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This article is about molecular simulation. However, the theoretical resultsapply for general overdamped Langevin dynamics simulations. Molecularsimulation is often used for determining the stability of a complex (e.g.,ligand-receptor). The stability can be measured by computing the expectedholding time of the complex before its dissociation. This dissociation can beseen as an exit event from a certain part S of the conformational state space.Determining exit rates (i.e, for SDE-based simulations exiting from a givenstarting set S) for a stochastic process in which the exit event occurs veryrarely is obviously hard to solve by straight forward simulation methods.Finding a low variance procedure for computing rare event statistics is stillan open problem. Imagine now, e.g., a simulation of a diffusion process. Aslong as the time-dependent state trajectory is inside the starting set S, noinformation is gained about the rare event statistics. Only at that point oftime, when the process leaves the starting set, a piece of information aboutthe exit rate is collected. If S, however, is a fuzzy set given by a membershipfunction, then there might be additional information of the kind "the processis about to leave the set". However, how to define an exit rate from a fuzzyset?

A fuzzy-set theoretical framework for computing exit rates of rare events in potential-driven diffusion processes