Modified Non-Linear Triangular Neutrosophic Numbers: Theory and Applications in Integral Equation

Existing methods for handling uncertainty and imprecision often fall short in addressing complex real-world problems. To overcome these limitations, this paper introduces a novel Generalized Non-Linear Triangular Neutrosophic Number (GNLTNN) that effectively captures uncertainty, indeterminacy, and falsity. By analysing GNLTNN through (α, β, γ)-cuts and defining arithmetic operations using the max-min principle, we provide a robust framework for handling neutrosophic information. The proposed neutrosophic Laplace transform method enables efficient solutions to integral equations involving non-linear neutrosophic numbers. The efficacy of our approach is demonstrated through graphical representations.