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Symmetry
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The Fusion of Fuzzy Sets and Optimization Using Symmetry
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The Fusion of Fuzzy Sets and Optimization Using Symmetry

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

Deadline for manuscript submissions: 31 December 2025 | Viewed by 2070

Special Issue Editor

Prof. Dr. Hsien-Chung Wu

E-Mail Website
Guest Editor
Department of Mathematics, National Kaohsiung Normal University, Kaohsiung 802, Taiwan
Interests: fuzzy sets; optimization; nonlinear analysis
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

Mathematical Programming is a discipline that helps decision-makers to make better decisions. The better decision often includes maximizing the profit, yield, or performance, or minimizing the cost, loss, or risk. In this case, the advanced analytical methods arising from mathematical analyses play an important role. Creating the suitable optimization problems that are heavily based on the data turns into a very important starting step. When the data in mathematical models involve the imprecision or fuzziness, the fuzzy sets theory becomes helpful in tackling the so-called fuzzy optimization problems.

On the other hand, studying the theory of fuzzy sets sometimes needs to utilize the technique of optimization. For example, the well-known Extension Principle that is frequently used in formulating and investigating the arithmetics of fuzzy numbers and fuzzification of crisp functions is expressed using the concept of supremum. Under suitable conditions, this kind of supremum can be realized as an optimization problem.

The relationship between maximum and minimum in optimization problems is termed “duality”. Studying this kind of symmetric concept will be helpful in solving the fuzzy optimization problems and fuzzy sets problems involving supremum. The topics of this Special Issue include, but are not limited to, the following:

  • Foundation of Fuzzy Sets (Fuzzy Arithmetic Operations, Extension Principle, Possibility Measures, etc.).
  • Fuzzy Logics (Many-Valued Logics, Type-2 Fuzzy Logics, Intuitionistic Fuzzy Logics, etc.).
  • Hybrid Systems (Fuzzy Control, Fuzzy Neural Networks, Genetic Fuzzy Systems, Fuzzy Intelligent Systems, Fuzzy Biomedical Systems, Fuzzy Chaotic Systems, Fuzzy Information Systems, etc.).
  • Nature of Computation (Ant Colony Optimization, Artificial Immune Systems, Genetic Algorithms, Particle Swarm Intelligence, Simulated Annealing, Tabu Search, etc.).
  • Numerical Methods of Fuzzy Optimization (Variants of Newton Method, Interior-point Method, Trust Region Method, etc.).
  • Operations Research and Management Sciences (Fuzzy Games Theory, Fuzzy Inventory Models, Fuzzy Queueing Theory, Fuzzy Scheduling Problems, Fuzzy Decision Making, Fuzzy Data Mining, Fuzzy Clustering, Stochastic Optimization, etc.).

Prof. Dr. Hsien-Chung Wu
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 games theory
  • fuzzy vector optimization
  • fuzzy goal programming
  • arithmetics of fuzzy intervals
  • fuzzification of crisp functions
  • extension principle

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Published Papers (3 papers)

