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Axioms
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Recent Advances in Fuzzy Sets and Related Topics
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Recent Advances in Fuzzy Sets and Related Topics

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

Deadline for manuscript submissions: 30 October 2024 | Viewed by 4742

Special Issue Editor

Dr. Boldizsár Tüű-Szabó

E-Mail Website
Guest Editor
Department of Information Technology, Széchenyi István University, 9026 Györ, Hungary
Interests: fuzzy modeling; evolutionary computation; optimization

Special Issue Information

Dear Colleagues,

The concept of fuzzy sets, introduced by Zadeh in 1965, is a simple yet very powerful and efficient mathematical framework that can formally characterize an imprecise concept. Fuzzy set theory can deal with problems relating to ambiguous, subjective, and imprecise judgments where the classical mathematical and statistical techniques are often unsatisfactory. Therefore, the applications of fuzzy sets and systems are wide, for example, in artificial intelligence, expert systems, decision making, control engineering, pattern recognition, data mining, and robotics.

We are pleased to invite you to contribute some of your most recent research to this Special Issue, titled "Advances in Fuzzy Sets and Related Topics".

The proposed Special Issue intends to cover all the aspects of theory and applications of fuzzy sets and its hybridizations with other artificial and computational intelligence techniques including, but not limited to:

  • Basics of fuzzy set theory: fuzzy relations, generalizations of fuzzy sets, etc.
  • Rough sets and formal concept analysis.
  • Intuitionistic fuzzy set.
  • Fuzzy data analysis.
  • Fuzzy information processing.
  • Fuzzy control and robotics.
  • Fuzzy systems: decision-making, inference systems, preference modeling, and optimization.
  • Hybrid systems of computational intelligence techniques.

Dr. Boldizsár Tüű-Szabó
Guest Editor

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

  • fuzzy set
  • soft computing
  • artificial intelligence
  • fuzzy systems
  • data mining
  • data analysis
  • intuitionistic fuzzy sets
  • decision making

Published Papers (6 papers)

