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

Fuzzy Opinion Networks: A Mathematical Framework for the Evolution of Opinions and Their Uncertainties Across Social Networks