  We propose a new mathematical framework for the evolution and propagation of
opinions, called Fuzzy Opinion Network, which is the connection of a number of
Gaussian Nodes, possibly through some weighted average, time-delay or logic
operators, where a Gaussian Node is a Gaussian fuzzy set with the center and
the standard deviation being the node inputs and the fuzzy set itself being the
node output. In this framework an opinion is modeled as a Gaussian fuzzy set
with the center representing the opinion itself and the standard deviation
characterizing the uncertainty about the opinion. We study the basic
connections of Fuzzy Opinion Networks, including basic center, basic standard
deviation (sdv), basic center-sdv, chain-in-center and chain-in-sdv
connections, and we analyze a number of dynamic connections to show how
opinions and their uncertainties propagate and evolve across different network
structures and scenarios. We explain what insights we might gain from these
mathematical results about the formation and evolution of human opinions.
