A hybrid adaptive granular approach to Takagi–Sugeno–Kang fuzzy rule discovery

• Published in: Applied soft computing 2019-08, Vol.81, p.105491, Article 105491
• Main Authors: Bemani-N., Alireza, Akbarzadeh-T., M.-R.
• Format: Article
• Language: English
• Subjects: Data preprocessing; Granulation; Interpretability; Knowledge discovery; Takagi–Sugeno–Kang fuzzy models
• ISSN: 1568-4946; 1872-9681
• DOI: 10.1016/j.asoc.2019.105491

In this paper, a hybrid adaptive granular fuzzy approach to rule discovery (HGFRD) is proposed that effectively utilizes the advantages of Mamdani and Takagi–Sugeno–Kang (TSK) fuzzy structures in a unique learning process, resulting in more compactness and better accuracy of the extracted TSK models. HGFRD’s primary adaptive granulation process, based on a Mamdani fuzzy structure, provides better generalization, more compactness, and a reasonable initial solution for the secondary optimization stage. On the other hand, the algorithm’s fine-tuning procedure is constructed of a TSK structure, offering lower process burden, universal approximation property, and the chance of using more effective optimization methods, leading to better model accuracy. The proposed process is independent of any a priori expert knowledge since it is purely data-driven and avoids initial parameter tuning. It also functions more desirably on a broader range of problem types and structures due to its adaptive behavior over normalized data spaces. Moreover, it is theoretically proven that HGFRD’s training error converges to zero in certain situations. Finally, the effect of several data preprocessing techniques such as normalization, feature selection, and outlier detection is investigated to improve HGFRD’s performance. To illustrate the utility of the proposed algorithm, it is applied to ten standard benchmarks, and the results are compared against twenty-two recent competing strategies. Numerical results confirm that HGFRD reaches higher model accuracy and more compactness simultaneously. •A Mamdani-TSK 2-stage adaptive granular approach is proposed for fuzzy rule discovery.•The Mamdani-based initial granulation leads to more compactness, while the TSK-based fine tuning leads to better accuracy.•Data normalization, feature selection and outlier detection improve the learning process.•The overall knowledge discovery process leads to simpler but more accurate fuzzy rules.•Theoretical analysis proves the algorithm’s convergence for the training error.•Performance is improved on most benchmarks when compared with 21 recent strategies.