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Axioms
Special Issues
Fuzzy Transforms and Their Applications II
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Fuzzy Transforms and Their Applications II

A special issue of Axioms (ISSN 2075-1680). This special issue belongs to the section "Logic".

Deadline for manuscript submissions: closed (30 November 2023) | Viewed by 5634

Special Issue Editors

Prof. Dr. Ferdinando Di Martino

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Dipartimento di Architettura, Università degli Studi di Napoli Federico II, Via Toledo 402, 80134 Napoli, Italy
Interests: fuzzy sets and fuzzy relations; soft computing; fuzzy transform image processing theory; machine learning; data mining
Special Issues, Collections and Topics in MDPI journals
Prof. Dr. Irina Perfilieva

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Centre of Excellence IT4Innovations, Institute for Research and Applications of Fuzzy Modeling, University of Ostrava, 30. dubna 22, 701 03 Ostrava, Czech Republic
Interests: fuzzy transform; fuzzy topology; image processing; computer graphics
Special Issues, Collections and Topics in MDPI journals
Prof. Dr. Salvatore Sessa

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Guest Editor
Department of Architecture, Federico II Naples University, Via Toledo 402, 80134 Naples, Italy
Interests: fixed point theory in metric spaces; fuzzy clustering algorithms; fuzzy relations and their fuzzy calculus; fuzzy relation equations; fuzzy relational systems
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

It is our pleasure to announce the launch of the second edition of our Special Issue focusing on "Fuzzy Transform". With this Special Issue, we aim to offer contributing authors the opportunity to present their recent results on fuzzy-transform-based methods and techniques applied in various fields, considering the rapid development of computational intelligence models applied in data science. Among the topics that this new Special Issue dedicated to fuzzy transforms will address, we consider the following non-exhaustive list:

  • Multidimensional and high-order fuzzy transform applied in signal analysis;
  • Multidimensional and high-order fuzzy transform applied in image and video processing;
  • Machine learning hybrid models based on fuzzy transform;
  • Multidimensional fuzzy transform applied to time series analysis;
  • Fuzzy transform methods for regression analysis;
  • Knowledge extraction models based on fuzzy transform;
  • Fuzzy transform methods applied for the analysis of massive data;
  • Mathematical correlations of fuzzy transform with classical theories;
  • Numerical methods for solving integrodifferential equations based on a high-order fuzzy transform;
  • High-order fuzzy transform with trigonometric components.

Moreover, this Special Issue is open to the discussion of new ideas, in addition to the aforementioned topics.

If this initiative suits your interests, please submit 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 submissions that pass pre-check are 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 monthly 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 2400 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 (4 papers)

