Transparent but Accurate Evolutionary Regression Combining New Linguistic Fuzzy Grammar and a Novel Interpretable Linear Extension

Abstract

Scientists must understand what machines do (systems should not behave like a black box), because in many cases how they predict is more important than what they predict. In this work, we propose a new extension of the fuzzy linguistic grammar and a mainly novel interpretable linear extension for regression problems, together with an enhanced new linguistic tree-based evolutionary multiobjective learning approach. This allows the general behavior of the data covered, as well as their specific variability, to be expressed as a single rule. In order to ensure the highest transparency and accuracy values, this learning process maximizes two widely accepted semantic metrics and also minimizes both the number of rules and the model mean squared error. The results obtained in 23 regression datasets show the effectiveness of the proposed method by applying statistical tests to the said metrics, which cover the different aspects of the interpretability of linguistic fuzzy models. This learning process has obtained the preservation of high-level semantics and less than 5 rules on average, while it still clearly outperforms some of the previous state-of-the-art linguistic fuzzy regression methods for learning interpretable regression linguistic fuzzy systems, and even to a competitive, pure accuracy-oriented linguistic learning approach. Finally, we analyze a case study in a real problem related to childhood obesity, and a real expert carries out the analysis shown.