Quantum computers can be a revolutionary tool to implement inference engines for fuzzy rule-based systems. In fact, the use of quantum mechanical principles can enable parallel execution of fuzzy rules and allow them to be used efficiently in complex contexts such as distributed and big data environments. This paper introduces the very first quantum-based fuzzy inference engine that is capable of providing exponential acceleration in fuzzy rule execution compared to its classical counterpart, and allows a quantum computer to be programmed by fuzzy linguistic rules. The proposed inference engine was implemented using a quantum algorithm design scheme based on the oracle notion. This scheme allows the modeling of a fuzzy rule-based system as a Boolean function, the oracle, which is able to reconstruct the relationships between the antecedent and consequent parts of fuzzy rules, and can be efficiently computed on a quantum computer. The suitability of the proposed quantum algorithm for use as a fuzzy inference engine was tested in a typical benchmark scenario, such as that provided by inverted pendulum control.

Fuzzy cognitive maps (FCMs) form an important class of models for describing and simulating the behavior of dynamic systems through causal reasoning. Owing to their abilities to make the symbolic knowledge processing simple and transparent, FCMs have been successfully used to model the behavior of complex systems originating from numerous application areas, such as economy, politics, medicine, and engineering. However, the design of FCMs necessarily involves domain experts to develop a graph-based model composed of a collection of system's concepts and causal relationships among them. Consequently, since humans exhibit an intrinsic factor of subjectivity and are only able to efficiently develop small-size graph-based models, there is a legitimate need to devise methods capable of automatically learning FCM models from data. This research addresses this need by introducing a competent memetic algorithm to generate FCM models from available historical data, with no human intervention. Extensive benchmarking tests performed on both synthetic and real-world data quantify the performance of the competent memetic method and emphasize its suitability over the models obtained by conventional and noncompetent hybrid evolutionary approaches in terms of accuracy, approximation ability, and convergence speed. Moreover, the proposed approach is shown to be scalable due to its capability to efficiently learn high-dimensional FCM models.