A Behavioral Distance for Fuzzy-Transition Systems
  In contrast to the existing approaches to bisimulation for fuzzy systems, we
introduce a behavioral distance to measure the behavioral similarity of states
in a nondeterministic fuzzy-transition system. This behavioral distance is
defined as the greatest fixed point of a suitable monotonic function and
provides a quantitative analogue of bisimilarity. The behavioral distance has
the important property that two states are at zero distance if and only if they
are bisimilar. Moreover, for any given threshold, we find that states with
behavioral distances bounded by the threshold are equivalent. In addition, we
show that two system combinators---parallel composition and product---are
non-expansive with respect to our behavioral distance, which makes
compositional verification possible.
