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Symmetry
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Research on Fuzzy Logic and Mathematics with Applications, 3rd Edition
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Research on Fuzzy Logic and Mathematics with Applications, 3rd Edition

A special issue of Symmetry (ISSN 2073-8994). This special issue belongs to the section "Mathematics".

Deadline for manuscript submissions: 31 May 2025 | Viewed by 1958

Special Issue Editor

Prof. Dr. Saeid Jafari

E-Mail Website
Guest Editor
Mathematics and Philosophy Department, College of Vestsjaelland South, Herrestraede 11, 4200 Slagelse, Denmark
Interests: fuzzy logic and fuzzy topology; neutrosophic theory; general topology; digital topology; topological groups; theory of multifunctions; mathematical aspects of particle physics
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

The notion of fuzzy sets was introduced by Lotfi A. Zadeh (February 4, 1921–September 6, 2017) in 1965, who also founded fuzzy logic. Since the advent of the notion of fuzzy sets, Zadeh and other researchers have used this important and interesting set to establish a great deal of important and interesting research in fuzzy logic, fuzzy topology, fuzzy arithmetics, etc. This Special Issue deals with fuzzy logic and mathematics with applications in decision making, fuzzy control systems, and other engineering applications.

We welcome such symmetry-related contributions to this Special Issue.

Due to the great success of our Special Issues "Research on Fuzzy Logic and Mathematics with Applications" and “Research on Fuzzy Logic and Mathematics with Applications II”, we decided to set up a third volume. We invite you to read the previous two Special Issues at https://www.mdpi.com/journal/symmetry/special_issues/Research_Fuzzy_Logic_Mathematics_Applications and https://www.mdpi.com/journal/symmetry/special_issues/Research_Fuzzy_Logic_Mathematics_Applications_2.

Prof. Dr. Saeid Jafari
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. Symmetry 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
  • nonstandard fuzzy set
  • fuzzy soft set
  • fuzzy logic
  • fuzzy topology
  • fuzzy algebra
  • fuzzy graph theory
  • fuzzy control
  • fuzzy decision making
  • fuzzy arithmetic
  • fuzzy classification and pattern recognition

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Further information on MDPI's Special Issue policies can be found here.

Published Papers (6 papers)