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Research

17 pages, 1018 KiB  
Article
Intelligent Task Planning System Based on Methods of Fuzzy Natural Logic
by Bogdan Walek and Vilém Novák
Axioms 2023, 12(6), 545; https://0-doi-org.brum.beds.ac.uk/10.3390/axioms12060545 - 31 May 2023
Viewed by 890
Abstract
In this paper, we present a novel approach to task planning based on an intelligent expert system that makes it possible to obtain a conclusion based on linguistically characterized knowledge. The main goal of the proposed task planning system is to arrange and [...] Read more.
In this paper, we present a novel approach to task planning based on an intelligent expert system that makes it possible to obtain a conclusion based on linguistically characterized knowledge. The main goal of the proposed task planning system is to arrange and display tasks for the solver in an effective way. Therefore, the system shows the most important tasks first and then the less important ones (in a determined ordering). The solver has a list of tasks arranged according to their importance at each time the task list is displayed. Another goal of the system is to show the effectiveness of all subordinate workers (solvers) for the manager. The expert knowledge contained in the system is characterized by three linguistic descriptions: determination of the task importance, determination of the final task importance, and determination of the efficiency of the task solvers. The system shows the ordered task list in real time. Evaluation of the relative and final importance of the tasks is performed periodically. The system has been implemented as a WEB application and verified on real data set. We also present experimental results of our system. Full article
(This article belongs to the Special Issue Fuzzy Transforms and Their Applications II)
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17 pages, 442 KiB  
Article
A Combination of Fuzzy Techniques and Chow Test to Detect Structural Breaks in Time Series
by Vilém Novák and Thi Thanh Phuong Truong
Axioms 2023, 12(2), 103; https://0-doi-org.brum.beds.ac.uk/10.3390/axioms12020103 - 19 Jan 2023
Cited by 1 | Viewed by 1281
Abstract
In a series of papers, we suggested a non-statistical method for the detection of structural breaks in a time series. It is based on the applications of special fuzzy modeling methods, namely Fuzzy transform (F-transform) and selected methods of Fuzzy Natural Logic (FNL). [...] Read more.
In a series of papers, we suggested a non-statistical method for the detection of structural breaks in a time series. It is based on the applications of special fuzzy modeling methods, namely Fuzzy transform (F-transform) and selected methods of Fuzzy Natural Logic (FNL). In this paper, we combine our method with the principles of the classical Chow test, which is a well-known statistical method for testing the presence of a structural break. The idea is to construct testing statistics similar to that of the Chow test which is formed from components of the first-degree F-transform. These components contain an estimation of the average values of the tangents (slopes) of the time series over an imprecisely specified time interval. In this paper, we illustrate our method and its statistical test on a real-time series and compare it with three classical statistical methods. Full article
(This article belongs to the Special Issue Fuzzy Transforms and Their Applications II)
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13 pages, 1658 KiB  
Article
A Multilevel Fuzzy Transform Method for High Resolution Image Compression
by Ferdinando Di Martino and Salvatore Sessa
Axioms 2022, 11(10), 551; https://0-doi-org.brum.beds.ac.uk/10.3390/axioms11100551 - 13 Oct 2022
Cited by 4 | Viewed by 1361
Abstract
The Multilevel Fuzzy Transform technique (MF-tr) is a hierarchical image compression method based on Fuzzy Transform, which is successfully used to compress images and manage the information loss of the reconstructed image. Unlike other lossy image compression methods, it ensures that the quality [...] Read more.
The Multilevel Fuzzy Transform technique (MF-tr) is a hierarchical image compression method based on Fuzzy Transform, which is successfully used to compress images and manage the information loss of the reconstructed image. Unlike other lossy image compression methods, it ensures that the quality of the reconstructed image is not lower than a prefixed threshold. However, this method is not suitable for compressing massive images due to the high processing times and memory usage. In this paper, we propose a variation of MF-tr for the compression of massive images. The image is divided into tiles, each of which is individually compressed using MF-tr; thereafter, the image is reconstructed by merging the decompressed tiles. Comparative tests performed on remote sensing images show that the proposed method provides better performance than MF-tr in terms of compression rate and CPU time. Moreover, comparison tests show that our method reconstructs the image with CPU times that are at least two times less than those obtained using the MF-tr algorithm. Full article
(This article belongs to the Special Issue Fuzzy Transforms and Their Applications II)
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29 pages, 682 KiB  
Article
Quadrature Rules for the Fm-Transform Polynomial Components
by Irina Perfilieva, Tam Pham and Petr Ferbas
Axioms 2022, 11(10), 501; https://0-doi-org.brum.beds.ac.uk/10.3390/axioms11100501 - 25 Sep 2022
Cited by 2 | Viewed by 1409
Abstract
The purpose of this paper is to reduce the complexity of computing the components of the integral Fm-transform, m≥0, whose analytic expressions include definite integrals. We propose to use nontrivial quadrature rules with nonuniformly distributed integration points instead [...] Read more.
The purpose of this paper is to reduce the complexity of computing the components of the integral Fm-transform, m≥0, whose analytic expressions include definite integrals. We propose to use nontrivial quadrature rules with nonuniformly distributed integration points instead of the widely used Newton–Cotes formulas. As the weight function that determines orthogonality, we choose the generating function of the fuzzy partition associated with the Fm-transform. Taking into account this fact and the fact of exact integration of orthogonal polynomials, we obtain exact analytic expressions for the denominators of the components of the Fm-transformation and their approximate analytic expressions, which include only elementary arithmetic operations. This allows us to effectively estimate the components of the Fm-transformation for 0≤m≤3. As a side result, we obtain a new method of numerical integration, which can be recommended not only for continuous functions, but also for strongly oscillating functions. The advantage of the proposed calculation method is shown by examples. Full article
(This article belongs to the Special Issue Fuzzy Transforms and Their Applications II)
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