Fuzzy Rule Interpolation with a Transformed Rule Base

Traditional fuzzy rule interpolation (FRI) methods typically utilise Euclidean distances between an observation and the rules in a given sparse rule base to select a set of rules closest to the observation to perform interpolation. However, simply applying the Euclidean distance metric may frequently lead to inferior results, because it cannot take into consideration the relevance degree of different features. To address this important issue, this paper presents an initial framework for a novel FRI approach which works based on exploiting a transformed rule base. Mahalanobis matrix learned by metric learning methods is used herein to transform the given sparse rule base to a new coordinates system where the distance between instances of the same category is closer, and instances of different categories is distant from each other. When a new observation is present which matches no rules, the selection of the nearest rules to implement the required interpolation is carried out in the transformed coordinates system. Then, the scale and move factors within the classical transformation-based FRI procedure are modified by Choquet integral. Experimental results obtained by employing different metric learning methods and Choquet integral over seven classification problems demonstrate that the proposed approach remarkably outperforms existing FRI methods.