Adaptive Membership Functions and F-Transform

The definition of the fuzzy-transform (F-transform) has been limited mainly to 1-D signals and 2-D data due to the difficulty of defining membership functions, their centres, and support on a domain with arbitrary dimensionality and topology. We propose a novel method for the adaptive selection of t...

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Bibliographic Details
Published in:IEEE transactions on fuzzy systems 2024-05, Vol.32 (5), p.2786-2796
Main Authors: Cammarasana, Simone, Patane, Giuseppe
Format: Article
Language:English
Subjects:
Adaptive systems
Computational efficiency
Continuity (mathematics)
Convolution
Data analysis
data-driven membership functions
Fuzzy systems
fuzzy-transform (F-transform)
Image reconstruction
Kernel
Minimization
radial basis functions
signal approximation
Topology
Weighted sum model
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Summary:The definition of the fuzzy-transform (F-transform) has been limited mainly to 1-D signals and 2-D data due to the difficulty of defining membership functions, their centres, and support on a domain with arbitrary dimensionality and topology. We propose a novel method for the adaptive selection of the optimal centres and supports of a class of radial membership functions based on minimizing the reconstruction error of the input signal as the F-transform and its inverse, or as a weighted linear combination of the membership functions. Replacing uniformly sampled centres of the membership functions with adaptive centres and fixed supports with adaptive supports allows us to preserve the input signal's local and global features and achieve a good approximation accuracy with fewer membership functions. We compare our method with uniform sampling and previous work. As a result, we improve the image reconstruction with respect to compared methods and we reduce the underlying computational cost and storage overhead. Finally, our approach applies to any class of continuous membership functions.
ISSN:1063-6706
1941-0034
DOI:10.1109/TFUZZ.2024.3360633