Numerical solution of an intuitionistic fuzzy parabolic partial differential equation using an explicit cubic spline method

This paper presents a numerical approach for solving intuitionistic fuzzy parabolic partial differential equations (IFPPDEs) using the explicit cubic spline method. Intuitionistic fuzzy systems, which extend classical fuzzy sets by incorporating a degree of non-membership, provide a more flexible framework for modelling uncertainty in real-world phenomena. The initial and boundary conditions of the intuitionistic fuzzy parabolic partial differential equation are considered intuitionistic triangular fuzzy numbers. The proposed cubic spline-based scheme ensures smooth and accurate approximations of the solution while maintaining stability and convergence properties. A discretization strategy is developed to transform the IFPPDE into a solvable system, and an iterative algorithm is introduced to handle the intuitionistic fuzzy parameters effectively. The efficiency and accuracy of the method are demonstrated through numerical experiments, comparing the results with the exact solution. The findings suggest that the cubic spline method provides good accuracy and computational efficiency, making it a promising tool for solving intuitionistic fuzzy parabolic partial differential problems in various scientific and engineering applications.