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Symmetry
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Fuzzy Relation Equations: Trends and Applications
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Fuzzy Relation Equations: Trends and Applications

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

Deadline for manuscript submissions: closed (30 November 2022) | Viewed by 5704

Special Issue Editors

Dr. Salvatore Sessa

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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
Prof. Dr. Ferdinando Di Martino

E-Mail Website
Guest Editor
Department of Architecture, University of Naples Federico II | UNINA, Napoli, Italy
Interests: fuzzy relations and fuzzy transform in image and data analysis; fuzzy intelligent systems in data and spatial data analysis; fuzzy clustering in spatial analysis and hot spot analysis fuzzy; fuzzy clustering in image segmentation; GIS; fuzzy reasoning in GIS environments
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 widely dealt with and known. Applications are oriented by looking for several types of relation equations. Mainly, fuzzy systems are ruled from suitable equations where internally the fuzzy relation mimics the ties between inputs and the outputs of the system. This Special Issue contains the most recent trends and related applications of fuzzy relation equations in the real world; many authors have implemented theory and practice within certain applications, publishing their works on many journals worldwide. We invite the authors to present their past and future ideas in papers limited to any topic connected to relation equations, revisiting either concepts which 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‘ work looked to complete Brouwerian lattices for finding an environment in which 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. Salvatore Sessa
Dr. Ferdinando Di Martino
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 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.

Published Papers (4 papers)

