Attribute Weighted Fuzzy Interpolative Reasoning

  • Fangyi Li

Student thesis: Doctoral ThesisDoctor of Philosophy


Approximate reasoning systems facilitate fuzzy inference through manipulating fuzzy if-then rules. Fuzzy rule interpolation (FRI) supports such reasoning with sparse rule bases where certain observations may not match any existing fuzzy rules. While offering a potentially powerful inference mechanism, in the current literature, it is typically assumed that all antecedent 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. Recently, interesting techniques have been reported for achieving weighted interpolative reasoning. However, they either employ attribute weights that are obtained using additional information (rather than just the given rules) or fail to enable the individual attribute weights to be integrated systematically with the corresponding FRI procedures. To devise a weighted interpolative reasoning that works effectively and efficiently, two major concerns need to be addressed. First, how the rule antecedent weights can be generated automatically and efficiently, without requiring further observations or triggering the entire unweighted FRI system. Second, how the generated weights may be integrated within any unweighted FRI mechanism. A further associated issue is how a weighted FRI method may be transplanted to another underlying FRI where no individual attribute weight is involved once the weights of rule antecedents are available. This thesis proposes a weighted fuzzy interpolative reasoning mechanism, leading to novel FRI approaches that significantly reinforce the power of approximate reasoning. It works by exploiting attribute ranking techniques to help determine the relative importance of rule antecedent attributes involved in a sparse rule base. In particular, the proposed approach employs feature selection (FS) techniques to adjudge the relative significance of individual attributes and therefore, in order to differentiate the contributions of the rule antecedents and their impacts on 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 weights are computed using a set of training samples that are artificially created from the rule base through an innovative reverse engineering procedure. This weight generation procedure is general as it allows for any established ranking method to be utilised to score the attributes without adversely affecting the interpolative inference accuracy. Given the generated weights of rule antecedent attributes, this thesis further presents three FRI approaches, each based on different type of fuzzy interpolative reasoning technique, for systematically integrating the weights within the FRI procedure. Such a weighted approach integrates the learned weights explicitly with all computational steps of the interpolation process. The implementation of each weighted FRI mechanism is of generality as it is achieved independently of the weight generation method. Thus, the underlying generic techniques can be extended to supporting any other FRI which involves multiple rule antecedents which are not assigned with individual weights. The proposed weighted FRI approaches have been statistically evaluated through a range of experimentations against various benchmark datasets. The results are reported in this thesis, demonstrating the superior and robust performance of the weighted methods over their originals (where the rule antecedent attributes are of equal significance). A specific and important outcome that is supported by attribute ranking is that only two (i.e., the least number of) nearest neighbouring rules are required to perform accurate interpolative reasoning. This avoids the need of both searching for and computing with multiple rules beyond the immediate neighbourhood of a given observation, thereby significantly enhancing computational efficiency. The proposed weight generation and weighted FRI mechanisms are integrated with the standard compositional rule of inference to develop application systems to perform real-world pattern recognition tasks, including classification and prediction (which in turn, involves both multivariate regression and time series prediction). Particularly, the thesis reports on a novel fuzzy rule-based diagnostic system for mammographic mass classification. This system is able not only to derive a conclusion for unknown observed masses that have no rules to match, but also to produce the diagnostic outcomes that are interpretable, thanks to the semantics-rich fuzzy rules with attribute values represented in linguistic terms. The success in all such realistic applications demonstrates the practicality of the proposed techniques for attribute weighted fuzzy interpolative reasoning.
Date of Award2020
Original languageEnglish
Awarding Institution
  • Aberystwyth University
SupervisorQiang Shen (Supervisor) & Changjing Shang (Supervisor)

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