Search for Articles:
Title / Keyword
Author / Affiliation / Email
Journal
Article Type
 
 
Advanced Search
 
Section
Special Issue
Volume
Issue
Number
Page
 
5.3
2.2
Journals
Symmetry
Special Issues
Research on Fuzzy Logic and Mathematics with Applications, 3rd Edition
share announcement

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: closed (28 February 2026) | Viewed by 13947

Special Issue Editor

Prof. Dr. Saeid Jafari

E-Mail Website
Guest Editor
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 250 words) can be sent to the Editorial Office for assessment.

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

Benefits of Publishing in a Special Issue

  • Ease of navigation: Grouping papers by topic helps scholars navigate broad scope journals more efficiently.
  • Greater discoverability: Special Issues support the reach and impact of scientific research. Articles in Special Issues are more discoverable and cited more frequently.
  • Expansion of research network: Special Issues facilitate connections among authors, fostering scientific collaborations.
  • External promotion: Articles in Special Issues are often promoted through the journal's social media, increasing their visibility.
  • Reprint: MDPI Books provides the opportunity to republish successful Special Issues in book format, both online and in print.

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

Published Papers (11 papers)

Download All Papers
Order results
Result details
Show export options expand_more Show export options expand_less
Select all
Export citation of selected articles as:

Research

31 pages, 422 KB  
Article
Double-Framed Bipolar Fuzzy Soft Sets and Algorithmic Approaches with Symmetry for Multi-Criteria Decision-Making Under Uncertainty
by Shadya M. Mershkhan and Baravan A. Asaad
Symmetry 2026, 18(1), 119; https://doi.org/10.3390/sym18010119 - 8 Jan 2026
Viewed by 544
Abstract
The bipolar fuzzy set and bipolar soft set have inspired the development of a new framework called double-framed bipolar fuzzy soft sets (DFBFSSs). This structure represents positive and negative membership information through ordered pairs, enabling a balanced treatment of uncertainty, imprecision, and bi-directional [...] Read more.
The bipolar fuzzy set and bipolar soft set have inspired the development of a new framework called double-framed bipolar fuzzy soft sets (DFBFSSs). This structure represents positive and negative membership information through ordered pairs, enabling a balanced treatment of uncertainty, imprecision, and bi-directional information in complex decision-making scenarios. The fundamental concepts and operations of DFBFSSs are rigorously defined and analyzed. The double-framed formulation is symmetric: exchanging the frames preserves the structure of DFBFSSs. This symmetry enables balanced handling of opposing or complementary information. The key properties of the proposed set show improved handling of uncertainty over existing fuzzy and soft set models. In addition, a decision-making algorithm based on DFBFSSs is developed and applied to a real-world problem to validate the framework’s feasibility. Comparative analysis confirms the method’s robustness and advantages in uncertain, dual-information settings. Full article
(This article belongs to the Special Issue Research on Fuzzy Logic and Mathematics with Applications, 3rd Edition)
►▼ Show Figures

Figure 1

28 pages, 350 KB  
Article
m-Polar Picture Fuzzy Bi-Ideals and Their Applications in Semigroups
by Warud Nakkhasen, Atthchai Chada and Teerapan Jodnok
Symmetry 2025, 17(12), 2051; https://doi.org/10.3390/sym17122051 - 1 Dec 2025
Viewed by 498
Abstract
The concept of symmetry is fundamental to the study of algebra; it serves as the basis for a branch of group theory that is essential to abstract algebra. A semigroup is a structure that builds upon the concept of a group, similarly extending [...] Read more.
The concept of symmetry is fundamental to the study of algebra; it serves as the basis for a branch of group theory that is essential to abstract algebra. A semigroup is a structure that builds upon the concept of a group, similarly extending the idea of symmetry found within groups. In this study, we specifically focus on semigroups. The main objective of this research is to apply the notion of m-polar picture fuzzy sets (m-PPFSs), with m being a natural number, in investigations into semigroups, as this concept generalizes m-polar fuzzy sets (m-PFSs) and picture fuzzy sets (PFSs). This research introduces the concepts of m-polar picture fuzzy left ideals (m-PPFLs), m-polar picture fuzzy right ideals (m-PPFRs), m-polar picture fuzzy ideals (m-PPFIs), m-polar picture fuzzy bi-ideals (m-PPFBs), and m-polar picture fuzzy generalized bi-ideals (m-PPFGBs) in semigroups. This study examines the relationships between these concepts, showing that every m-PPFL (m-PPFR) in the semigroups is also an m-PPFB, and that every m-PPFB in the semigroups is an m-PPFGB. However, the opposite is not true. Additionally, we provide the characteristics of the m-PPFLs, m-PPFRs, m-PPFIs, m-PPFBs, and m-PPFGBs in semigroups. We further discuss the connections between the m-PPFLs (m-PPFIs) and the m-PPFBs within the framework of regular semigroups, and most importantly, we show that, if the semigroup is regular, then the m-PPFBs and m-PPFGBs are equal. Finally, we utilize the properties of the m-PPFLs, m-PPFRs, m-PPFIs, m-PPFBs, and m-PPFGBs within semigroups to explore the classifications of regular semigroups. Full article
(This article belongs to the Special Issue Research on Fuzzy Logic and Mathematics with Applications, 3rd Edition)
27 pages, 3758 KB  
Article
Belief Entropy-Based MAGDM Algorithm Under Double Hierarchy Quantum-like Bayesian Networks and Its Application to Wastewater Reuse
by Juxiang Wang, Yaping Li, Xin Wang and Yanjun Wang
Symmetry 2025, 17(11), 2013; https://doi.org/10.3390/sym17112013 - 20 Nov 2025
Viewed by 564
Abstract
The traditional multi-attribute group decision-making (MAGDM) method easily ignores the interference effect among decision-makers (DMs), while quantum theory can effectively portray the uncertainty in the decision-making process and quantify the preference interference among DMs. The asymmetry of evaluation information in social networks can [...] Read more.
The traditional multi-attribute group decision-making (MAGDM) method easily ignores the interference effect among decision-makers (DMs), while quantum theory can effectively portray the uncertainty in the decision-making process and quantify the preference interference among DMs. The asymmetry of evaluation information in social networks can have a significant impact on decision-making. In this paper, a quantum MAGDM algorithm based on probabilistic linguistic term sets (PLTSs) and a quantum-like Bayesian network (QLBN) is proposed (PL-QLBN), utilizing quantum theory and social network concepts and introducing a novel method for calculating interference effects based on belief entropy. Firstly, a complete trust network is constructed based on the probabilistic linguistic trust transfer operator and the minimum path method. A trust aggregation method, considering interference effects, is proposed for the QLBN to determine the DM weights. Next, the attribute weights are calculated based on the entropy weight method. Then, a probabilistic linguistic MAGDM considering interference effects is proposed based on the QLBN. Finally, the feasibility and validity of the provided method are verified through Hefei City’s selection of wastewater reuse alternatives. Full article
(This article belongs to the Special Issue Research on Fuzzy Logic and Mathematics with Applications, 3rd Edition)
►▼ Show Figures

