Abstract
The purpose of this paper is to introduce the notation of single-valued neutrosophic hyper BCK-subalgebras and a novel concept of neutro hyper BCK-algebras as a generalization and alternative of hyper BCK-algebras, that have a larger applicable field. In order to realize the article’s goals, we construct single-valued neutrosophic hyper BCK-subalgebras and neutro hyper BCK-algebras on a given nonempty set. The result of the research is the generalization of single-valued neutrosophic BCK-subalgebras and neutro BCK-algebras to single-valued neutrosophic hyper BCK-subalgebras and neutro hyper BCK-algebras, respectively. Also, some results are obtained between extended (extendable) single-valued neutrosophic BCK-subalgebras and single-valued neutrosophic hyper BCK-subalgebras via fundamental relation. The paper includes implications for the development of single-valued neutrosophic BCK-subalgebras and neutro BCK-algebras and for modelling the uncertainty problems by single-valued neutrosophic hyper BCK-subalgebras and neutro hyper BCK-algebras. The new conception of single-valued neutrosophic hyper BCK-subalgebras and neutro hyper BCK-algebras was given for the first time in this paper. We find a method that can apply these concepts in some complex networks.
Highlights
A neutro algebra is a system that has at least one neutro operation or one neutro axiom, while a partial algebra is a algebra that has at least one partial
Smarandache proved that a neutron algebra is a generalization of a partial algebra and showed that neutro algebras are not partial algebras, necessarily
One of the aims of this paper is to introduce the concept of single-valued neutrosophic hyper BCK-subalgebras and extendable single-valued neutrosophic BCK-subalgebras and generalize the notion of single-valued neutrosophic hyper BCK-subalgebras by considering the notion of single-valued neutrosophic BCKsubalgebras
Summary
Definition 1 (see [2]) Let X ≠ ∅. en a universal algebra (X, θ , 0) of type (2, 0) is called a BCK-algebra if, for all, x, y, z ∈ X:. Definition 1 (see [2]) Let X ≠ ∅. En a universal algebra (X, θ , 0) of type (2, 0) is called a BCK-algebra if, for all, x, y, z ∈ X:. (BCK − 5) 0ρx 0, where ρ(x, y) is denoted by xρy. We will call X is a weak commutative hyper BCK-algebra if ∀x, y ∈ X, (x θ (x θ y)) ∩ (y θ (y θ x)) ≠ ∅ [21]. Let (X, θ , 0) be a hyper BCK-algebra. A fuzzy set μ: X ⟶ [0, 1] is called a fuzzy hyper BCK-subalgebra if ∀x, y ∈ X, ∧ (μ(x θ y)) ≥ Tmin(μ(x), μ(y)). Ere is no restriction on the sum of TX(x), IX(x), and FX(x)
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