A Specificity-Based Approach to Semantic Interpretation and Hierarchical Complexity Reduction in Fuzzy Models

The existing approaches to interpretability in data-driven fuzzy models are reliant, heavily, on constraining different components of the model, and subsequently on sophisticated learning methods. This article, however, puts forward an alternative view of the interpretability of fuzzy models based on the concept of specificity. In addition to being free of constraints, this view can effectively deal with the subjectivity inherent in the linguistic interpretation of fuzzy sets and rules rather than suppressing it, as the constraint-based approaches do. Second to this semantic improvement, a specificity-based hierarchical fuzzy structure is also proposed to deal with the complexity-based aspect of interpretability. It achieves this purpose by means of a two-level hierarchy, in which a number of general rules at the first level localize both the inference and learning processes of the second level to a small number of relevant, specific rules. Such a localization, besides employment of the recursive least squares algorithm for parameter learning, reduces the computational burden of the model significantly, making it capable of real-time operation. The experimental results of applying the proposed fuzzy modeling approach to a variety of synthetic and real-world datasets confirm its efficacy in the sense of interpretability, accuracy, and computational simplicity.