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Research

14 pages, 1485 KiB  
Article
Hybrid Fuzzy K-Medoids and Cat and Mouse-Based Optimizer for Markov Weighted Fuzzy Time Series
by Deshinta Arrova Dewi, Sugiyarto Surono, Rajermani Thinakaran and Afif Nurraihan
Symmetry 2023, 15(8), 1477; https://doi.org/10.3390/sym15081477 - 25 Jul 2023
Viewed by 847
Abstract
This study seeks to test novel capabilities, specifically those of the hybrid fuzzy k-medoids (FKM) and cat and mouse-based optimizer (CMBO) partitioning approach, in overcoming the Markov weighted fuzzy time series (MWFTS) limitation in creating U talk intervals without fundamental standards. Researchers created [...] Read more.
This study seeks to test novel capabilities, specifically those of the hybrid fuzzy k-medoids (FKM) and cat and mouse-based optimizer (CMBO) partitioning approach, in overcoming the Markov weighted fuzzy time series (MWFTS) limitation in creating U talk intervals without fundamental standards. Researchers created a hybrid cat and mouse-based optimizer–fuzzy k-medoids (CMBOFKM) approach to be used with MWTS, since these limits may impair the accuracy of the MWFTS approach. Symmetrically, the hybrid method of CMBOFKM is an amalgamation of the FKM and CMBO methods, with the CMBO method playing a part in optimizing the cluster center of the FKM partition method to obtain the best U membership matrix value as the medoid value that will be used in the MWFTS’s fuzzification stage. Air quality data from Klang, Malaysia are used in the MWFTS–CMBOFKM technique. The evaluation of the model error values, known as mean absolute percentage error (MAPE) and root mean square error, yields the MWFTS–CMBOFKM evaluation findings that are displayed (RMSE). A 6.85% MAPE percentage and a 6071 RMSE score are shown by MWFTS–CMBOFKM using air quality data from Klang, Malaysia. The FKM partition approach can be hybridized with additional optimization techniques in the future to increase the MWFTS method’s precision. Full article
(This article belongs to the Special Issue Fuzzy Relation Equations: Trends and Applications)
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27 pages, 763 KiB  
Article
Complex Intuitionistic Fuzzy Aczel-Alsina Aggregation Operators and Their Application in Multi-Attribute Decision-Making
by Tahir Mahmood, Zeeshan Ali, Samruam Baupradist and Ronnason Chinram
Symmetry 2022, 14(11), 2255; https://doi.org/10.3390/sym14112255 - 27 Oct 2022
Cited by 17 | Viewed by 1225
Abstract
To handle complex, risk-illustrating, and asymmetric information, the theory discussed in this analysis is much more suitable for evaluating the above dilemmas. To manage ambiguity and inconsistency in real-life problems, the principle of Aczel–Alsina (AA) t-norm and t-conorm was initiated in 1980. These [...] Read more.
To handle complex, risk-illustrating, and asymmetric information, the theory discussed in this analysis is much more suitable for evaluating the above dilemmas. To manage ambiguity and inconsistency in real-life problems, the principle of Aczel–Alsina (AA) t-norm and t-conorm was initiated in 1980. These norms are massively modified and different from prevailing norms due to parameter p, where 0<p<+∞. The major contribution of this analysis is to analyze the AA operational laws (addition, multiplication, score value, accuracy value) under the complex intuitionistic fuzzy (CIF) settings. Furthermore, we initiated the principle of CIFAA weighted averaging (CIFAAWA), CIFAA ordered weighted averaging (CIFAAOWA), CIFAA hybrid averaging (CIFAAHA), CIFAA weighted geometric (CIFAAWG), CIFAA ordered weighted geometric (CIFAAOWG), CIFAA hybrid geometric (CIFAAHG), as well as their beneficial results. Additionally, to consider the elaborated works, a multi-attribute decision-making (MADM) technique was explored to investigate the supremacy and feasibility of the developed works. The main influence of this manuscript is how to choose the best decision under the availability of asymmetric types of information given by different experts. Finally, we performed the sensitivity analysis and graphically show the presented work with the help of several examples. Full article
(This article belongs to the Special Issue Fuzzy Relation Equations: Trends and Applications)
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13 pages, 303 KiB  
Article
A Weak Tripled Contraction for Solving a Fuzzy Global Optimization Problem in Fuzzy Metric Spaces
by Hasanen A. Hammad and Manuel De la Sen
Symmetry 2021, 13(4), 565; https://doi.org/10.3390/sym13040565 - 29 Mar 2021
Cited by 2 | Viewed by 1142
Abstract
In the setting of fuzzy metric spaces (FMSs), a global optimization problem (GOP) obtaining the distance between two subsets of an FMS is solved by a tripled fixed-point (FP) technique here. Also, fuzzy weak tripled contractions (WTCs) for that are given. This problem [...] Read more.
In the setting of fuzzy metric spaces (FMSs), a global optimization problem (GOP) obtaining the distance between two subsets of an FMS is solved by a tripled fixed-point (FP) technique here. Also, fuzzy weak tripled contractions (WTCs) for that are given. This problem was known before in metric space (MS) as a proximity point problem (PPP). The result is correct for each continuous τ—norms related to the FMS. Furthermore, a non-trivial example to illustrate the main theorem is discussed. Full article
(This article belongs to the Special Issue Fuzzy Relation Equations: Trends and Applications)
15 pages, 1363 KiB  
Article
Dimensional Analysis under Linguistic Pythagorean Fuzzy Set
by Aldo Joel Villa Silva, Luis Pérez-Domínguez, Erwin Martínez Gómez, David Luviano-Cruz and Delia Valles-Rosales
Symmetry 2021, 13(3), 440; https://doi.org/10.3390/sym13030440 - 08 Mar 2021
Cited by 8 | Viewed by 1534
Abstract
Dimensional analysis under linguistic Pythagorean fuzzy set (DA-LPFS) is a technique to handle qualitative (intangible) as well as the interactions between criteria, by combining dimensional analysis (DA) and Pythagorean fuzzy set (PFS) with linguistic variables. In this paper, a novel DA method is [...] Read more.
Dimensional analysis under linguistic Pythagorean fuzzy set (DA-LPFS) is a technique to handle qualitative (intangible) as well as the interactions between criteria, by combining dimensional analysis (DA) and Pythagorean fuzzy set (PFS) with linguistic variables. In this paper, a novel DA method is proposed for LPFSs based in a PFS extension, in order to consider the mutual relationship among criteria and handle qualitative (fuzzy) and quantitative (crisp) information usually involved in Multi-criteria decision making (MCDM) problems. Finally, DA-LPFS is applied to handle a case concerning the selection of CNC router to illustrate the applicability of the method. Full article
(This article belongs to the Special Issue Fuzzy Relation Equations: Trends and Applications)
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