Quantum Fuzzy Sets: Blending Fuzzy Set Theory and Quantum Computation

Abstract

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.