Symmetry in Fuzzy Relation Equations

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

Deadline for manuscript submissions: 30 April 2025 | Viewed by 4065

Special Issue Editors


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Dipartimento di Architettura, Università degli Studi di Napoli Federico II, Via Toledo 402, 80134 Napoli, Italy
Interests: fuzzy sets and fuzzy relations; soft computing; fuzzy transform image processing theory; machine learning; data mining
Special Issues, Collections and Topics in MDPI journals

E-Mail Website
Guest Editor
Dipartimento di Architettura, Università degli Studi di Napoli Federico II, Via Toledo 402, 80134 Napoli, Italy
Interests: fuzzy relation equations; fixed point theory; geographical information systems
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues, 

Since the late Elie Sanchez, in 1976, started the study of fuzzy relation equations, a lot of water has passed under the bridge; theory and practice were and are being widely dealt with and known. Applications are oriented by looking for several types of relation equations. Fuzzy systems are mainly governed by suitable equations where, internally, the fuzzy relation mimics the ties between inputs and the system outputs. This Special Issue will present the most recent trends and fuzzy-related applications and equations in the real world; many authors have implemented theory and practice within certain applications, publishing their works in many journals worldwide. We invite the authors to present their past and future ideas in papers on any topic connected to relation equations, revisiting either concepts that have not had their due and necessary attention, or new concepts or new types of relation equations motivated from applicational aspects. Papers connected to the mathematical aspects of relation equations are also welcome; giving the fundamentals of algebraic structures is an important and cogent topic. On the other hand, Sanchez’s work looked to complete Brouwerian lattices for determining an environment in which the diagnosis of diseases is well adapted to the symptoms displayed by patients (Sanchez was also a practicing doctor). This Special Issue is dedicated to him. In summary, we welcome papers dealing with any aspect of fuzzy relation equations, either theoretical or/and applicative.

Prof. Dr. Ferdinando Di Martino
Prof. Dr. Salvatore Sessa
Guest Editors

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Keywords

  • fuzzy relations
  • fuzzy equations
  • fuzzy similarity
  • fuzzy equivalence
  • fuzzy systems

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Published Papers (2 papers)

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Research

16 pages, 286 KiB  
Article
Neutrosophic 𝔑-Structures in Semimodules over Semirings
by Ghulam Muhiuddin, Nabilah Abughazalah, Balasubramanian Elavarasan, Kasi Porselvi and Deena Al-Kadi
Symmetry 2024, 16(1), 41; https://doi.org/10.3390/sym16010041 - 28 Dec 2023
Viewed by 1745
Abstract
The study of symmetry is a fascinating and unifying subject that connects various areas of mathematics in the twenty-first century. Algebraic structures offer a framework for comprehending the symmetries of geometric objects in pure mathematics. This paper introduces new concepts in algebraic structures, [...] Read more.
The study of symmetry is a fascinating and unifying subject that connects various areas of mathematics in the twenty-first century. Algebraic structures offer a framework for comprehending the symmetries of geometric objects in pure mathematics. This paper introduces new concepts in algebraic structures, concentrating on semimodules over semirings and analysing the neutrosophic structure in this context. We explore the properties of neutrosophic subsemimodules and neutrosophic ideals after defining them. We discuss, utilizing neutrosophic products, the representations of neutrosophic ideals and subsemimodules, as well as the relationship between neutrosophic products and intersections. Finally, we derive equivalent criteria in terms of neutrosophic structures for a semiring to be fully idempotent. Full article
(This article belongs to the Special Issue Symmetry in Fuzzy Relation Equations)
12 pages, 3091 KiB  
Article
A Novel Image Similarity Measure Based on Greatest and Smallest Eigen Fuzzy Sets
by Ferdinando Di Martino and Salvatore Sessa
Symmetry 2023, 15(5), 1104; https://doi.org/10.3390/sym15051104 - 18 May 2023
Cited by 2 | Viewed by 1682
Abstract
A novel image similarity index based on the greatest and smallest fuzzy set solutions of the max–min and min–max compositions of fuzzy relations, respectively, is proposed. The greatest and smallest fuzzy sets are found symmetrically as the min–max and max–min solutions, respectively, to [...] Read more.
A novel image similarity index based on the greatest and smallest fuzzy set solutions of the max–min and min–max compositions of fuzzy relations, respectively, is proposed. The greatest and smallest fuzzy sets are found symmetrically as the min–max and max–min solutions, respectively, to a fuzzy relation equation. The original image is partitioned into squared blocks and the pixels in each block are normalized to [0, 1] in order to have a fuzzy relation. The greatest and smallest fuzzy sets, found for each block, are used to measure the similarity between the original image and the image reconstructed by joining the squared blocks. Comparison tests with other well-known image metrics are then carried out where source images are noised by applying Gaussian filters. The results show that the proposed image similarity measure is more effective and robust to noise than the PSNR and SSIM-based measures. Full article
(This article belongs to the Special Issue Symmetry in Fuzzy Relation Equations)
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