This paper develops a non-singleton type-2 fuzzy neural network (NT2FNN) with type-2 3-dimensional
membership functions (MFs) and adaptive secondary membership. A new approach based on the squareroot cubature quadrature Kalman filter (SR-CQKF) is proposed for the training the level of the secondary
membership and the centers of membership functions. The consequent parameters are learned by using rule-ordered extended Kalman filter (EKF). To show the applicability and effectiveness of proposed
NT2FNN in high dimensional problems, four real-world datasets with 4, 7, 13 and 32 input variables are
considered. Additionally, the performance of NT2FNN with the proposed learning algorithm is compared
with other well-known neural networks and learning algorithms. The simulations demonstrate that the
developed method results in high performance in contrast to the other methods.