  Fuzzy discrete event systems as a generalization of (crisp) discrete event
systems have been introduced in order that it is possible to effectively
represent uncertainty, imprecision, and vagueness arising from the dynamic of
systems. A fuzzy discrete event system has been modelled by a fuzzy automaton;
its behavior is described in terms of the fuzzy language generated by the
automaton. In this paper, we are concerned with the supervisory control problem
for fuzzy discrete event systems with partial observation. Observability,
normality, and co-observability of crisp languages are extended to fuzzy
languages. It is shown that the observability, together with controllability,
of the desired fuzzy language is a necessary and sufficient condition for the
existence of a partially observable fuzzy supervisor. When a decentralized
solution is desired, it is proved that there exist local fuzzy supervisors if
and only if the fuzzy language to be synthesized is controllable and
co-observable. Moreover, the infimal controllable and observable fuzzy
superlanguage, and the supremal controllable and normal fuzzy sublanguage are
also discussed. Simple examples are provided to illustrate the theoretical
development.
