Fuzzy Rule Based Interpolative Reasoning Supported by Attribute Ranking

Abstract

Q. (2018). Fuzzy rule-based interpolative reasoning supported by attribute ranking. IEEE Transactions on Fuzzy Systems, (99). https://doi.This work is licensed under a Creative Commons Attribution 3.0 License. For more information, see Abstract-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.

Interpolation With Just Two Nearest Neighboring Weighted Fuzzy Rules

“…Most recently, a weighted interpolative reasoning scheme has been reported [7], where the weights of individual antecedent attributes are learned from the given knowledge (i.e., the sparse rule base) in support of attribute ranking. Such weights are explicitly integrated with the procedures of the popular scale and move transformation-based FRI (T-FRI) [3].…”

“…Given this exciting empirical outcome for weighted T-FRI, it is interesting to investigate whether the discovery that "least number of neighbouring rules does better" is common to other FRI methods if a similar weighting scheme is adopted. Fortunately, the weights learning mechanism as proposed in [7] is independent of the FRI process, which works by exploiting the sparse rule base only. Inspired by this observation, this short paper presents a further development that enhances two other commonly used FRI algorithms (namely, those first presented in [1] and [4]), by following the ideas of [7].…”

“…Fortunately, the weights learning mechanism as proposed in [7] is independent of the FRI process, which works by exploiting the sparse rule base only. Inspired by this observation, this short paper presents a further development that enhances two other commonly used FRI algorithms (namely, those first presented in [1] and [4]), by following the ideas of [7]. The resultant weighted FRI methods are systematically evaluated via addressing ten benchmark classification problems, in comparison with their corresponding unweighted originals.…”

“…The rest of this paper is structured as follows. Section II reviews the relevant background, including the weighted T-FRI as proposed in [7] and the two selected representative FRI methods to be enhanced with the weighting approach. Section III presents the modification of those two FRI methods with the use of attribute weights.…”

“…For completion, this section first shows the basic notations used throughout the paper, followed by a summary of the weighted T-FRI method as proposed in [7] and then, by an overview of the two representative FRI methods that will be extended with the inclusion of attribute weights.…”