Transformation-Based Fuzzy Rule Interpolation With Mahalanobis Distance Measures Supported by Choquet Integral

Mou Zhou, Changjing Shang, Guobin Li, Liang Shen, Nitin Naik, Shangzhu Jin, Jun Peng, Qiang Shen

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Abstract

Fuzzy rule interpolation (FRI) strongly supports approximate inference when a new observation matches no rules, through selecting and subsequently interpolating appropriate rules close to the observation from the given (sparse) rule base. Traditional ways of implementing the critical rule selection process are typically based on the exploitation of Euclidean distances between the observation and rules. It is conceptually straightforward for implementation but applying this distance metric may systematically lead to inferior results because it fails to reflect the variations of the relevance or significance levels among different domain features. To address this important issue, a novel transformation-based FRI approach is presented, on the basis of utilizing the Mahalanobis distance metric. The new FRI method works by transforming a given sparse rule base into a coordinates system where the distance between instances of the same category becomes closer while that between different categories becomes further apart. In so doing, when an observation is present that matches no rules, the most relevant neighboring rules to implement the required interpolation are more likely to be selected. Following this, the scale and move factors within the classical transformation-based FRI procedure are also modified by Choquet integral. Systematic experimental investigation over a range of classification problems demonstrates that the proposed approach remarkably outperforms the existing state-of-the-art FRI methods in both accuracy and efficiency.

Original languageEnglish
Pages (from-to)1083-1097
Number of pages15
JournalIEEE Transactions on Fuzzy Systems
Volume31
Issue number4
Early online date29 Jul 2022
DOIs
Publication statusPublished - 01 Apr 2023

Keywords

  • Approximate inference
  • choquet integral
  • choquet integral approximate inference
  • Cognition
  • Euclidean distance
  • fuzzy rule interpolation
  • Fuzzy sets
  • Interpolation
  • mahalanobis distance
  • Measurement
  • Shape
  • Systematics
  • transformation -based FRI,
  • transformation -based FRI.
  • Choquet integral
  • transformation-based FRI
  • Mahalanobis distance
  • Artificial Intelligence
  • Control and Systems Engineering
  • Computational Theory and Mathematics
  • Applied Mathematics

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