Deep Takagi–Sugeno–Kang Fuzzy Classifier With Shared Linguistic Fuzzy Rules

In many practical applications of classifiers, not only high accuracy but also high interpretability is required. Among a wide variety of existing classifiers, Takagi–Sugeno–Kang (TSK) fuzzy classifiers may be one of the best choices for achieving a good balance between interpretability and accuracy. In order to further improve their accuracy without losing their interpretability, we propose a highly interpretable deep TSK fuzzy classifier HID-TSK-FC (deep shared-linguistic-rule-based TSK fuzzy classifier) based on the concept of shared linguistic fuzzy rules. The proposed classifier has two characteristics: One is a stacked hierarchical structure of component TSK fuzzy classifiers for high accuracy, and the other is the use of interpretable linguistic rules with the same set of linguistic labels for all inputs. High interpretability is achieved at each layer by using the same set of linguistic values for all inputs, including the outputs from the previous layers in the stacked hierarchical structure. We show that a linguistic rule with the outputs from the previous layers as its inputs is equivalent to a fuzzy rule with a nonlinear consequent or a linear consequent with a certainty factor. We also show that HID-TSK-FC is mathematically equivalent to a novel TSK fuzzy classifier with shared interpretable linguistic fuzzy rules. Promising performance of HID-TSK-FC is demonstrated through extensive computational experiments on benchmark datasets and a real-world application case.