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Mathematics
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Fuzzy Systems and Optimization
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Fuzzy Systems and Optimization

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "Mathematics and Computer Science".

Deadline for manuscript submissions: closed (28 February 2022) | Viewed by 8993

Special Issue Editors

Prof. Dr. Martin Gavalec

E-Mail Website
Guest Editor
Department of Information Technologies, University of Hradec Králové, Hradec Králové, Czech Republic
Interests: applied algebra; discrete mathematics; fuzzy set theory; machine learning; artificial intelligence; optimization; discrete events systems
Dr. Daniela Ponce

E-Mail Website
Guest Editor
Department of Information Technologies, University of Hradec Králové, Czech Republic
Interests: knowledge-based technologies; optimization methods; decision making; multiagent systems; web technologies

Special Issue Information

Dear Colleagues,

Fuzzy systems and fuzzy optimization are applied in situations when crisp input values are not available or are not reliable. Important use of fuzzy principles is involved in human control of various mechanical devices, in transport, or in behaviour-prediction of nature phenomenons such as weather or earthquakes. Fuzzy logic also provides important help in support of medical decision making. The medical and healthcare data are often subjective or fuzzy, hence applications in computer-aided diagnosis (CAD) can be used to help physicians in many different aspects within this area. Such aspects are found, for example, in medical image analysis, biomedical signal analysis, segmentation of images or signals, and feature extraction/selection of images or signals.

Fuzzy systems are also useful in optimization of systems working in discrete events (DES). The state-sequence of a DES is described by linear systems in max-min algebra, or in max-T algebra using a t-norm T. The behaviour of a given DES, for example, the robustness, reaching a steady state, or various types of interval fuzzy properties, such as tolerance or universality, are described using fuzzy logic with various t-norm T: Łukasiewicz fuzzy logic (MV-algebras), Gödel fuzzy logic (G-algebras), product fuzzy logic (product algebras) and others.

We invite our colleagues to submit papers related to both the aspects of fuzzy systems and optimization.

Prof. Dr. Martin Gavalec
Dr. Daniela Ponce
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. Mathematics is an international peer-reviewed open access semimonthly 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 2600 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

  • computer-aided diagnosis
  • biomedical signal analysis
  • medical image analysis
  • discrete events system
  • max-min algebra
  • Łukasiewicz fuzzy logic
  • Gödel fuzzy logic
  • product fuzzy logic.

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Published Papers (4 papers)

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Research

13 pages, 276 KiB  
Article
Hyers Stability and Multi-Fuzzy Banach Algebra
by Parvaneh Lo′lo′, Ehsan Movahednia and Manuel De la Sen
Mathematics 2022, 10(1), 106; https://doi.org/10.3390/math10010106 - 29 Dec 2021
Cited by 2 | Viewed by 1412
Abstract
In this paper, we define multi-fuzzy Banach algebra and then prove the stability of involution on multi-fuzzy Banach algebra by fixed point method. That is, if f:A→A is an approximately involution on multi-fuzzy Banach algebra A, then there [...] Read more.
In this paper, we define multi-fuzzy Banach algebra and then prove the stability of involution on multi-fuzzy Banach algebra by fixed point method. That is, if f:A→A is an approximately involution on multi-fuzzy Banach algebra A, then there exists an involution H:A→A which is near to f. In addition, under some conditions on f, the algebra A has multi C*-algebra structure with involution H. Full article
(This article belongs to the Special Issue Fuzzy Systems and Optimization)
11 pages, 2810 KiB  
Article
Contracting and Involutive Negations of Probability Distributions
by Ildar Z. Batyrshin
Mathematics 2021, 9(19), 2389; https://doi.org/10.3390/math9192389 - 25 Sep 2021
Cited by 10 | Viewed by 2174
Abstract
A dozen papers have considered the concept of negation of probability distributions (pd) introduced by Yager. Usually, such negations are generated point-by-point by functions defined on a set of probability values and called here negators. Recently the class of pd-independent linear negators has [...] Read more.
A dozen papers have considered the concept of negation of probability distributions (pd) introduced by Yager. Usually, such negations are generated point-by-point by functions defined on a set of probability values and called here negators. Recently the class of pd-independent linear negators has been introduced and characterized using Yager’s negator. The open problem was how to introduce involutive negators generating involutive negations of pd. To solve this problem, we extend the concepts of contracting and involutive negations studied in fuzzy logic on probability distributions. First, we prove that the sequence of multiple negations of pd generated by a linear negator converges to the uniform distribution with maximal entropy. Then, we show that any pd-independent negator is non-involutive, and any non-trivial linear negator is strictly contracting. Finally, we introduce an involutive negator in the class of pd-dependent negators. It generates an involutive negation of probability distributions. Full article
(This article belongs to the Special Issue Fuzzy Systems and Optimization)
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12 pages, 948 KiB  
Article
Principal Component Analysis and Factor Analysis for an Atanassov IF Data Set
by Viliam Ďuriš, Renáta Bartková and Anna Tirpáková
Mathematics 2021, 9(17), 2067; https://doi.org/10.3390/math9172067 - 26 Aug 2021
Cited by 5 | Viewed by 2640
Abstract
The present contribution is devoted to the theory of fuzzy sets, especially Atanassov Intuitionistic Fuzzy sets (IF sets) and their use in practice. We define the correlation between IF sets and the correlation coefficient, and we bring a new perspective to solving the [...] Read more.
The present contribution is devoted to the theory of fuzzy sets, especially Atanassov Intuitionistic Fuzzy sets (IF sets) and their use in practice. We define the correlation between IF sets and the correlation coefficient, and we bring a new perspective to solving the problem of data file reduction in case sets where the input data come from IF sets. We present specific applications of the two best-known methods, the Principal Component Analysis and Factor Analysis, used to solve the problem of reducing the size of a data file. We examine input data from IF sets from three perspectives: through membership function, non-membership function and hesitation margin. This examination better reflects the character of the input data and also better captures and preserves the information that the input data carries. In the article, we also present and solve a specific example from practice where we show the behavior of these methods on data from IF sets. The example is solved using R programming language, which is useful for statistical analysis of data and their graphical representation. Full article
(This article belongs to the Special Issue Fuzzy Systems and Optimization)
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16 pages, 321 KiB  
Article
A Study of GD′- Implications, a New Hyper Class of Fuzzy Implications
by Dimitrios S. Grammatikopoulos and Basil Papadopoulos
Mathematics 2021, 9(16), 1925; https://doi.org/10.3390/math9161925 - 12 Aug 2021
Cited by 4 | Viewed by 1601
Abstract
In this paper, we introduce and study the GD′-operations, which are a hyper class of the known D′-operations. GD′-operations are in fact D′-operations, that are generated not only from the same fuzzy negation. Similar with [...] Read more.
In this paper, we introduce and study the GD′-operations, which are a hyper class of the known D′-operations. GD′-operations are in fact D′-operations, that are generated not only from the same fuzzy negation. Similar with D′-operations, they are not always fuzzy implications. Nevertheless, some sufficient, but not necessary conditions for a GD′-operation to be a fuzzy implication, will be proved. A study for the satisfaction, or the violation of the basic properties of fuzzy implications, such as the left neutrality property, the exchange principle, the identity principle and the ordering property will also be made. This study also completes the study of the basic properties of D′-implications. At the end, surprisingly an unexpected new result for the connection of the QL-operations and D-operations will be presented. Full article
(This article belongs to the Special Issue Fuzzy Systems and Optimization)
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