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Symmetry
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Symmetry/Asymmetry in Fuzzy Sets and Fuzzy Systems
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Symmetry/Asymmetry in Fuzzy Sets and Fuzzy Systems

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

Deadline for manuscript submissions: 30 June 2026 | Viewed by 1870

Special Issue Editors

Dr. Tengyu Yin

E-Mail Website
Guest Editor
School of Computer and Information Engineering, Henan University, Kaifeng 475004, China
Interests: data mining; uncertain artificial intelligence; fuzzy computing; fuzzy system; multi-label learning
Dr. Wei Zhang

E-Mail Website
Guest Editor
School of Artificial Intelligence and Computer Science, Nantong University, Nantong 226019, China
Interests: data mining; fuzzy computing; fuzzy system; artificial intelligence and pattern recognition; interpretability and fuzzy uncertainty learning; bioinformatics; uncertainty learning and modeling

Special Issue Information

Dear Colleagues,

In recent years, fuzzy systems have continued to demonstrate significant value in automatic control, pattern recognition, and decision support. Unlike traditional precise modeling, fuzzy systems represent inputs, outputs, and states with fuzzy sets and integrate fuzzy rules, fuzzy reasoning, and fuzzy logic—offering a unified paradigm for handling uncertainty, vagueness, and incompleteness. As data scale and complexity grow, symmetry/asymmetry becomes increasingly central to fuzzy-system design: it emerges in fuzzy similarity, dependency measures, membership-function construction, neighborhood and granularity structures, and the design of losses and regularizers (e.g., the structural symmetry between fuzzification and defuzzification).

This Special Issue focuses on methodological advances at the intersection of fuzzy–rough computing and granular computing with uncertainty learning. We particularly welcome cutting-edge research on uncertain information processing and intelligent reasoning, spanning the full spectrum from theoretical modeling to algorithm design and application-oriented validation, including—but not limited to—uncertainty modeling and learning, robust representation and feature selection, symmetric/asymmetric reasoning mechanisms, and their practice across diverse data types and tasks. We also encourage works that apply these methods to multi-label learning, graph/manifold similarity learning, multi-source information fusion, multimodal learning, and medical image analysis.

Dr. Tengyu Yin
Dr. Wei Zhang
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 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 systems
  • fuzzy logic
  • fuzzy reasoning
  • fuzzy–rough sets
  • fuzzy control
  • symmetry and asymmetry
  • artificial intelligence logic
  • collaborative computing
  • machine learning
  • data mining
  • computer vision
  • granular computing
  • multimodal learning
  • biomedical applications

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Published Papers (4 papers)

