Recent Developments on Fuzzy Sets Extensions

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

Deadline for manuscript submissions: 30 June 2024 | Viewed by 11836

Special Issue Editor


E-Mail Website
Guest Editor
Department of Industrial Engineering, Istanbul Technical University, Istanbul, Turkey
Interests: engineering economics; quality control and management; statistical decision making; multicriteria decision making; fuzzy decision making
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

This Special Issue covers symmetry and asymmetry phenomena occurring in recent developments in fuzzy research problems. We invite authors to submit their theoretical or experimental research presenting engineering models under fuzziness dealing with the symmetry or asymmetry of different types of information.

This Special Issue is focused on the recent theoretical developments of ordinary fuzzy set extensions for modeling under vague and imprecise conditions. Topics of interest include, but are not limited to, the following theoretical and/or practical developments for modeling under fuzziness:

  • Type-2 fuzzy sets;
  • Hesitant fuzzy sets;
  • Intuitionistic fuzzy sets;
  • Spherical fuzzy sets;
  • Picture fuzzy sets;
  • Pythagorean fuzzy sets;
  • Q-rung orthopair fuzzy sets;
  • Neutrosophic sets;
  • Fermatean fuzzy sets;
  • Circular intuitionistic fuzzy sets.

Prof. Dr. Cengız Kahraman
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.

Published Papers (10 papers)

Order results
Result details
Select all
Export citation of selected articles as:

Research

23 pages, 3731 KiB  
Article
Selection of a Green Contractor for the Implementation of a Solar Power Plant Project
by Ilija Stojanović
Symmetry 2024, 16(4), 441; https://doi.org/10.3390/sym16040441 - 06 Apr 2024
Viewed by 348
Abstract
This study is focused on the problem of contractor selection for the implementation of a solar power plant project to produce electricity from sustainable sources for the needs of the company Voćar. The goal of this research is to select a construction contractor [...] Read more.
This study is focused on the problem of contractor selection for the implementation of a solar power plant project to produce electricity from sustainable sources for the needs of the company Voćar. The goal of this research is to select a construction contractor to install a solar power plant using sustainability criteria. With this power plant, the company Voćar can reduce its electricity costs and contribute to the production of sustainable energy. A total of three main sustainability criteria were used, in which six auxiliary criteria were symmetrically distributed. With these criteria, six suppliers were analyzed, and expert decision making was carried out with the application of the fuzzy–rough approach. To define the weights of the criteria, the SWARA method was utilized in this study. Based on the findings of this method, the most important criteria are the ecological criteria. Using the CRADIS method, the contractors were ranked, and the results show that contractor C6 has the best results and is the first choice for implementing this project. Choosing the best supplier increases the sustainability of project implementation and the realization of the expected effects. Full article
(This article belongs to the Special Issue Recent Developments on Fuzzy Sets Extensions)
Show Figures

Figure 1

24 pages, 774 KiB  
Article
Enhancing Similarity and Distance Measurements in Fermatean Fuzzy Sets: Tanimoto-Inspired Measures and Decision-Making Applications
by Hongpeng Wang, Caikuan Tuo, Zhiqin Wang, Guoye Feng and Chenglong Li
Symmetry 2024, 16(3), 277; https://doi.org/10.3390/sym16030277 - 27 Feb 2024
Viewed by 653
Abstract
Fermatean fuzzy sets (FFSs) serve as a nascent yet potent approach for coping with fuzziness, with their efficacy recently being demonstrated across a spectrum of practical contexts. Nevertheless, the scholarly literature remains limited in exploring the similarity and distance measures tailored for FFSs. [...] Read more.
Fermatean fuzzy sets (FFSs) serve as a nascent yet potent approach for coping with fuzziness, with their efficacy recently being demonstrated across a spectrum of practical contexts. Nevertheless, the scholarly literature remains limited in exploring the similarity and distance measures tailored for FFSs. The limited existing measures on FFSs sometimes yield counter-intuitive outcomes, which can obfuscate the accurate quantification of similarity and difference among FFSs. This paper introduces a suite of similarity and distance measures tailored for FFSs, drawing inspiration from the Tanimoto measure. We delve into the characteristics of these novel measures and offer some comparative studies with existing FFSs measures, highlighting their superior efficacy in the processing of fuzzy data from FFSs. Our proposed measures effectively rectify the counter-intuitive situations encountered with many existing measures and demonstrate a significant enhancement in differentiating between diverse FFSs. Moreover, we showcase the real-world applicability of our proposed measures through case studies in pattern recognition, medical diagnostics, and multi-attribute decision-making. Full article
(This article belongs to the Special Issue Recent Developments on Fuzzy Sets Extensions)
Show Figures

