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High-order Takagi-Sugeno-Kang (TSK) fuzzy classifiers possess powerfulclassification performance yet have fewer fuzzy rules, but always be impairedby its exponential growth training time and poorer interpretability owing toHigh-order polynomial used in consequent part of fuzzy rule, while Low-orderTSK fuzzy classifiers run quickly with high interpretability, however theyusually require more fuzzy rules and perform relatively not very well. Addressthis issue, a novel TSK fuzzy classifier embeded with knowledge distillation indeep learning called HTSK-LLM-DKD is proposed in this study. HTSK-LLM-DKDachieves the following distinctive characteristics: 1) It takes High-order TSKclassifier as teacher model and Low-order TSK fuzzy classifier as studentmodel, and leverages the proposed LLM-DKD (Least Learning Machine basedDecoupling Knowledge Distillation) to distill the fuzzy dark knowledge fromHigh-order TSK fuzzy classifier to Low-order TSK fuzzy classifier, whichresulting in Low-order TSK fuzzy classifier endowed with enhanced performancesurpassing or at least comparable to High-order TSK classifier, as well as highinterpretability; specifically 2) The Negative Euclidean distance between theoutput of teacher model and each class is employed to obtain the teacherlogits, and then it compute teacher/student soft labels by the softmax functionwith distillating temperature parameter; 3) By reformulating theKullback-Leibler divergence, it decouples fuzzy dark knowledge into targetclass knowledge and non-target class knowledge, and transfers them to studentmodel. The advantages of HTSK-LLM-DKD are verified on the benchmarking UCIdatasets and a real dataset Cleveland heart disease, in terms of classificationperformance and model interpretability.

Fuzzy Knowledge Distillation from High-Order TSK to Low-Order TSK