A class of interval type-2 fuzzy neural networks illustrated with application to non-linear identification

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.