학술논문

Transformation-Based Fuzzy Rule Interpolation With Mahalanobis Distance Measures Supported by Choquet Integral
Document Type
Periodical
Source
IEEE Transactions on Fuzzy Systems IEEE Trans. Fuzzy Syst. Fuzzy Systems, IEEE Transactions on. 31(4):1083-1097 Apr, 2023
Subject
Computing and Processing
Measurement
Interpolation
Cognition
Fuzzy sets
Systematics
Shape
Euclidean distance
Approximate inference
Choquet integral
fuzzy rule interpolation
Mahalanobis distance
transformation-based FRI
Language
ISSN
1063-6706
1941-0034
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.