Figure 1

12 pages, 2666 KiB  
Article
Proposal for Mediative Fuzzy Control: From Type-1 to Type-3
by Oscar Castillo and Patricia Melin
Symmetry 2023, 15(10), 1941; https://doi.org/10.3390/sym15101941 - 20 Oct 2023
Viewed by 1146
Abstract
This paper presents an initial proposal for the utilization of mediative fuzzy logic in control problems. Mediative fuzzy logic (MFL) was originally proposed with the idea of modeling situations in which there exists contradictory knowledge among several experts in an application domain. In [...] Read more.
This paper presents an initial proposal for the utilization of mediative fuzzy logic in control problems. Mediative fuzzy logic (MFL) was originally proposed with the idea of modeling situations in which there exists contradictory knowledge among several experts in an application domain. In this situation, a mediative solution may be a better choice in this particular decision-making situation. In this paper, we are extending the concept of fuzzy control to the realm of MFL for situations in which we have two or more control experts, and the design of the fuzzy controller has to be based on their knowledge. In this situation, we are taking advantage of the symmetrical nature of membership functions in reducing the complexity of designing the fuzzy controllers. The goal of this study was to improve control results by combining the knowledge of several experts, which MFL is aimed at executing. The initial architecture of mediative fuzzy control for type-1 fuzzy logic is presented, and an illustrative example is used to better comprehend the proposed approach. Later, we extend type-1 MFL to the realms of type-2 and type-3 fuzzy logic, and we also provide a comparative study that exhibits that the type-3 version surpasses the type-2 and type-1 versions of mediative fuzzy control. The idea of utilizing type-2 and type-3 is to improve the capabilities of the fuzzy controller in handling uncertainty coming from noise in the control process. Full article
(This article belongs to the Special Issue Recent Developments on Fuzzy Sets Extensions)
Show Figures

Figure 1

19 pages, 665 KiB  
Article
A Fuzzy Parameterized Multiattribute Decision-Making Framework for Supplier Chain Management Based on Picture Fuzzy Soft Information
by Atiqe Ur Rahman, Tmader Alballa, Haifa Alqahtani and Hamiden Abd El-Wahed Khalifa
Symmetry 2023, 15(10), 1872; https://doi.org/10.3390/sym15101872 - 05 Oct 2023
Viewed by 695
Abstract
Supplier selection as a multiattribute decision-making (MADM) problem has various inherent uncertainties due to a number of symmetrical variables. In order to handle such information-based uncertainties, rational models like intuitionistic fuzzy sets have already been introduced in the literature. However, a picture fuzzy [...] Read more.
Supplier selection as a multiattribute decision-making (MADM) problem has various inherent uncertainties due to a number of symmetrical variables. In order to handle such information-based uncertainties, rational models like intuitionistic fuzzy sets have already been introduced in the literature. However, a picture fuzzy set (PiFS) with four dimensions of positive, neutral, negative, and rejection is better at capturing and interpreting such kinds of ambiguous information. Additionally, fuzzy parameterization (FPara) is helpful for evaluating the degree of uncertainty in the parameters. This study aims to develop a fuzzy parameterized picture fuzzy soft set (FpPiFSS) by integrating the ideas of PiFS and FPara. This integration is more adaptable and practical since it helps decision makers manage approximation depending on their objectivity and parameterization uncertainty. With the assistance of instructive examples, some of the set-theoretic operations are examined. A decision support framework is constructed using matrix manipulation, preferential weighting, fuzzy parameterized grades based on Pythagorean means, and the approximations of decision makers. This framework proposes a reliable algorithm to evaluate four timber suppliers (initially scrutinized by perusal process) based on eight categorical parameters for real estate projects. In order to accomplish suppliers evaluation, crucial validation outcomes are taken into account, including delivery level, purchase cost, capacity, product quality, lead time, green degree, location, and flexibility. To assess the advantages, dependability, and flexibility of the recommended strategy, comparisons in terms of computation and structure are provided. Consequently, the results are found to be reliable, analog, and consistent despite the use of fuzzy parameterization and picture fuzzy setting. Full article
(This article belongs to the Special Issue Recent Developments on Fuzzy Sets Extensions)
Show Figures

