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

Towards a fuzzy control theory, we investigate the influence of some parameters on some control system performances. We focus on fuzzy implication because, in practice, control engineers often proceed to simplification that mask the effects of this parameter; although these simplification were aimed to solve another parameter problem-the defuzzification problem. Moreover, the fuzzy parameters are related to each other. We study 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.