A defuzzification method respecting the fuzzification

Abstract When designing a fuzzy controller, the first thing to do is to choose input and output fuzzifications. The next step consists of building the fuzzy rules table describing the behaviour of the controller. Finally, in order to convert the fuzzy output in a usable form, we need to select a defuzzification strategy. This selection can be realized by testing one by one the defuzzification methods available in the literature, and taking the best one in terms of output error. However, this approach is not theoretically convincing. This selection can also be realized by considering the following logical criterion: fuzzification and defuzzification are, by nature, two complementary processes. In other words, the choice of a defuzzification strategy must be made with respect to the output fuzzification. In this paper, we present a defuzzification method which takes into account the parameters of the fuzzification in order to respect it.