Applications of $$\alpha$$-level neutrosophic set and strong $$\alpha$$-level neutrosophic set

Abstract In this article, we present an innovative extension of the concept of $$\alpha$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>α</mml:mi> </mml:math> -level neutrosophic set (NS). Building upon the pioneering work of Johnson Awolola [14] in 2020, who initially defined $$\alpha$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>α</mml:mi> </mml:math> -level NS, our research introduces a new notion of $$\alpha$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>α</mml:mi> </mml:math> -level NS, aimed at enhancing the precision and practicality of outcomes. Within this context, we establish both the concept of an $$\alpha$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>α</mml:mi> </mml:math> -level NS and a robust variant termed the strong $$\alpha$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>α</mml:mi> </mml:math> -level NS. These novel concepts are then applied to the domain of neutrosophic graphs (NG), enabling the exploration of diverse properties and their implications.