Multi-objective based Fuzzy Rule Based Systems (FRBSs) for trade-off improvement in accuracy and interpretability

Fuzzy rule-based systems (FRBSs) are a common alternative for applying fuzzy logic in different areas and real-world problems. The schemes and algorithms used to generate these types of systems imply that their performance can be analyzed from different points of view, not only model accuracy. Any model, including fuzzy models, needs to be sufficiently accurate, but other perspectives, such as interpretability, are also possible for the FRBSs. Thus, the Accuracy-Interpretability trade-off arises as a challenge for fuzzy systems, as approaches are currently able to generate FRBSs with different trade-offs.Here, rule Relevance is added to Accuracy and Interpretability for a better trade-off in FRBSs. These three factors are involved in this approach to make a rule selection using a multi-objective evolutionary algorithm.The proposal has been tested and compared with nine datasets, two linguistic and two scatter fuzzy algorithms, four measures of interpretability and two rule relevance formulations. The results have been analyzed for different views of Interpretability, Accuracy and Relevance, and the statistical tests have shown that significant improvements have been achieved. On the other hand, the Relevance-based role of fuzzy rules has been checked, and it has been shown that low Relevance rules have a relevant role for trade-off, while some rules with high Relevance must sometimes be removed to reach an adequate trade-off.