Stability of Fuzzy Dynamic Systems

where [f̂(x,K)]α e [X0] α are the α−levels of the fuzzy subsets f̂(x,K) and X̃0, respectively. As in [1] we saw that for each t > 0, the attainable set obtained under the Hüllermeier’s interpretation for (2), or rather, through a family of differential inclusions of the type gives in (3) coincides with the solution obtained applying the principle extension of Zadeh in deterministic solution We will define fuzzy flow and a fuzzy equilibrium point for (2) for the deterministic flow extended, in other words, applying the principle extension of Zadeh in deterministic flow. Since then, the theory of stability for (2) will also be established through the extended solution. We verify that there is an equivalence of stability for the equilibrium points x̄ of (1) and fuzzy of type χ{x̄} (characteristic of x̄) of (2). Also we present some results that relate attractors of (1) and the fuzzy asymptotically stable equilibrium of (2). We explored the malthusian and logistic models with the initial condition being a fuzzy subset, with the fuzzy coefficient and finally both, coefficient and initial condition.