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The notion of a neutrosophic quadruple BCI-commutative ideal in a neutrosophic quadruple BCI-algebra is introduced, and several properties are investigated. Relations between a neutrosophic quadruple ideal and a neutrosophic quadruple BCI-commutative ideal are discussed, and conditions for the neutrosophic quadruple ideal to be a neutrosophic quadruple BCI-commutative ideal are given. Conditions for the neutrosophic quadruple set to be a neutrosophic quadruple BCI-commutative ideal are provided, and the extension property of a neutrosophic quadruple BCI-commutative ideal is considered.
Commutative neutrosophic quadruple ideals and BCK-algebras are discussed, and related properties are investigated. Conditions for the neutrosophic quadruple BCK-algebra to be commutative are considered. Given subsets A and B of a neutrosophic quadruple BCK-algebra, conditions for the set NQ(A;B) to be a commutative ideal of a neutrosophic quadruple BCK-algebra are provided.
Commutative neutrosophic quadruple ideals and BCK-algebras are discussed, and related properties are investigated. Conditions for the neutrosophic quadruple BCK-algebra to be commutative are considered. Given subsets A and B of a neutrosophic quadruple BCK-algebra, conditions for the set NQ(A;B) to be a commutative ideal of a neutrosophic quadruple BCK-algebra are provided.
A neutrosophic set is initiated by Smarandache, and it is a novel tool to deal with vagueness considering the truth, indeterminacy and falsity memberships satisfying the condition that their sum is less than 3. The concept of neutrosophic quadruple numbers was introduced by Florentin Smarandache. Using this idea, Jun et al. introduced the notion of neutrosophic quadruple BCK/BCI-numbers, and studied neutrosophic quadruple BCK/BCI-algebras.
In the present paper, we discuss the Neutrosophic quadruple q-ideals and (regular) neutrosophic quadruple ideals and investigate their related properties.
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.
This paper presents a new concept in neutrosophic sets (NS) called neutrosophic structured element (NSE). Based on this concept, we define the operational laws, score function, and some aggregation operators of NS. Finally, as an application of this concept, we propose a decision-making method for a multi-attribute decision making (MADM) problem under NSE information. The results indicate that this concept is a useful tool for dealing with neutrosophic decision problems.
The theory of soluble groups and nilpotent groups is old and hence a generalized on. In this paper, we introduced neutrosophic soluble groups and neutrosophic nilpotent groups which have some kind of indeterminacy. These notions are generalized to the classic notions of soluble groups and nilpotent groups. We also derive some new type of series which derived some new notions of soluble groups and nilpotent groups. They are mixed neutrosophic soluble groups and mixed neutrosophic nilpotent groups as well as strong neutrosophic soluble groups and strong neutrosophic nilpotent groups.
In the present paper, we discuss the Neutrosophic quadruple q-ideals and (regular) neutrosophic quadruple ideals and investigate their related properties.
This paper concerns the study of the notions of neutrosophic soft s-open set, neutrosophic soft s-neighborhood and neutrosophic soft s-separation axioms in neutrosophic soft topological spaces. By using such notions and that of neutrosophic soft point, we study the separation axioms s-Ti (with i = 0, . . .4), the s-regular and the s-normal neutrosophic soft topological spaces by proving some relationships between these classes of spaces and other results concerning hereditary and subspaces.