fuzzy relational matrix-based stability analysis for first-order fuzzy relational dynamic systems

in this paper, two sets of sufficient conditions are obtained to ensure the existence and stability of a unique equilibrium point of unforced first-order fuzzy relational dynamical systems by using two different approaches which are both based on the fuzzy relational matrix of the model.in the first approach, the equilibrium point of the system is one of the centers of the related membership functions.in the second approach, the equilibrium point of the system is the origin (the center of the middle membership function) and the behavior of the system, though can be nonlinear, is symmetric around the origin.the results are approved by numerical examples.