated. Conditions for an MBJ-neutrosophic set to be a ...BMBJ-neutrosophic ideal in BCK/BCI-algebras are provided. Characterizations of BMBJ-neutrosophic ideal are discussed. Relations between a BMBJ-neutrosophic subalgebra, a BMBJ-neutrosophic -subalgebra and a (closed) BMBJ-neutrosophic ideal are considered.
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