Mamdani-Driven Fuzzy Reaction Systems

Reaction Systems (RSs) provide a successful qualitative modelling framework inspired by biochemical reactions. In a RS a computation starts from an initial state given by a set of entities and each following computation state is determined by the application of all the enabled reactions to the previous state. RSs can also model the interaction with the environment. Each entity can either be present or absent in a computation state, as a crisp boolean condition, and also reactions are (or not) enabled under crisp conditions. This framework has proved to have many applications for modelling biomedical and computer science systems, but it can become restrictive when laboratory measurements exhibit graded concentrations, partial inhibition, and noise. We thus introduce Mamdani-driven Fuzzy Reaction Systems (M-FRS), as a graded conservative extension of RSs. Each reaction in the style of RSs is now interpreted as a Mamdani rule, and we formalise a single four-stage fuzzy inference cycle (fuzzification, rule evaluation, aggregation, optional defuzzification) which defines a deterministic discrete-time graded update operator. Fuzzy inference yields a discrete dynamical system. As a first case study, we develop a compact M-FRS model of the hypothalamic–pituitary–thyroid axis.