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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Vydané v:	IEEE transactions on fuzzy systems Ročník 32; číslo 5; s. 2786 - 2796
Hlavní autori:	Cammarasana, Simone, Patane, Giuseppe
Médium:	Journal Article
Jazyk:	English
Vydavateľské údaje:	New York IEEE 01.05.2024 The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Predmet:	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
ISSN:	1063-6706, 1941-0034
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Abstract	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.
AbstractList	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.
Author	Cammarasana, Simone Patane, Giuseppe
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SubjectTerms	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
Title	Adaptive Membership Functions and F-Transform
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