More Than Accuracy: A Composite Learning Framework for Interval Type-2 Fuzzy Logic Systems

In this article, we propose a novel composite learning framework for interval type-2 (IT2) fuzzy logic systems (FLSs) to train regression models with a high accuracy performance and capable of representing uncertainty. In this context, we identify three challenges, first, the uncertainty handling capability, second, the construction of the composite loss, and third, a learning algorithm that overcomes the training complexity while taking into account the definitions of IT2-FLSs. This article presents a systematic solution to these problems by exploiting the type-reduced set of IT2-FLS via fusing quantile regression and deep learning (DL) with IT2-FLS. The uncertainty processing capability of IT2-FLS depends on employed center-of-sets calculation methods, while its representation capability is defined via the structure of its antecedent and consequent membership functions. Thus, we present various parametric IT2-FLSs and define the learnable parameters of all IT2-FLSs alongside their constraints to be satisfied during training. To construct the loss function, we define a multiobjective loss and then convert it into a constrained composite loss composed of the log-cosh loss for accuracy purposes and a tilted loss for uncertainty representation, which explicitly uses the type-reduced set. We also present a DL approach to train IT2-FLS via unconstrained optimizers. In this context, we present parameterization tricks for converting the constraint optimization problem of IT2-FLSs into an unconstrained one without violating the definitions of fuzzy sets. Finally, we provide comprehensive comparative results for hyperparameter sensitivity analysis and an inter/intramodel comparison on various benchmark datasets.

Automated summary

In this article, a novel composite learning framework for interval type-2 (IT2) fuzzy logic systems (FLSs) is proposed to train regression models with high accuracy performance and uncertainty representation. The challenges of uncertainty handling capability, construction of composite loss, and learning algorithm complexity for IT2-FLSs are addressed. The proposed solution combines quantile regression and deep learning with IT2-FLS to exploit the type-reduced set and provides various parametric IT2-FLSs with defined learnable parameters and constraints. The article also presents a DL approach for training IT2-FLS using unconstrained optimizers and provides comprehensive comparative results for hyperparameter sensitivity analysis and inter/intramodel comparison on benchmark datasets.