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Research

19 pages, 304 KiB  
Article
Some Characterizations of k-Fuzzy γ-Open Sets and Fuzzy γ-Continuity with Further Selected Topics
by Fahad Alsharari, Hind Y. Saleh and Islam M. Taha
Symmetry 2025, 17(5), 678; https://doi.org/10.3390/sym17050678 (registering DOI) - 29 Apr 2025
Abstract
In the present paper, we first introduced the notion of k-fuzzy γ-open (k-F-γ-open) sets as a generalized novel class of fuzzy open (F-open) sets on fuzzy topological spaces (FTSs) in [...] Read more.
In the present paper, we first introduced the notion of k-fuzzy γ-open (k-F-γ-open) sets as a generalized novel class of fuzzy open (F-open) sets on fuzzy topological spaces (FTSs) in the sense of Šostak. The class of k-F-γ-open sets is contained in the class of k-F-β-open sets and contains all k-F-semi-open and k-F-pre-open sets. Also, we introduced the closure and interior operators with respect to the classes of k-F-γ-closed and k-F-γ-open sets and discussed some of their properties. After that, we defined and studied the notions of F-γ-continuous (resp. F-γ-irresolute) functions between FTSs(M,ℑ) and (N,ϝ). However, we displayed and investigated the notions of F-almost (resp. F-weakly) γ-continuous functions, which are weaker forms of F-γ-continuous functions. Next, we presented and characterized some new F-functions via k-F-γ-open and k-F-γ-closed sets, called F-γ-open (resp. F-γ-irresolute open, F-γ-closed, F-γ-irresolute closed, and F-γ-irresolute homeomorphism) functions. The relationships between these classes of functions were investigated with the help of some examples. We also introduced some new types of F-separation axioms called k-F-γ-regular (resp. k-F-γ-normal) spaces via k-F-γ-closed sets and discussed some properties of them. Lastly, we explored and studied some new types of F-compactness called k-F-almost (resp. k-F-nearly) γ-compact sets. Full article
(This article belongs to the Special Issue Research on Fuzzy Logic and Mathematics with Applications, 3rd Edition)
28 pages, 424 KiB  
Article
Characterization of Degree Energies and Bounds in Spectral Fuzzy Graphs
by Ruiqi Cai, Buvaneswari Rangasamy, Senbaga Priya Karuppusamy and Aysha Khan
Symmetry 2025, 17(5), 644; https://doi.org/10.3390/sym17050644 - 25 Apr 2025
Viewed by 153
Abstract
This study explores the degree energy of fuzzy graphs to establish fundamental spectral bounds and characterize adjacency structures. We derive upper bounds on the sum of squared degree eigenvalues based on vertex degree distributions and formulate constraints using the characteristic polynomial of the [...] Read more.
This study explores the degree energy of fuzzy graphs to establish fundamental spectral bounds and characterize adjacency structures. We derive upper bounds on the sum of squared degree eigenvalues based on vertex degree distributions and formulate constraints using the characteristic polynomial of the maximum degree matrix. Furthermore, we demonstrate that the average degree energy of a connected fuzzy graph remains strictly positive. The proposed framework is applied to protein–protein interaction networks, identifying critical proteins and enhancing network resilience analysis. Full article
(This article belongs to the Special Issue Research on Fuzzy Logic and Mathematics with Applications, 3rd Edition)
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17 pages, 254 KiB  
Article
Some Properties of Boolean-like Laws in Fuzzy Logic
by Sevilay Demir Sağlam and Gül Karadeniz Gözeri
Symmetry 2025, 17(4), 548; https://doi.org/10.3390/sym17040548 - 3 Apr 2025
Viewed by 196
Abstract
This article focuses on the relationships between fuzzy logic and classical logic properties using fuzzy t-norms, t-conorms, and fuzzy implications. It aims to contribute to fuzzy set theory by extending the Boolean laws in classical logic to fuzzy logic. We determine [...] Read more.
This article focuses on the relationships between fuzzy logic and classical logic properties using fuzzy t-norms, t-conorms, and fuzzy implications. It aims to contribute to fuzzy set theory by extending the Boolean laws in classical logic to fuzzy logic. We determine the necessary and sufficient conditions for validating the generalizations of the proposed properties from classical to fuzzy logic. Additionally, we provide examples demonstrating the practical applicability of this approach and its advantages over conventional methodologies, reinforcing its effectiveness. Full article
(This article belongs to the Special Issue Research on Fuzzy Logic and Mathematics with Applications, 3rd Edition)
21 pages, 415 KiB  
Article
A New Graph Vulnerability Parameter: Fuzzy Node Integrity
by Ferhan Nihan Murater and Goksen Bacak-Turan
Symmetry 2025, 17(4), 474; https://doi.org/10.3390/sym17040474 - 21 Mar 2025
Viewed by 157
Abstract
Robustness in networks plays a vital role in mitigating the effects of failures caused by nodes or links, which can disrupt essential services. Among the various vulnerability parameters in graph theory, such as connectivity and integrity, their applications to fuzzy graphs remain underexplored, [...] Read more.
