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Special Issue "Recent Developments on Fuzzy Sets Extensions"

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

Deadline for manuscript submissions: closed (15 May 2023) | Viewed by 3701

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Prof. Dr. Cengız Kahraman

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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
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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 2000 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 (5 papers)

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Research

Open AccessArticle

Geometric Aggregation Operators for Solving Multicriteria Group Decision-Making Problems Based on Complex Pythagorean Fuzzy Sets

and

Symmetry 2023, 15(4), 826; https://doi.org/10.3390/sym15040826 - 29 Mar 2023

Viewed by 431

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 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)

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Open AccessArticle

Enhancing Interval-Valued Pythagorean Fuzzy Decision-Making through Dombi-Based Aggregation Operators

and

Symmetry 2023, 15(3), 765; https://doi.org/10.3390/sym15030765 - 20 Mar 2023

Cited by 2 | Viewed by 431

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 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)

Open AccessArticle

An Intuitionistic Fuzzy Version of Hellinger Distance Measure and Its Application to Decision-Making Process

and

Symmetry 2023, 15(2), 500; https://doi.org/10.3390/sym15020500 - 14 Feb 2023

Viewed by 657

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 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

D_{I F S}

, 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

D_{I F S}

, which means it can measure the difference between IFSs well. Besides, on the basis of

D_{I F S}

, we further present a normalized distance measure of IFSs, denoted

D_{\tilde{I F S}}

. Moreover, numerical examples verify that

D_{\tilde{I F S}}

can obtain more reasonable and superior results. Finally, we further develop a new decision-making method on top of

D_{\tilde{I F S}}

and evaluate its performance in two applications. Full article

(This article belongs to the Special Issue Recent Developments on Fuzzy Sets Extensions)

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Open AccessArticle

Distributed and Asynchronous Population-Based Optimization Applied to the Optimal Design of Fuzzy Controllers

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 1 | Viewed by 602

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 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)

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Open AccessArticle

Supervised Machine Learning–Based Detection of Concrete Efflorescence

Ching-Lung Fan

and

Yu-Jen Chung

Symmetry 2022, 14(11), 2384; https://doi.org/10.3390/sym14112384 - 11 Nov 2022

Cited by 1 | Viewed by 863

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 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)

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