Implementing Defuzzification Operators on Quantum Annealers

Due to the built-in parallelism of quantum computing, there is an unexplored potential for some complex fuzzy logic computations to take the advantage of the future quantum computers. Recently, it has been introduced a novel representation of fuzzy sets and implementations of some basic fuzzy logic operators (union, intersection, alpha-cut and maximum) based on solving a Quadratic Unconstrained Binary Optimization (QUBO) problems, on a type of quantum computers known as quantum annealers. In this paper, this work is extended by presenting an implementation of centroid defuzzification on quantum annealer machines, based on binary quadratic model (BQM) but this time using Ising model. Having the basic operations and defuzzification implemented on quantum computers, this paper paves the way towards the implementation of a whole fuzzy inference engine on enhanced devices, such as quantum annealers.