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Research

27 pages, 1533 KB  
Article
Fuzzy Granular Ball-Based Attribute Reduction for Interval-Valued Decision Systems
by Yuxuan He, Nan Zhang and Ruilin Wei
Symmetry 2026, 18(5), 728; https://doi.org/10.3390/sym18050728 - 24 Apr 2026
Viewed by 188
Abstract
Feature selection is a core step in data analysis and is referred to as attribute reduction in rough set theory. Granular ball computing has emerged as a novel data analysis paradigm characterized by high computational efficiency, robustness, and scalability. However, in previous attribute [...] Read more.
Feature selection is a core step in data analysis and is referred to as attribute reduction in rough set theory. Granular ball computing has emerged as a novel data analysis paradigm characterized by high computational efficiency, robustness, and scalability. However, in previous attribute reduction methods for interval numbers, the construction of tolerance classes and the reduction iteration process suffer from inefficiency. To address these limitations, this paper proposes an efficient attribute reduction method based on fuzzy interval-valued granular balls. This method integrates fuzzy interval-valued granular balls with an acceleration strategy based on the positive region. Specifically, we first construct tolerance classes efficiently using fuzzy interval-valued granular balls, thereby enabling a reasonable partition of the universe. We then remove redundant objects in the positive region during the reduction iteration to avoid unnecessary computations. On this basis, we further propose a conditional entropy-based algorithm for attribute reduction. Experimental results show that this algorithm substantially improves computational efficiency while maintaining high classification accuracy. Full article
(This article belongs to the Special Issue Symmetry/Asymmetry in Fuzzy Sets and Fuzzy Systems)
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24 pages, 2933 KB  
Article
A Global Unsupervised Feature Selection Method Based on Fuzzy Mutual Information
by Haiyan Xu, Yulin Xie and Xin Liu
Symmetry 2026, 18(4), 633; https://doi.org/10.3390/sym18040633 - 9 Apr 2026
Viewed by 276
Abstract
With the rapid growth of data, feature selection has become essential for improving machine learning performance. However, most existing unsupervised feature selection methods rely on greedy strategies, which often lead to suboptimal solutions. Moreover, traditional information–theoretic approaches are primarily designed for discrete data [...] Read more.
With the rapid growth of data, feature selection has become essential for improving machine learning performance. However, most existing unsupervised feature selection methods rely on greedy strategies, which often lead to suboptimal solutions. Moreover, traditional information–theoretic approaches are primarily designed for discrete data and require discretization when applied to continuous data, potentially causing information loss. To address these issues, this paper proposes a global unsupervised feature selection method based on fuzzy mutual information (UFS-FMI). The proposed method integrates fuzzy set theory with information measures to quantify feature relevance and redundancy, and formulates a fractional optimization model. A combination of projection neural networks and kWTA neural networks is employed to achieve global optimization. Experimental results on nine UCI benchmark datasets demonstrate that UFS-FMI consistently outperforms several representative methods in terms of classification accuracy, clustering accuracy, and normalized mutual information (NMI). In particular, on datasets such as Movement_libras, Ionosphere, and Control, the proposed method achieves significantly improved classification performance, confirming its effectiveness and robustness. Full article
(This article belongs to the Special Issue Symmetry/Asymmetry in Fuzzy Sets and Fuzzy Systems)
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50 pages, 1701 KB  
Article
Information Aggregation and Psychological Risk Dual-Driven Sustainable Supplier Selection Method Based on Extended Fuzzy Set and Choquet Integral
by Jian Ren, Feiyan Li, Keting Ye, Shuang Chen and Tianyang Yin
Symmetry 2026, 18(3), 489; https://doi.org/10.3390/sym18030489 - 12 Mar 2026
Viewed by 313
Abstract
A novel sustainable supplier selection (SSS) method is proposed to address the interrelation among attributes and the psychological state and risk attitude of decision-makers (DMs). The method integrates proportional interval type-2 hesitant fuzzy sets (PIT2HFSs), a generalized Shapley-based aggregation operator, and a modified [...] Read more.
A novel sustainable supplier selection (SSS) method is proposed to address the interrelation among attributes and the psychological state and risk attitude of decision-makers (DMs). The method integrates proportional interval type-2 hesitant fuzzy sets (PIT2HFSs), a generalized Shapley-based aggregation operator, and a modified regret theory combined with a normalized bidirectional projection (NBP) measure. The aggregation operators handle the correlations among attributes, while the NBP and regret theory reflect DMs’ risk preferences by considering both the best and worst alternatives. An application case study in a manufacturing enterprise, along with sensitivity and comparative analyses, demonstrates the effectiveness and robustness of the proposed approach. The results indicate that the method outperforms existing approaches in handling attribute interdependencies, decision uncertainty, and human risk behavior, providing a comprehensive and practical framework for sustainable supplier selection in the manufacturing industry. Full article
(This article belongs to the Special Issue Symmetry/Asymmetry in Fuzzy Sets and Fuzzy Systems)
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18 pages, 966 KB  
Article
Anomaly Detection Based on Hybrid Kernelized Fuzzy Density
by Kaitian Luo, Shenhong Lei, Chaoqing Li and Yi Li
Symmetry 2026, 18(1), 192; https://doi.org/10.3390/sym18010192 - 20 Jan 2026
Viewed by 410
Abstract
Unsupervised anomaly detection has been extensively studied. However, most existing methods are designed for either numerical or nominal data, which struggle to detect anomalies effectively in real-world mixed-type datasets. Fuzzy information granulation is a key concept in granular computing, which offers a potent [...] Read more.
Unsupervised anomaly detection has been extensively studied. However, most existing methods are designed for either numerical or nominal data, which struggle to detect anomalies effectively in real-world mixed-type datasets. Fuzzy information granulation is a key concept in granular computing, which offers a potent framework for managing uncertainty in mixed-type data and provides a viable pathway for unsupervised anomaly detection. Nevertheless, conventional fuzzy information granulation-based detection methods often model only simple, linear fuzzy relations between samples. This limitation prevents them from capturing the complex, nonlinear structures inherent in the data, leading to a degradation in detection performance. To address these shortcomings, we propose a Hybrid Kernelized Fuzzy Density-based anomaly detector (HKFD). HKFD pioneers a hybrid kernelized fuzzy relation by integrating a hybrid distance metric with kernel methods. This new relation allows us to define a hybrid kernelized fuzzy density for each sample within every feature subspace, effectively capturing the local data dispersion. Crucially, we introduce an information-theoretic weighting mechanism. By calculating the fuzzy information entropy of each feature’s distribution, HKFD automatically assigns higher weights to more informative feature subspaces that contribute more to identifying anomalies. The final anomaly factor is then calculated by the weighted fusion of these densities. Comprehensive experiments on 20 datasets demonstrate that HKFD significantly outperforms state-of-the-art methods, achieving superior anomaly detection performance. Full article
(This article belongs to the Special Issue Symmetry/Asymmetry in Fuzzy Sets and Fuzzy Systems)
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