Membership Conditions in Neutrosophic N-Normed Linear Spaces

This paper explores the establishment of truth, falsy, and indeterminacy membership functions within the framework of neutrosophic n-normed linear spaces (Nn-NLSs). These membership functions form the core of the theoretical foundation for handling uncertainty, indeterminacy, and vagueness in complex mathematical spaces. The conditions governing these functions are rigorously defined, ensuring consistency and applicability in finite and infinite-dimensional cases. Truth membership functions are shown to be non-decreasing and converge to unity, falsy membership functions are non-increasing and converge to zero, while indeterminacy membership functions maintain constancy and eventually diminish to zero. These findings contribute to the robust theoretical modeling of Nn-NLSs and provide a pathway for future applications in uncertainty analysis and decision-making frameworks.