  There has been a long history of using fuzzy language equivalence to compare
the behavior of fuzzy systems, but the comparison at this level is too coarse.
Recently, a finer behavioral measure, bisimulation, has been introduced to
fuzzy finite automata. However, the results obtained are applicable only to
finite-state systems. In this paper, we consider bisimulation for general fuzzy
systems which may be infinite-state or infinite-event, by modeling them as
fuzzy transition systems. To help understand and check bisimulation, we
characterize it in three ways by enumerating whole transitions, comparing
individual transitions, and using a monotonic function. In addition, we address
composition operations, subsystems, quotients, and homomorphisms of fuzzy
transition systems and discuss their properties connected with bisimulation.
The results presented here are useful for comparing the behavior of general
fuzzy systems. In particular, this makes it possible to relate an infinite
fuzzy system to a finite one, which is easier to analyze, with the same
behavior.
