Comparison and design of interpretable linguistic vs. scatter FRBSs: Gm3m generalization and new rule meaning index for global assessment and local pseudo-linguistic representation

Abstract

This work is devoted to defining more general interpretability indexes to be applied to any scatter or linguistic model implemented by any type of membership functions. They are based on metrics that should take into account the semantic and inference issues: the semantic issue in order to preserve the meaning of the linguistic labels and the inference issue since this can influence the behavior of the rules. On the other hand, these metrics have been designed to be intuitive in order to support the analysis or selection of a final model and to favor a low computational cost within an optimization process. In order to check their usefulness, a multi-objective evolutionary algorithm, simultaneously performing a rule selection and an adjustment of the fuzzy partitions, is guided by the proposed indexes on several benchmark data sets to obtain models with different degrees of accuracy and interpretability. In addition, using these metrics, a local analysis can be carried out between models of a different nature. This local analysis through the model components, gives support to the user to make the best choice from among the models.