Universal Approximation of a Class of Interval Type-2 Fuzzy Neural Networks Illustrated with the Case of Non-linear Identification
Juan R. Castro, Oscar Castillo, Patricia Melín, Antonio Rodríguez-Díaz, Olivia D. Mendoza · European Society for Fuzzy Logic and Technology Conference · 2009
Neural Networks (NN), Type-1 Fuzzy Logic Systems (T1FLS) and Interval Type-2 Fuzzy Logic Systems (IT2FLS) are universal approximators, they can approximate any non-linear function. Recent research shows that embedding T1FLS on an NN or embedding IT2FLS on an NN can be very effective for a wide number of non-linear complex systems, especially when handling imperfect information. In this paper we show that an Interval Type- 2 Fuzzy Neural Network (IT2FNN) is a universal approximator with some precision using a set of rules and Interval Type-2 membership functions (IT2MF) and the Stone-Weierstrass Theorem. Also, simulation results of non-linear function identification using the IT2FNN for one and three variables with 10-fold cross-validation are presented.