Fuzzy Rule Based Interpolative Reasoning Supported by Attribute Ranking

Using fuzzy rule interpolation (FRI) interpolative reasoning can be effectively performed with a sparse rule base where a given system observation does not match any fuzzy rules. Whilst offering a potentially powerful inference mechanism, in the current literature, typical representation of fuzzy rules in FRI assumes that all attributes in the rules are of equal significance in deriving the consequents. This is a strong assumption in practical applications, thereby often leading to less accurate interpolated results. To address this challenging problem, this work employs feature selection (FS) techniques to adjudge the relative significance of individual attributes and therefore, to differentiate the contributions of the rule antecedents and their impact upon FRI. This is feasible because FS provides a readily adaptable mechanism for evaluating and ranking attributes, being capable of selecting more informative features. Without requiring any acquisition of real observations, based on the originally given sparse rule base, the individual scores are computed using a set of training samples that are artificially created from the rule base through an innovative reverse engineering procedure. The attribute scores are integrated within the popular scale and move transformation-based FRI algorithm (while other FRI approaches may be similarly extended following the same idea), forming a novel method for attribute ranking-supported fuzzy interpolative reasoning. The efficacy and robustness of the proposed approach is verified through systematic experimental examinations in comparison with the original FRI technique, over a range of benchmark classification problems while utilising different FS methods. A specific and important outcome is that supported by attribute ranking, only two (i.e., the least number of) nearest adjacent rules are required to perform accurate interpolative reasoning, avoiding the need of searching for and computing with multiple rules beyond the immediate neighbourhood of a given observation.