The simplest computational models in artificial intelligence are so-called single hidden-layer feed-forward neural networks. These neural networks have to be trained, but the slow learning rate of simple algorithms makes this time-consuming. Extreme learning machines (ELMs) speed up this learning significantly, and they are much simpler to manage and require no tuning. The price to be paid is that ELMs are not capable of modeling uncertainties. But of course, the real-world data that is input to a training algorithm is full of uncertainties.

One could say that real-world data is not just a set of numbers, but rather a fuzzy set. In other words, it is an element not exclusively outside (0) or inside (1) the set; the extent of its membership is an arbitrary real number between 0 and 1. These are fuzzy sets of type 1. If we cannot even determine a crisp number in [0,1], we can use fuzzy sets of type 2, where the membership function ranges over a fuzzy set of type 1. Using type-2 fuzzy sets leads to another way of training feed-forward neural networks, called type-2 fuzzy logic systems (T2FLSs).

This paper marries the two notions of ELM and T2FLS to enable learning of uncertain real-world data in an efficient way. The proposed hybrid system is put to the test on real-world data obtained from five Middle Eastern oil wells, with the goal of learning to predict permeability. The results show that the hybrid system outperforms either ELM and T2FLS alone. Depending on which metric is used, improvements of up to 50 percent are reported. The hybrid system is also compared to two other popular methods, which it also outperforms.