Affiliations: [a] Department of Mathematics, Hazara University, Mansehra, Pakistan
| [b] Department of Mathematics, College of Science Al-Zulfi, Majmaah University, Al-Zulfi, Saudi Arabia
| [c] Department of Mathematics, Quaid-i-Azam University, Islamabad, Pakistan
Correspondence:
[*]
Corresponding author. Muhammad Gulistan, Department of Mathematics, Hazara University, Mansehra, Pakistan. E-mail: [email protected].
Abstract: The semigroups have many applications in finite state machines, transformations etc. So, the abstract concept of neutrosophic cubic sets were required to be established in semigroups. This motivate the authors to present the idea of neutrosophic cubic semigroups and neutrosophic cubic points. In this work, we study the truth, indeterminacy and falsehood in algebraic structures and deduce some results. We generalize the concept of fuzzy points, intuitionistic fuzzy points and cubic points by introducing the concept of neutrosophic cubic points. Based on neutrosophic cubic points, we generalize the idea of (α, β)-fuzzy ideals, (α, β) -intuitionistic fuzzy ideals and (α, β)-cubic ideals in semigroups. Particularly, we give the idea of neutrosophic cubic (∈, ∈ ∨ q)-ideals (resp., subsemigroups, generalized bi-ideals, bi-ideals, quasi-ideals, interior ideals, prime and semiprime ideals) of semigroups.
