A framework for learning fuzzy rule-based models with epistemic set-valued data and generalized loss functions

A framework is proposed for learning fuzzy rule-based systems from low quality data where the differences between observed and true values may introduce systematic bias in the model. It is argued that there are problems where aggregating imprecise losses into numerical or fuzzy-valued risk functions discards useful information, thus generalizing the risk of a model to a vector of fuzzy losses is preferred. The principles governing a learner that is capable of optimizing these fuzzy multivariate risk functions are discussed. Illustrative use cases are worked to exemplify those situations where new framework could become the alternative of choice.