Using Multi-valued Logic Implications in a Mamdani-type Fuzzy Controller

In this paper we present a study on inference in a Fuzzy Logic Controller (FLC). Many different implication operators have been proposed in the Fuzzy Logic literature; we take into account five of them that have already been used in fuzzy control. In order to evaluate the advantages and disadvantages of each implication in practical applications, we consider the controller's defuzzified output that is applied to a deterministic plant. We focus on four of the so-called multi-valued logic implications, often viewed in literature as not suitable for control applications, as they produce a bias in the final fuzzy set to defuzzify of a Mamdani-type fuzzy controller. We show that their use is on the contrary feasible when a particular partition of the input universe of discourse is performed: the deformation does no longer affect the output and we can thus benefit by the lower sensitivity that a FLC performing these implications possesses.