An analytical approach for choosing the right fuzzy implication based on performance criteria for the fuzzy control.

Unlike many control techniques, fuzzy control is dealing with a great number of parameters. This represents, at the same time, its richness and one of the major impediments for the institution of a sound fuzzy control theory. Nevertheless, practical implementations of fuzzy control revealed many interesting applications. Towards a fuzzy control theory, we investigated the influence of some parameters on some control system performances. We focused on fuzzy implication, because, in practice, control engineers often proceed to simplifications that mask the effects of this parameter. Although, these simplifications were aimed to solve another parameter problem the defuzzification problem. Moreover, the fuzzy parameters are related to each other. We studied three families of fuzzy implications in relation with the two center of gravity defuzzification methods, in order to understand their influence on control performances and to justify the choice of a given implication by a certain performance criterion minimization. This article demonstrates that the family of T-implications (modeled by t-norms) is more suitable for fuzzy control when considering the rapidity and the precision criteria.