Special Issue "Fuzzy Transforms and Their Applications"

A special issue of Axioms (ISSN 2075-1680).

Deadline for manuscript submissions: 30 October 2019.

Special Issue Editors

Guest Editor
Prof. Dr. Ferdinando Di Martino

Dipartimento di Architettura, Università degli Studi di Napoli Federico II, via Toledo 402, 80134 Napoli, Italy
Website | E-Mail
Interests: fuzzy logic; soft computing; image analysis; geographical information system
Guest Editor
Prof. Dr. Irina Perfilieva

University of Ostrava, Centre of Excellence IT4Innovations, Institute for Research and Applications of Fuzzy Modeling, 30. dubna 22, 701 03 Ostrava 1, Czech Republic
Website | E-Mail
Interests: fuzzy transform; fuzzy topology; image processing; computer graphics
Guest Editor
Prof. Dr. Salvatore Sessa

Dipartimento di Architettura, Università degli Studi di Napoli Federico II, via Toledo 402, 80134 Napoli, Italy
Website 1 | Website 2 | E-Mail
Phone: 390812538907
Interests: fuzzy sets and fuzzy relations; soft computing; fuzzy transform image processing theory; machine learning; data mining

Special Issue Information

Dear Colleagues,

We propose to launch a new Special Issue of Axioms. The main topic is focused on “Fuzzy Transforms”. With this Special Issue, we aim to provide contributing authors an opportunity to present their recent results in the mathematical theory of Fuzzy Transforms with applications to various fields, such as signal processing, image processing, machine learning, and data analysis. Among the topics that this Special Issue will address, we consider the following non-exhaustive list:

Multidimensional Fuzzy Transform, higher order Fuzzy Transform, Fuzzy transforms applied in coding/decoding signals, images and videos, Fuzzy Transforms methods in image reduction, image fusion, image segmentation, image tamper detection, Fuzzy Transforms-based models for data classification,  forecasting, data mining, and Fuzzy Transforms in massive data knowledge extraction.

In addition, this Special Issue is open to discussing new ideas, apart from the aforementioned topics.

If this initiative meets your interests, we solicit you to send your contributions to be included in this Special Issue.

Prof. Dr. Ferdinando Di Martino
Prof. Dr. Irina Perfilieva
Prof. Dr. Salvatore Sessa
Guest Editors

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All papers will be peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Axioms is an international peer-reviewed open access quarterly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 1000 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • Direct and inverse Fuzzy Transform
  • Discrete Fuzzy Transform
  • Multidimensional Fuzzy Transform
  • High order Fuzzy Transform
  • Fuzzy Transform applications

Published Papers (2 papers)

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Research

Open AccessArticle
Why Triangular Membership Functions Are Successfully Used in F-Transform Applications: A Global Explanation to Supplement the Existing Local Ones
Received: 22 April 2019 / Revised: 1 August 2019 / Accepted: 2 August 2019 / Published: 5 August 2019
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Abstract
The main ideas of F-transform came from representing expert rules. It would be therefore reasonable to expect that the more accurately the membership functions describe human reasoning, the more successful will be the corresponding F-transform formulas. We know that an adequate description of [...] Read more.
The main ideas of F-transform came from representing expert rules. It would be therefore reasonable to expect that the more accurately the membership functions describe human reasoning, the more successful will be the corresponding F-transform formulas. We know that an adequate description of our reasoning corresponds to complicated membership functions—however, somewhat surprisingly, many successful applications of F-transform use the simplest possible triangular membership functions. There exist some explanations for this phenomenon, which are based on local behavior of the signal. In this paper, we supplement these local explanations by a global one: namely, we prove that triangular membership functions are the only one that provide the exact reconstruction of the appropriate global characteristic of the signal. Full article
(This article belongs to the Special Issue Fuzzy Transforms and Their Applications)
Open AccessArticle
Why Use a Fuzzy Partition in F-Transform?
Received: 21 April 2019 / Revised: 31 July 2019 / Accepted: 1 August 2019 / Published: 2 August 2019
PDF Full-text (252 KB) | HTML Full-text | XML Full-text
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 a weighted average can be naturally explained, e.g., by the fact that this is [...] Read more.
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. Full article
(This article belongs to the Special Issue Fuzzy Transforms and Their Applications)
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