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Symmetry
Special Issues
Symmetry and Fuzzy Set
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Symmetry and Fuzzy Set

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

Deadline for manuscript submissions: 31 January 2026 | Viewed by 599

Special Issue Editor

Dr. Panagiotis Chountas

E-Mail Website
Guest Editor
School of Computer Science and Engineering, University of Westminster, London, UK
Interests: machine learning; data mining; big data; data science; intuitionistic fuzzy sets

Special Issue Information

Dear Colleagues,

This Special Issue aims to provide a comprehensive platform for presenting cutting-edge research that bridges the gap between fuzzy logic and its extensions in the practical application of symmetry across various domains, including fuzzy measures, fuzzy relations, fuzzy control, fuzzy logic and data mining/machine learning, fuzzy decision making, fuzzy modeling, and fuzzy information retrieval. In recent years, the integration of fuzzy logic with multi-criteria methods has gained traction, improving the robustness of results obtained by MCDM/MCDA models. However, traditional MCDM methods encounter bottlenecks in high-dimensional problems. Limited research has evaluated the effectiveness of LLMs in tackling specific MCDM problems where symmetry may be present. We wish to further explore the capability of LLMs by proposing approaches for automatically addressing general, complex MCDM problems. Submissions involving applications of fuzzy theory and/or its extensions—where symmetry, or a deliberate lack thereof, is present—are also welcome. 

Dr. Panagiotis Chountas
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 theory and symmetry
  • fuzzy decision making
  • intuitionistic fuzzy sets
  • multiple-criteria decision-making methods (MCDMs)
  • fuzzy fractional Brownian motion
  • large language models (LLMs)
  • data and knowledge engineering

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Published Papers (1 paper)

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Research

39 pages, 995 KB  
Article
Multi-Granulation Variable Precision Fuzzy Rough Set Based on Generalized Fuzzy Remote Neighborhood Systems and the MADM Application Design of a Novel VIKOR Method
by Xinyu Mei and Yaoliang Xu
Symmetry 2026, 18(1), 84; https://doi.org/10.3390/sym18010084 - 3 Jan 2026
Viewed by 259
Abstract
Variable precision fuzzy rough sets (VPFRSs) and multi-granulation fuzzy rough sets (MGFRSs) are both significant extensions of rough sets. However, existing variable precision models generally lack the inclusion property, which poses potential risks in applications. Meanwhile, multi-granulation models tend to emphasize either optimistic [...] Read more.
Variable precision fuzzy rough sets (VPFRSs) and multi-granulation fuzzy rough sets (MGFRSs) are both significant extensions of rough sets. However, existing variable precision models generally lack the inclusion property, which poses potential risks in applications. Meanwhile, multi-granulation models tend to emphasize either optimistic or pessimistic scenarios but overlook compromise situations. A generalized fuzzy remote neighborhood system is a symmetric union-fuzzified form of the neighborhood system, which can extend the fuzzy rough set model to a more general framework. Moreover, semi-grouping functions eliminate the left-continuity required for grouping functions and the associativity in t-conorms, making them more suitable for information aggregation. Therefore, to overcome the limitations of existing models, we propose an optimistic (OP), pessimistic (PE), and compromise (CO) variable precision fuzzy rough set (OPCAPFRS) based on generalized fuzzy remote neighborhood systems. The semi-grouping function and its residual minus are employed in the OPCAPFRS. We discuss the basic properties of the OPCAPFRS and prove that it satisfies the generalized inclusion property (GIP). This partially addresses the issue that a VPFRS cannot fulfill the inclusion property. A novel methodology for addressing multi-attribute decision-making (MADM) problems is developed through the fusion of the proposed OPCAPFRS framework and the VIKOR technique. The proposed method is applied to the problem of selecting an optimal CPU. Subsequently, comparative experiments and a parameter analysis are conducted to validate the effectiveness and stability of the proposed method. Finally, three sets of experiments are performed to verify the reliability and robustness of the new approach. It should be noted that the new method performed ranking on a dataset containing nearly ten thousand samples, obtaining both the optimal solution and a complete ranking, thereby validating its scalability. Full article
(This article belongs to the Special Issue Symmetry and Fuzzy Set)
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