Dynamical membership functions: an approach for adaptive fuzzy modelling

New approaches in fuzzy modelling in order to solve practical limitations found in classic adaptive fuzzy modelling, are considered an interesting contribution in the fuzzy logic field. In this work, an approach for the development of dynamical fuzzy models is presented. The approach allows to incorporate the system dynamics into the fuzzy membership functions, which are defined in terms of the sample mean value and the variance of each variable of the fuzzy model from the input and output values of the system to be modelled. These fuzzy membership functions, defined as dynamical functions, have adjustable parameters which are adapted by using a conventional off-line gradient descent-based algorithm. In this way, after the learning process, the resulted fuzzy model has non-static membership functions dependent on the available values of the variables at time t. Some application examples to illustrate the performance of the proposed dynamical adaptive fuzzy model on system identification are presented, and the experimental results are discussed in order to remark the capabilities of the new fuzzy model.