Systems of First-Order Linear Fuzzy Initial Value Problems and Their Applications

This study primarily addresses solutions to a system of first-order linear fuzzy initial value problems in the context of granular differentiability, and explores the real-life applications of such systems.We recall the concepts of the horizontal membership function, granular metrics, limits, continuity, differentiability, and integrability for fuzzy functions with ndimensional fuzzy numbers.We then present a fundamental theorem that establishes the existence and uniqueness of solutions for both homogeneous and nonhomogeneous systems of first-order linear fuzzy initial value problems.In addition, we describe an algorithm for solving nonhomogeneous systems under granular differentiability.Finally, we provide real-life applications -including models for lidocaine and irregular heartbeats, Richardson's arms race, and radioactive decay phenomena in a fuzzy environment -to demonstrate the practical utility of the proposed algorithm.