Figure 1

21 pages, 3503 KiB  
Article
New Variants of the Multi-Verse Optimizer Algorithm Adapting Chaos Theory in Benchmark Optimization
by Lucio Amezquita, Oscar Castillo, Jose Soria and Prometeo Cortes-Antonio
Symmetry 2023, 15(7), 1319; https://doi.org/10.3390/sym15071319 - 27 Jun 2023
Cited by 1 | Viewed by 1123
Abstract
In this work, we present multiple variations of the Multi-verse Optimizer Algorithm (MVO) using chaotic maps, using it in the formation of new solutions. In these new variations of the MVO algorithm, which we call the Fuzzy-Chaotic Multi-verse Optimizer (FCMVO), we use multiple [...] Read more.
In this work, we present multiple variations of the Multi-verse Optimizer Algorithm (MVO) using chaotic maps, using it in the formation of new solutions. In these new variations of the MVO algorithm, which we call the Fuzzy-Chaotic Multi-verse Optimizer (FCMVO), we use multiple chaotic maps used in the literature to substitute some of the parameters for which the original algorithm used a random value in the formation of new universes or solutions. To implement chaos theory on these new variants, we also use Fuzzy Logic for dynamic parameter adaptation; the first tests are performed only using chaotic maps, and then we merge the use of Fuzzy Logic in each of these cases to analyze the improvement over the Fuzzy MVO. Subsequently, we use only the best-performing chaos maps in a new set of variants for the same cases; after these results, we observe the behavior of the algorithm in different cases. The objective of this study is to compare whether there is a significant improvement over the MVO algorithm using some of the best-performing chaotic maps in conjunction with Fuzzy Logic in benchmark mathematical functions prior to moving on to other case studies. Full article
(This article belongs to the Special Issue Recent Developments on Fuzzy Sets Extensions)
Show Figures

Figure 1

23 pages, 1891 KiB  
Article
Geometric Aggregation Operators for Solving Multicriteria Group Decision-Making Problems Based on Complex Pythagorean Fuzzy Sets
by Ibrahim M. Hezam, Khaista Rahman, Ahmad Alshamrani and Darko Božanić
Symmetry 2023, 15(4), 826; https://doi.org/10.3390/sym15040826 - 29 Mar 2023
Cited by 2 | Viewed by 1014
Abstract
The Complex Pythagorean fuzzy set (CPyFS) is an efficient tool to handle two-dimensional periodic uncertain information, which has various applications in fuzzy modeling and decision making. It is known that the aggregation operators influence decision-making processes. Algebraic aggregation operators are the important and [...] Read more.
The Complex Pythagorean fuzzy set (CPyFS) is an efficient tool to handle two-dimensional periodic uncertain information, which has various applications in fuzzy modeling and decision making. It is known that the aggregation operators influence decision-making processes. Algebraic aggregation operators are the important and widely used operators in decision making techniques that deal with uncertain problems. This paper investigates some complex Pythagorean fuzzy geometric aggregation operators, such as complex Pythagorean fuzzy weighted geometric (CPyFWG), complex Pythagorean fuzzy ordered weighted geometric (CPyFOWG), complex Pythagorean fuzzy hybrid geometric (CPyFHG), induced complex Pythagorean fuzzy ordered weighted geometric (I-CPyFOWG), and induced complex Pythagorean fuzzy hybrid geometric (I-CPyFHG), and their structure properties, such as idempotency, boundedness, and monotonicity. In addition, we compare the proposed model with their existing models, such as complex fuzzy set and complex intuitionistic fuzzy set. We analyze an example involving the selection of an acceptable location for hospitals in order to demonstrate the effectiveness, appropriateness, and efficiency of the novel aggregation operators. Full article
(This article belongs to the Special Issue Recent Developments on Fuzzy Sets Extensions)
Show Figures

