Mixture data-driven Takagi-Sugeno fuzzy model

The conventional Takagi-Sugeno (T-S) fuzzy model is an effective tool used to approximating behaviors of nonlinear systems on the basis of precise and certain input and output observations. In some situations, however, we can only obtain mixture of precise data (for input variables), imprecise and uncertain data (for output variable/response). This paper presents a method used to constructing T-S fuzzy model in such case where the imprecise and uncertain output observations are represented as fuzzy belief function, and then proposes the so-called mixture data-driven T-S fuzzy model, among which, the consequents are identified by using a novel fuzzy evidential Expectation-Maximization (EM) algorithm and the antecedents are automatically constructed by using a data-driven strategy, considering both the accuracy and complexity of model. The performance of such mixture data data-driven fuzzy model was validated by conducting some unreliable sensor experiments. The numerical simulations suggest that the proposed fuzzy model can be used to approximate nonlinear systems with high accuracy when the outputs of systems are imprecisely and uncertainly observed.