Why use a fuzzy partition in F-transform?

© 2019 by the authors. In many application problems, F-transform algorithms are very efficient. In F-transform techniques, we replace the original signal or image with a finite number of weighted averages. The use of a weighted average can be naturally explained, e.g., by the fact that this is what...

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Main Authors: Vladik Kreinovich, Olga Kosheleva, Songsak Sriboonchitta
Format: Journal
Published: 2019
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http://cmuir.cmu.ac.th/jspui/handle/6653943832/66702
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Institution: Chiang Mai University
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spelling th-cmuir.6653943832-667022019-09-16T12:55:41Z Why use a fuzzy partition in F-transform? Vladik Kreinovich Olga Kosheleva Songsak Sriboonchitta Mathematics © 2019 by the authors. In many application problems, F-transform algorithms are very efficient. In F-transform techniques, we replace the original signal or image with a finite number of weighted averages. The use of a weighted average can be naturally explained, e.g., by the fact that this is what we get anyway when we measure the signal. However, most successful applications of F-transform have an additional not-so-easy-to-explain feature: the fuzzy partition requirement that the sum of all the related weighting functions is a constant. In this paper, we show that this seemingly difficult-to-explain requirement can also be naturally explained in signal-measurement terms: namely, this requirement can be derived from the natural desire to have all the signal values at different moments of time estimated with the same accuracy. This explanation is the main contribution of this paper. 2019-09-16T12:55:41Z 2019-09-16T12:55:41Z 2019-01-01 Journal 20751680 2-s2.0-85071379679 10.3390/axioms8030094 https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=85071379679&origin=inward http://cmuir.cmu.ac.th/jspui/handle/6653943832/66702
institution Chiang Mai University
building Chiang Mai University Library
country Thailand
collection CMU Intellectual Repository
topic Mathematics
spellingShingle Mathematics
Vladik Kreinovich
Olga Kosheleva
Songsak Sriboonchitta
Why use a fuzzy partition in F-transform?
description © 2019 by the authors. In many application problems, F-transform algorithms are very efficient. In F-transform techniques, we replace the original signal or image with a finite number of weighted averages. The use of a weighted average can be naturally explained, e.g., by the fact that this is what we get anyway when we measure the signal. However, most successful applications of F-transform have an additional not-so-easy-to-explain feature: the fuzzy partition requirement that the sum of all the related weighting functions is a constant. In this paper, we show that this seemingly difficult-to-explain requirement can also be naturally explained in signal-measurement terms: namely, this requirement can be derived from the natural desire to have all the signal values at different moments of time estimated with the same accuracy. This explanation is the main contribution of this paper.
format Journal
author Vladik Kreinovich
Olga Kosheleva
Songsak Sriboonchitta
author_facet Vladik Kreinovich
Olga Kosheleva
Songsak Sriboonchitta
author_sort Vladik Kreinovich
title Why use a fuzzy partition in F-transform?
title_short Why use a fuzzy partition in F-transform?
title_full Why use a fuzzy partition in F-transform?
title_fullStr Why use a fuzzy partition in F-transform?
title_full_unstemmed Why use a fuzzy partition in F-transform?
title_sort why use a fuzzy partition in f-transform?
publishDate 2019
url https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=85071379679&origin=inward
http://cmuir.cmu.ac.th/jspui/handle/6653943832/66702
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