  In this article we investigate a way in which quantum computing can be used
to extend the class of fuzzy sets. The core idea is to see states of a quantum
register as characteristic functions of quantum fuzzy subsets of a given set.
As the real unit interval is embedded in the Bloch sphere, every fuzzy set is
automatically a quantum fuzzy set. However, a generic quantum fuzzy set can be
seen as a (possibly entangled) superposition of many fuzzy sets at once,
offering new opportunities for modeling uncertainty. After introducing the main
framework of quantum fuzzy set theory, we analyze the standard operations of
fuzzification and defuzzification from our viewpoint. We conclude this
preliminary paper with a list of possible applications of quantum fuzzy sets to
pattern recognition, as well as future directions of pure research in quantum
fuzzy set theory.
