Preprint Article Version 1 This version is not peer-reviewed

Why Fuzzy Partition in F-Transform?

Version 1 : Received: 21 April 2019 / Approved: 23 April 2019 / Online: 23 April 2019 (13:02:27 CEST)

A peer-reviewed article of this Preprint also exists.

Kreinovich, V.; Kosheleva, O.; Sriboonchitta, S. Why Use a Fuzzy Partition in F-Transform? Axioms 2019, 8, 94. Kreinovich, V.; Kosheleva, O.; Sriboonchitta, S. Why Use a Fuzzy Partition in F-Transform? Axioms 2019, 8, 94.

Journal reference: Axioms 2019, 8, 94
DOI: 10.3390/axioms8030094

Abstract

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 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 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-measuring 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.

Subject Areas

F-transform; fuzzy partition; measurements; measurementuncertainty

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