Affiliations: [a] School of Medical Informatics, Nantong University, Nantong, China
| [b] School of Digital Media, Jiangnan University, Wuxi, China
| [c] Department of Computing, Hong Kong Polytechnic University, Hong Kong
Correspondence:
[*]
Corresponding author. Shitong Wang, School of Digital Media, Jiangnan University, Wuxi 214122, China. E-mail: wxwangst@yahoo.com.
Abstract: Fuzzy rules are very important in Takagi-Sugeno-Kang (TSK) fuzzy systems as they not only provide a mapping mechanism for input patterns but also make fuzzy systems interpretable. Current works further introduce rule weights to restrict/strengthen fuzzy rules for more situations. However, most of the embedded rule weights in fuzzy rules are static. In other words, the rule weights keep unchanged once they have been determined by the learning algorithms. In practical applications, it is often expected that each fuzzy rule should deduce different confidence degrees with respect to different input patterns. In this paper, a new TSK fuzzy system is proposed, in which each fuzzy rule is empowered by an individual dynamic rule weight (DRW). DRW is basically a nonlinear function of the input pattern to reflect the confidence degree (acceptability) the fuzzy rule acting on the input pattern. Furthermore, for an input pattern, its “isolation” level can be measured by the aggregated DRW values of the fuzzy rules in the proposed fuzzy system. Specifically, the proposed fuzzy system can be used to identify outliers whose aggregated DRW values of all fuzzy rules are very small. In order to effectively embed DRW to each fuzzy rule, an analogous stacked structure consisting of a basic input-output unit and an augmenting unit is proposed. The stacked architecture is characterized by three features: (i) the augmented information from the augmenting unit can provide indirect pattern information for DRW learning; (ii) the predictive information from the augmenting unit can be differentiated from the interpretability of fuzzy rules; and (iii) the modeling performance can be improved by the stacked generalization principle which leverages the predictive information in the manifold of the input pattern space in the system approximation process. Experimental results on 16 real-life datasets demonstrate the approximation accuracy, interpretability and outlier detection ability of the proposed fuzzy system.