Figure 1

16 pages, 319 KB  
Article
Fuzzy Graphic Binary Matroid Approach to Power Grid Communication Network Analysis
by Jing Li, Buvaneswari Rangasamy, Saranya Shanmugavel and Aysha Khan
Symmetry 2025, 17(10), 1628; https://doi.org/10.3390/sym17101628 - 2 Oct 2025
Viewed by 751
Abstract
Matroid is a mathematical structure that extends the concept of independence. The fuzzy graphic binary matroid serves as a generalization of linear dependence, and its properties are examined. Power grid networks, which manage the generation, transmission, and distribution of electrical energy from power [...] Read more.
Matroid is a mathematical structure that extends the concept of independence. The fuzzy graphic binary matroid serves as a generalization of linear dependence, and its properties are examined. Power grid networks, which manage the generation, transmission, and distribution of electrical energy from power plants to consumers, are inherently a complex system. A key objective in analyzing these networks is to ensure a reliable and uninterrupted supply of electricity. However, several critical issues must be addressed, including uncertainty in communication links, detection of redundant or sensitive circuits, evaluation of network resilience under partial failures, and optimization of reliability in interconnected network systems. To support this goal, the concept of a fuzzy graphic binary matroid is applied in the analysis of power grid communication network, offering a framework that not only incorporates fuzziness and binary conditions but also enables systematic identification of weak circuits, redundancy planning, and reliability enhancement. This approach provides a more realistic representation of operational conditions, ensuring better fault tolerance and improved efficiency of the grid. Full article
(This article belongs to the Special Issue Research on Fuzzy Logic and Mathematics with Applications, 3rd Edition)
►▼ Show Figures

Figure 1

31 pages, 651 KB  
Article
Distance Measures of (m,a,n)-Fuzzy Neutrosophic Sets and Their Applications in Decision Making
by Samajh Singh Thakur
Symmetry 2025, 17(6), 939; https://doi.org/10.3390/sym17060939 - 12 Jun 2025
Cited by 1 | Viewed by 2030
Abstract
A neutrosophic set is an important tool for handling vagueness and impreciseness in real-world problems, and distance measures are also exhibited in neutrosophic set theory. The (m,a,n)-fuzzy neutrosophic set is more flexible and efficient than the existing extensions of neutrosophic sets when discussing [...] Read more.
A neutrosophic set is an important tool for handling vagueness and impreciseness in real-world problems, and distance measures are also exhibited in neutrosophic set theory. The (m,a,n)-fuzzy neutrosophic set is more flexible and efficient than the existing extensions of neutrosophic sets when discussing the distance between multiple objects. This paper invents ten distance measures for comparing (m,a,n)-fuzzy neutrosophic sets. Moreover, the created distance measures are applied in pattern classifications and multi-criteria decisions. Additionally, numerical examples demonstrate these distance measures in practical and scientific applications involving classifying materials and investment problems. The comparative analysis, along with graphical interpretations, further illustrates the effectiveness and superiority of the proposed measures. Full article
(This article belongs to the Special Issue Research on Fuzzy Logic and Mathematics with Applications, 3rd Edition)
►▼ Show Figures

Figure 1

19 pages, 308 KB  
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 - 29 Apr 2025
Cited by 1 | Viewed by 825
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 KB  
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
Cited by 3 | Viewed by 1810
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)
►▼ Show Figures

Figure 1

17 pages, 254 KB  
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
Cited by 1 | Viewed by 1804
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 KB  
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 898
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)
►▼ Show Figures

Figure 1

16 pages, 279 KB  
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 1137
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 KB  
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
Cited by 6 | Viewed by 1381
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)
►▼ Show Figures

Figure 1

Show export options expand_more Show export options expand_less
Select all
Export citation of selected articles as:
 
Displaying articles 1-11
Back to TopTop