  In this paper the Distributed Consensus and Synchronization problems with
fuzzy-valued initial conditions are introduced, in order to obtain a shared
estimation of the state of a system based on partial and distributed
observations, in the case where such a state is affected by ambiguity and/or
vagueness. The Discrete-Time Fuzzy Systems (DFS) are introduced as an extension
of scalar fuzzy difference equations and some conditions for their stability
and representation are provided. The proposed framework is then applied in the
field of Critical Infrastructures; the consensus framework is used to represent
a scenario where human operators, each able to observe directly the state of a
given infrastructure (or of a given area considering vast and geographically
dispersed infrastructures), reach an agreement on the overall situation, whose
severity is expressed in a linguistic, fuzzy way; conversely synchronization is
used to provide a distributed interdependency estimation system, where an array
of interdependency models is synchronized via partial observation.