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Research

54 pages, 506 KB  
Article
Enhancing Complex Decision-Making Under Uncertainty: Theory and Applications of q-Rung Neutrosophic Fuzzy Sets
by Omniyyah Saad Alqurashi and Kholood Mohammad Alsager
Symmetry 2025, 17(8), 1224; https://doi.org/10.3390/sym17081224 - 3 Aug 2025
Cited by 1 | Viewed by 524
Abstract
This thesis pioneers the development of q-Rung Neutrosophic Fuzzy Rough Sets (q-RNFRSs), establishing the first theoretical framework that integrates q-Rung Neutrosophic Sets with rough approximations to break through the conventional μq+ηq+νq≤1 constraint of existing [...] Read more.
This thesis pioneers the development of q-Rung Neutrosophic Fuzzy Rough Sets (q-RNFRSs), establishing the first theoretical framework that integrates q-Rung Neutrosophic Sets with rough approximations to break through the conventional μq+ηq+νq≤1 constraint of existing fuzzy–rough hybrids, achieving unprecedented capability in extreme uncertainty representation through our generalized model (Tq+Iq+Fq≤3). The work makes three fundamental contributions: (1) theoretical innovation through complete algebraic characterization of q-RNFRSs, including two distinct union/intersection operations and four novel classes of complement operators (with Theorem 1 verifying their involution properties via De Morgan’s Laws); (2) clinical breakthrough via a domain-independent medical decision algorithm featuring dynamic q-adaptation (q = 2–4) for criterion-specific uncertainty handling, demonstrating 90% diagnostic accuracy in validation trials—a 22% improvement over static models (p<0.001); and (3) practical impact through multi-dimensional uncertainty modeling (truth–indeterminacy–falsity), robust therapy prioritization under data incompleteness, and computationally efficient approximations for real-world clinical deployment. Full article
(This article belongs to the Special Issue The Fusion of Fuzzy Sets and Optimization Using Symmetry)
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19 pages, 293 KB  
Article
On Some Characterization Theorems for New Classes of Multiple-Objective Control Models
by Tareq Saeed and Savin Treanţă
Symmetry 2025, 17(5), 705; https://doi.org/10.3390/sym17050705 - 5 May 2025
Viewed by 349
Abstract
This paper introduces a new class of multiple-objective control models driven by path-independent curvilinear integrals involving the partial derivatives of the control variable. We investigate its solution set by considering a dual problem. Various duality results are formulated and proved in order to [...] Read more.
This paper introduces a new class of multiple-objective control models driven by path-independent curvilinear integrals involving the partial derivatives of the control variable. We investigate its solution set by considering a dual problem. Various duality results are formulated and proved in order to study and investigate the relationships between the set of solutions for these two variational control problems. Specifically, first, we establish that the value of the cost functional associated with the primal model cannot be greater than the value of the cost functional associated with the dual model. Secondly, the following two results present a strong-type duality between the variational models considered. At the end, we illustrate the main findings of the current paper with a numerical example. Full article
(This article belongs to the Special Issue The Fusion of Fuzzy Sets and Optimization Using Symmetry)
33 pages, 981 KB  
Article
Parallel Smell Agent Optimization (SAO): Collaborative Subpopulations for Accelerated Convergence
by Glykeria Kyrou, Ioannis G. Tsoulos, Anna Maria Gianni and Vasileios Charilogis
Symmetry 2025, 17(4), 592; https://doi.org/10.3390/sym17040592 - 13 Apr 2025
Cited by 1 | Viewed by 624
Abstract
In the dynamically evolving field of collective computational optimization, modern approaches increasingly incorporate bio-inspired techniques, such as Smell Agent Optimization (SAO), to address complex, high-dimensional problems inherent to contemporary scientific and industrial applications. While these methods are distinguished by their dynamic convergence and [...] Read more.
In the dynamically evolving field of collective computational optimization, modern approaches increasingly incorporate bio-inspired techniques, such as Smell Agent Optimization (SAO), to address complex, high-dimensional problems inherent to contemporary scientific and industrial applications. While these methods are distinguished by their dynamic convergence and heuristic ability to explore vast solution spaces, their growing computational complexity hinders their application in real-world, large-scale scenarios where simultaneous speed and precision are critical. To overcome this challenge, the present research advances a pioneering parallel implementation of SAO, which transcends simple workload distribution by integrating dynamic collaboration mechanisms and intelligent information dispersal among autonomous subpopulations. Concurrently, the method is enriched with innovative rules for exchanging optimal solutions between subpopulations. These rules not only prevent premature convergence to local minima but also establish a continuous flow of information that accelerates the global exploration of the solution space. Experimental validation of the proposed method demonstrated that, through optimized parameterization of the diffusion mechanisms, SAO’s efficiency can exceed 50%, achieving simultaneous reductions in both the number of objective function evaluations and total execution time. This outcome holds particular significance in high-dimensional problems, where balancing computational cost and accuracy is a decisive factor. These findings not only underscore the potential of parallel SAO to deliver sustainable solutions to real-world challenges but also open new horizons in the theory and practice of collective optimization. The implications extend to domains such as large-scale data analysis, autonomous systems, and adaptive resource management, where rapid and precise optimization is paramount. Full article
(This article belongs to the Special Issue The Fusion of Fuzzy Sets and Optimization Using Symmetry)
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