Some studies on uncertainty management in dynamical systems using cybernetic approaches and fuzzy techniques with applications

Abstract

Uncertain information processing by fuzzy if–then rules has received much attention. Here we have taken a different path to model a system, about which we do not have precise information, namely modelling the system by fuzzy-valued functions without resorting to fuzzy if–then rules. As a result, the phase (state) space of the system becomes a fuzzy set and the underlying fuzzy mapping becomes a fuzzy attainability set mapping. Uncertain or fuzzy dynamical systems have been defined in terms of fuzzy attainability set mappings. Fuzzy differentiable dynamical systems have been discussed with a particular emphasis on fuzzy differential inclusion (FDI) relations. An evolutionary algorithm for solving one-dimensional FDIs has been developed. A model of the creation of a tropical cyclone in the form of a vortex, created by winds coming from different directions and colliding under certain conditions, has been proposed in terms of FDIs. A model has been considered for the highly uncertain system of evolution of a tumour in a human body and an FDI relation model of the whole system has been proposed and simulated. The model of an evolution of turbulence, as a random occurrence of vortices in a three-dimensional dynamic fluid, has been proposed and simulated, where each vortex is modelled by a fuzzy-valued function, where uncertain parameter and variable values are fuzzy numbers. All the systems represented by FDI relations have been simulated with the help of the evolutionary algorithm mentioned above.