Figure 1

23 pages, 1842 KiB  
Article
Enhancing Interval-Valued Pythagorean Fuzzy Decision-Making through Dombi-Based Aggregation Operators
by Ghaliah Alhamzi, Saman Javaid, Umer Shuaib, Abdul Razaq, Harish Garg and Asima Razzaque
Symmetry 2023, 15(3), 765; https://doi.org/10.3390/sym15030765 - 20 Mar 2023
Cited by 12 | Viewed by 1233
Abstract
The success of any endeavor or process is heavily contingent on the ability to reconcile and satisfy balance requirements, which are often characterized by symmetry considerations. In practical applications, the primary goal of decision-making processes is to efficiently manage the symmetry or asymmetry [...] Read more.
The success of any endeavor or process is heavily contingent on the ability to reconcile and satisfy balance requirements, which are often characterized by symmetry considerations. In practical applications, the primary goal of decision-making processes is to efficiently manage the symmetry or asymmetry that exists within different sources of information. In order to address this challenge, the primary aim of this study is to introduce novel Dombi operation concepts that are formulated within the framework of interval-valued Pythagorean fuzzy aggregation operators. In this study, an updated score function is presented to resolve the deficiency of the current score function in an interval-valued Pythagorean fuzzy environment. The concept of Dombi operations is used to introduce some interval-valued Pythagorean fuzzy aggregation operators, including the interval-valued Pythagorean fuzzy Dombi weighted arithmetic (IVPFDWA) operator, the interval-valued Pythagorean fuzzy Dombi ordered weighted arithmetic (IVPFDOWA) operator, the interval-valued Pythagorean fuzzy Dombi weighted geometric (IVPFDWG) operator, and the interval-valued Pythagorean fuzzy Dombi ordered weighted geometric (IVPFDOWG) operator. Moreover, the study investigates many important properties of these operators that provide new semantic meaning to the evaluation. In addition, the suggested score function and newly derived interval-valued Pythagorean fuzzy Dombi aggregation (IVPFDA) operators are successfully employed to select a subject expert in a certain institution. The proposed approach is demonstrated to be successful through empirical validation. Lastly, a comparative study is conducted to demonstrate the validity and applicability of the suggested approaches in comparison with current techniques. This research contributes to the ongoing efforts to advance the field of evaluation and decision-making by providing novel and effective tools and techniques. Full article
(This article belongs to the Special Issue Recent Developments on Fuzzy Sets Extensions)
16 pages, 1682 KiB  
Article
An Intuitionistic Fuzzy Version of Hellinger Distance Measure and Its Application to Decision-Making Process
by Xiang Li, Zhe Liu, Xue Han, Nan Liu and Weihua Yuan
Symmetry 2023, 15(2), 500; https://doi.org/10.3390/sym15020500 - 14 Feb 2023
Cited by 12 | Viewed by 1236
Abstract
Intuitionistic fuzzy sets (IFSs), as a representative variant of fuzzy sets, has substantial advantages in managing and modeling uncertain information, so it has been widely studied and applied. Nevertheless, how to perfectly measure the similarities or differences between IFSs is still an open [...] Read more.
Intuitionistic fuzzy sets (IFSs), as a representative variant of fuzzy sets, has substantial advantages in managing and modeling uncertain information, so it has been widely studied and applied. Nevertheless, how to perfectly measure the similarities or differences between IFSs is still an open question. The distance metric offers an elegant and desirable solution to such a question. Hence, in this paper, we propose a new distance measure, named DIFS, inspired by the Hellinger distance in probability distribution space. First, we provide the formal definition of the new distance measure of IFSs, and analyze the outstanding properties and axioms satisfied by DIFS, which means it can measure the difference between IFSs well. Besides, on the basis of DIFS, we further present a normalized distance measure of IFSs, denoted DIFS˜. Moreover, numerical examples verify that DIFS˜ can obtain more reasonable and superior results. Finally, we further develop a new decision-making method on top of DIFS˜ and evaluate its performance in two applications. Full article
(This article belongs to the Special Issue Recent Developments on Fuzzy Sets Extensions)
Show Figures

