Capturing Uncertainty with Interval Fuzzy Logic Systems through Composite Deep Learning

In this paper, we propose a learning approach for interval Fuzzy Logic Systems (FLSs) to end up with models that are capable to cover an expected amount of uncertainty with a high accuracy by exploiting a composite learning method with quantile regression. Within this paper, we construct two interval FLSs that have a different representation of uncertainty. One of them models the uncertainty in its consequents while the other one within its antecedents that are defined with interval type-2 Fuzzy Sets (FSs). The learning approach uses a multi-objective composite loss that is formed by the mean square error for accuracy purposes along with tilted loss for enforcing the bounds of the FLSs to capture the expected amount of uncertainty. In that way, it is not only possible to learn the FLSs that represent the uncertainty within their MFs (which can be used as prediction intervals) but also to improve the regression performance since the composite loss provides a more complete representation of the data. We present the proposed learning approach alongside parameterization tricks so that they can be trained within the frameworks of deep learning while not violating the definitions of FSs. We present comparative results on benchmark datasets that have different characteristics.