Eigen neutrosophic Z-set and neutrosophic Z-relation: A nonlinear dynamic modeling approach under uncertainty

The modelling and Analysis of nonlinear systems under uncertainty are particularly difficult in scientific and engineering discipline.In many problems involving real world complex data, the inherent indeterminacy, vagueness and partial truth value associated with various real world complex phenomena is difficult to effectively capture using traditional frameworks.This study presents a novel nonlinear dynamic modelling framework based on Eigen Neutrosophic Z-Set and Neutrosophic Z-Relations framework to systematically handle the above challenges.The mathematical foundations of Neutrosophic Z sets are set up and discrete time dynamical systems given by Neutrosophic relational compositions are formulated.Properties of stability are rigorously analysed and proofs that convergence to fixed point eigen structures are derived.Details are presented of computational algorithms for determining Greatest Eigen Neutrosophic Z-Set (GENZS) and Least Eigen Neutrosophic Z-Set (LENZS).The theoretical framework is validated through the simulations on representative systems in which the numerically generated solutions accommodate the fast convergence and retain the stability of the systems under variation of the uncertainty conditions.The proposed approach provides a powerful and general means of modelling the nonlinear systems subject to uncertainty and could be applied, for example, in the area of engineering design, decision making systems and complex socio-economic modelling.