Robustness in networks plays a vital role in mitigating the effects of failures caused by nodes or links, which can disrupt essential services. Among the various vulnerability parameters in graph theory, such as connectivity and integrity, their applications to fuzzy graphs remain underexplored, despite fuzzy graphs being a powerful tool for modeling uncertainty. In this paper, we introduce the parameter ’fuzzy node integrity’, which considers both the number of disrupted elements and the strength of residual connections. We derive general formulas for different types of symmetric and asymmetric fuzzy graph structures, including cycle graphs, wheel graphs, and star graphs, to systematically demonstrate the utility of this parameter. The proposed parameter is then applied to a military logistics problem to gain insights into the identification of critical nodes and route optimization under uncertainty. This study bridges an important gap in fuzzy graph theory by redefining node integrity through the inclusion of connection strength, offering a promising tool for assessing network vulnerability. These findings lay the foundation not only for theoretical research but also for practical improvements in transportation, disaster management, and communication networks. Full article
(This article belongs to the Special Issue Research on Fuzzy Logic and Mathematics with Applications, 3rd Edition)
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16 pages, 279 KiB  
Article
The Neutrosophization of δ-Separation Axioms
by Ahu Açikgöz, Ferhat Esenbel, Abdulhamit Maman and Seher Zorlu
Symmetry 2025, 17(2), 271; https://doi.org/10.3390/sym17020271 - 10 Feb 2025
Viewed by 470
Abstract
Fuzzy topology has long been celebrated for its ability to address real-world challenges in areas such as information systems and decision making. However, with ongoing technological advancements and the increasing complexity of practical requirements, the focus has gradually shifted toward neutrosophic topology, a [...] Read more.
Fuzzy topology has long been celebrated for its ability to address real-world challenges in areas such as information systems and decision making. However, with ongoing technological advancements and the increasing complexity of practical requirements, the focus has gradually shifted toward neutrosophic topology, a broader and more inclusive framework than fuzzy topology. While neutrosophic topology is primarily rooted in neutrosophic open sets, other related families, including neutrosophic pre-open sets, neutrosophic semi-open sets, and neutrosophic beta-open sets, have also proven instrumental in driving progress in this field. This study introduces neutrosophic δ-open sets as a significant enhancement to the current theoretical framework. In addition, we propose a novel category of separation axioms, termed neutrosophic δ-separation axioms, which are derived from the concept of neutrosophic δ-open sets. Moreover, we explore the interplay between these separation properties and their characteristics within subspaces. Our findings confirm that neutrosophic δ-separation axioms are reliably upheld in neutrosophic regular open subspaces. Full article
(This article belongs to the Special Issue Research on Fuzzy Logic and Mathematics with Applications, 3rd Edition)
35 pages, 4965 KiB  
Article
A Novel IVBPRT-ELECTRE III Algorithm Based on Bidirectional Projection and Its Application
by Juxiang Wang, Min Xu, Yanjun Wang and Ziqi Zhu
Symmetry 2025, 17(1), 26; https://doi.org/10.3390/sym17010026 - 26 Dec 2024
Viewed by 588
Abstract
Fuzzy semantics have a wide range of applications in life, and especially when expressing people’s evaluation information, it is more specific. As people increasingly prefer to express their personal opinions through media platforms, the opinions of the general public have become an indispensable [...] Read more.
Fuzzy semantics have a wide range of applications in life, and especially when expressing people’s evaluation information, it is more specific. As people increasingly prefer to express their personal opinions through media platforms, the opinions of the general public have become an indispensable reference. However, information asymmetry can have a significant impact on the rationality of decision-making. Based on the above considerations, this paper extends bidirectional projection to probabilistic linguistic term sets to preserve the completeness of information as much as possible. The large-scale group decision-making problem under the probabilistic linguistic environment is extended to limited interval values, and a new group decision-making method named IVBPRT-ELECTRE III algorithm (ELECTRE III based on bidirectional projection and regret theory under limited interval-valued probabilistic linguistic term set) is proposed. The method is an extended ELECTRE III method based on limited interval-valued probabilistic linguistic term set (l-IVPLTS) bidirectional projection by regret theory approach. Firstly, this involves mining the online text comment information on social media about an emergency and considering the effect of the number of fans, determining the attributes and their initial weights for judging the strengths and weaknesses of the emergency management alternative using the TF-IDF and the Word2vec technology, and using the entropy value to adjust the initial weight of attributes, not only considering the real opinions of the public, but also combining with the views of experts, making the decision-making alternative selection more scientific and reasonable. Secondly, this paper fills the gap of bidirectional projection under l-IVPLTS environment; then, combining l-IVPLTS bidirectional projection and regret theory to determine the objective weights of experts, combines the differences in individual expertise of experts to obtain the comprehensive weights of experts, and uses the extended ELECTRE III method to rank the alternatives. Finally, the feasibility and validity of the provided method is verified through the Yanjiao explosion incident as a case. Full article
(This article belongs to the Special Issue Research on Fuzzy Logic and Mathematics with Applications, 3rd Edition)
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