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Fuzzy differential systems and Malliavin calculus. (English) Zbl 0845.34029
Summary: We consider fuzzy differential systems, or differential equations with fuzzy inputs and fuzzy initial conditions. Using a fuzzy sample path approach, we derive partial differential equations for the resulting membership functions. We also demonstrate sufficient continuity conditions under which the solutions exist and are fuzzy convex. The membership functions are shown to be identical to those for a time varying deterministic differential equation with a fuzzy initial condition. Under sufficient stability conditions, we also consider the membership functions in steady state.
MSC:
34A99General theory of ODE
94D05Fuzzy sets and logic in connection with communication
34A60Differential inclusions
28E10Fuzzy measure theory