Figure 1

21 pages, 760 KiB  
Article
Distributed and Asynchronous Population-Based Optimization Applied to the Optimal Design of Fuzzy Controllers
by Mario García-Valdez, Alejandra Mancilla, Oscar Castillo and Juan Julián Merelo-Guervós
Symmetry 2023, 15(2), 467; https://doi.org/10.3390/sym15020467 - 09 Feb 2023
Cited by 4 | Viewed by 1066
Abstract
Designing a controller is typically an iterative process during which engineers must assess the performance of a design through time-consuming simulations; this becomes even more burdensome when using a population-based metaheuristic that evaluates every member of the population. Distributed algorithms can mitigate this [...] Read more.
Designing a controller is typically an iterative process during which engineers must assess the performance of a design through time-consuming simulations; this becomes even more burdensome when using a population-based metaheuristic that evaluates every member of the population. Distributed algorithms can mitigate this issue, but these come with their own challenges. This is why, in this work, we propose a distributed and asynchronous bio-inspired algorithm to execute the simulations in parallel, using a multi-population multi-algorithmic approach. Following a cloud-native pattern, isolated populations interact asynchronously using a distributed message queue, which avoids idle cycles when waiting for other nodes to synchronize. The proposed algorithm can mix different metaheuristics, one for each population, first because it is possible and second because it can help keep total diversity high. To validate the speedup benefit of our proposal, we optimize the membership functions of a fuzzy controller for the trajectory tracking of a mobile autonomous robot using distributed versions of genetic algorithms, particle swarm optimization, and a mixed-metaheuristic configuration. We compare sequential versus distributed implementations and demonstrate the benefits of mixing the populations with distinct metaheuristics. We also propose a simple migration strategy that delivers satisfactory results. Moreover, we compare homogeneous and heterogenous configurations for the populations’ parameters. The results show that even when we use random heterogeneous parameter configuration in the distributed populations, we obtain an error similar to that in other work while significantly reducing the execution time. Full article
(This article belongs to the Special Issue Recent Developments on Fuzzy Sets Extensions)
Show Figures

Figure 1

21 pages, 3261 KiB  
Article
Supervised Machine Learning–Based Detection of Concrete Efflorescence
by Ching-Lung Fan and Yu-Jen Chung
Symmetry 2022, 14(11), 2384; https://doi.org/10.3390/sym14112384 - 11 Nov 2022
Cited by 2 | Viewed by 1592
Abstract
The development of automated systems for detecting defects in and damage to buildings is ongoing in the construction industry. Remaining aware of the surface conditions of buildings and making timely decisions regarding maintenance are crucial. In recent years, machine learning has emerged as [...] Read more.
The development of automated systems for detecting defects in and damage to buildings is ongoing in the construction industry. Remaining aware of the surface conditions of buildings and making timely decisions regarding maintenance are crucial. In recent years, machine learning has emerged as a key technique in image classification methods. It can quickly handle large amounts of symmetry and asymmetry in images. In this study, three supervised machine learning models were trained and tested on images of efflorescence, and the performance of the models was compared. The results indicated that the support vector machine (SVM) model achieved the highest accuracy in classifying efflorescence (90.2%). The accuracy rates of the maximum likelihood (ML) and random forest (RF) models were 89.8% and 87.0%, respectively. This study examined the influence of different light sources and illumination intensity on classification models. The results indicated that light source conditions cause errors in image detection, and the machine learning field must prioritize resolving this problem. Full article
(This article belongs to the Special Issue Recent Developments on Fuzzy Sets Extensions)
Show Figures

Figure 1

Back to TopTop