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Research

14 pages, 295 KiB  
Article
Some Applications of Fuzzy Sets in Residuated Lattices
by Cristina Flaut, Dana Piciu and Bianca Liana Bercea
Axioms 2024, 13(4), 267; https://doi.org/10.3390/axioms13040267 - 18 Apr 2024
Viewed by 311
Abstract
Many papers have been devoted to applying fuzzy sets to algebraic structures. In this paper, based on ideals, we investigate residuated lattices from fuzzy set theory, lattice theory, and coding theory points of view, and some applications of fuzzy sets in residuated lattices [...] Read more.
Many papers have been devoted to applying fuzzy sets to algebraic structures. In this paper, based on ideals, we investigate residuated lattices from fuzzy set theory, lattice theory, and coding theory points of view, and some applications of fuzzy sets in residuated lattices are presented. Since ideals are important concepts in the theory of algebraic structures used for formal fuzzy logic, first, we investigate the lattice of fuzzy ideals in residuated lattices and study some connections between fuzzy sets associated to ideals and Hadamard codes. Finally, we present applications of fuzzy sets in coding theory. Full article
(This article belongs to the Special Issue Recent Advances in Fuzzy Sets and Related Topics)
20 pages, 5301 KiB  
Article
Novel Method for Ranking Generalized Fuzzy Numbers Based on Normalized Height Coefficient and Benefit and Cost Areas
by Thi Hong Phuong Le and Ta-Chung Chu
Axioms 2023, 12(11), 1049; https://doi.org/10.3390/axioms12111049 - 13 Nov 2023
Viewed by 751
Abstract
This paper proposes a method for ranking generalized fuzzy numbers, which guarantees that both horizontal and vertical values are important parameters affecting the final ranking score. In this method, the normalized height coefficient is introduced to evaluate the influence of the height of [...] Read more.
This paper proposes a method for ranking generalized fuzzy numbers, which guarantees that both horizontal and vertical values are important parameters affecting the final ranking score. In this method, the normalized height coefficient is introduced to evaluate the influence of the height of fuzzy numbers on the final ranking score. The higher the normalized height coefficient of a generalized fuzzy number is, the higher its ranking. The left and right areas are presented to calculate the impact of the vertical value on the final ranking score. The left area is considered the benefit area. The right area is considered the cost area. A generalized fuzzy number is preferred if the benefit area is larger and the cost area is smaller. The proposed method can be employed to rank both normal and non-normal fuzzy numbers without normalization or height minimization. Numerical examples and comparisons with other methods highlight the feasibility and robustness of the proposed method, which can overcome the shortcomings of some existing methods and can support decision-makers in selecting the best alternative. Full article
(This article belongs to the Special Issue Recent Advances in Fuzzy Sets and Related Topics)
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20 pages, 368 KiB  
Article
Extension of Fuzzy ELECTRE I for Evaluating Demand Forecasting Methods in Sustainable Manufacturing
by Ta-Chung Chu and Thi Bich Ha Nghiem
Axioms 2023, 12(10), 926; https://doi.org/10.3390/axioms12100926 - 28 Sep 2023
Viewed by 625
Abstract
The selection of a demand forecasting method is critical for companies aiming to avoid manufacturing overproduction or shortages in pursuit of sustainable development. Various qualitative and quantitative criteria with different weights must be considered during the evaluation of a forecasting method. The qualitative [...] Read more.
The selection of a demand forecasting method is critical for companies aiming to avoid manufacturing overproduction or shortages in pursuit of sustainable development. Various qualitative and quantitative criteria with different weights must be considered during the evaluation of a forecasting method. The qualitative criteria and criteria weights are usually assessed in linguistic terms. Aggregating these various criteria and linguistic weights for evaluating and selecting demand forecasting methods in sustainable manufacturing is a major challenge. This paper proposes an extension of fuzzy elimination and choice translating reality (ELECTRE) I to resolve this problem. In the proposed method, fuzzy weighted ratings are defuzzified with the signed distance to develop a crisp ELECTRE I model. Moreover, an extension to ELECTRE I is developed by suggesting an extended modified discordance matrix and a closeness coefficient for ranking alternatives. The proposed extension can overcome the problem of information loss, which can lead to incorrect ranking results when using the Hadamard product to combine concordance and modified discordance matrices. A comparison is conducted to show the advantage of the proposed extension. Finally, a numerical example is used to demonstrate the feasibility of the proposed method. Furthermore, a numerical comparison is made to display the advantage of the proposed method. Full article
(This article belongs to the Special Issue Recent Advances in Fuzzy Sets and Related Topics)
16 pages, 324 KiB  
Article
Left and Right Operator Rings of a Γ Ring in Terms of Rough Fuzzy Ideals
by Durgadevi Pushpanathan and Ezhilmaran Devarasan
Axioms 2023, 12(9), 808; https://doi.org/10.3390/axioms12090808 - 22 Aug 2023
Viewed by 590
Abstract
The relationship between Rough Set (RS) and algebraic systems has been long studied by mathematicians. RS is a growing research area that encourages studies into both real-world applications and the theory itself. In RS, a universe subset is characterized by a pair of [...] Read more.
The relationship between Rough Set (RS) and algebraic systems has been long studied by mathematicians. RS is a growing research area that encourages studies into both real-world applications and the theory itself. In RS, a universe subset is characterized by a pair of ordinary sets called lower and upper approximations. In this study, we look attentively at the use of rough sets when the universe set has a ring structure. The main contribution of the paper is to concentrate on the study of rough fuzzy ideals concerning the gamma ring and to describe some properties of its lower and upper approximations. This paper deals with the connection between Rough Fuzzy Sets (RFS) and ring theory. The goal of this paper is to present the notion of Left Operator Rings (LOR) and Right Operator Rings (ROR) in the gamma ring structure. We introduce some basic concepts of rough fuzzy left and right operator rings. Furthermore, we investigate some characterizations of left and right operator rings and prove some theorems based on these results. Full article
(This article belongs to the Special Issue Recent Advances in Fuzzy Sets and Related Topics)
13 pages, 314 KiB  
Article
A Novel Study of Fuzzy Bi-Ideals in Ordered Semirings
by Ghulam Muhiuddin, Nabilah Abughazalah, Ahsan Mahboob and Deena Al-Kadi
Axioms 2023, 12(7), 626; https://doi.org/10.3390/axioms12070626 - 24 Jun 2023
Cited by 2 | Viewed by 716
Abstract
In this study, by generalizing the notion of fuzzy bi-ideals of ordered semirings, the notion of (∈,∈∨(κ*,qκ))-fuzzy bi-ideals is established. We prove that [...] Read more.
In this study, by generalizing the notion of fuzzy bi-ideals of ordered semirings, the notion of (∈,∈∨(κ*,qκ))-fuzzy bi-ideals is established. We prove that (∈,∈∨(κ*,qκ))-fuzzy bi-ideals are fuzzy bi-ideals but that the converse is not true, and an example is provided to support this proof. A condition is given under which fuzzy bi-ideals of ordered semirings coincide with (∈,∈∨(κ*,qκ))-fuzzy bi-ideals. An equivalent condition and certain correspondences between bi-ideals and (∈,∈∨(κ*,qκ))-fuzzy bi-ideals are presented. Moreover, the (κ*,κ)-lower part of (∈,∈∨(κ*,qκ))-fuzzy bi-ideals is described and depicted in terms of several classes of ordered semirings. Furthermore, it is shown that the ordered semiring is bi-simple if and only if it is (∈,∈∨(κ*,qκ))-fuzzy bi-simple. Full article
(This article belongs to the Special Issue Recent Advances in Fuzzy Sets and Related Topics)
18 pages, 545 KiB  
Article
Quaternionic Fuzzy Sets
by Songsong Dai
Axioms 2023, 12(5), 490; https://doi.org/10.3390/axioms12050490 - 18 May 2023
Viewed by 921
Abstract
A novel concept of quaternionic fuzzy sets (QFSs) is presented in this paper. QFSs are a generalization of traditional fuzzy sets and complex fuzzy sets based on quaternions. The novelty of QFSs is that the range of the membership function is the set [...] Read more.
A novel concept of quaternionic fuzzy sets (QFSs) is presented in this paper. QFSs are a generalization of traditional fuzzy sets and complex fuzzy sets based on quaternions. The novelty of QFSs is that the range of the membership function is the set of quaternions with modulus less than or equal to one, of which the real and quaternionic imaginary parts can be used for four different features. A discussion is made on the intuitive interpretation of quaternion-valued membership grades and the possible applications of QFSs. Several operations, including quaternionic fuzzy complement, union, intersection, and aggregation of QFSs, are presented. Quaternionic fuzzy relations and their composition are also investigated. QFS is designed to maintain the advantages of traditional FS and CFS, while benefiting from the properties of quaternions. Cuts of QFSs and rotational invariance of quaternionic fuzzy operations demonstrate the particularity of quaternion-valued grades of membership. Full article
(This article belongs to the Special Issue Recent Advances in Fuzzy Sets and Related Topics)
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