Symmetry

Research

14 pages, 300 KiB

Open AccessArticle

Interval-Valued Linguistic q-Rung Orthopair Fuzzy TODIM with Unknown Attribute Weight Information

by Yushu Zhang, Fangcheng Tang, Zeyuan Song and Jun Wang

Symmetry 2024, 16(9), 1161; https://doi.org/10.3390/sym16091161 - 5 Sep 2024

Viewed by 788

It is widely known that symmetry does exist in management systems, such as economics, management, and even daily life. In addition, effective and qualified decision-making methods can enhance the performance and symmetry of management systems. Hence, this paper focuses on a decision-making method. [...] Read more.

It is widely known that symmetry does exist in management systems, such as economics, management, and even daily life. In addition, effective and qualified decision-making methods can enhance the performance and symmetry of management systems. Hence, this paper focuses on a decision-making method. Linguistic interval-valued q-rung orthopair fuzzy sets (LIVq-ROFSs) have recently been proposed as being effective in describing decision-makers’ evaluation values in complex situations. This paper proposes a novel multi-attribute group decision-making (MAGDM) method with LIVq-ROFSs to handle realistic decision-making problems. The main contributions of this study are three-fold. First, a new method for determining the weight information of attributes based on decision makers’ evaluation values is proposed. Second, the classical TODIM is extended into LIVq-ROFSs and a new decision-making method is proposed. Third, our proposed MAGDM method is applied to a real decision-making problem to reveal its effectiveness. Full article

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

16 pages, 323 KiB

Open AccessArticle

An Innovative Algorithm Based on Octahedron Sets via Multi-Criteria Decision Making

by Güzide Şenel

Symmetry 2024, 16(9), 1107; https://doi.org/10.3390/sym16091107 - 26 Aug 2024

Viewed by 859

Abstract

Octahedron sets, which extend beyond the previously defined fuzzy set and soft set concepts to address uncertainty, represent a hybrid set theory that incorporates three distinct systems: interval-valued fuzzy sets, intuitionistic fuzzy sets, and traditional fuzzy set components. This comprehensive set theory is [...] Read more.

Octahedron sets, which extend beyond the previously defined fuzzy set and soft set concepts to address uncertainty, represent a hybrid set theory that incorporates three distinct systems: interval-valued fuzzy sets, intuitionistic fuzzy sets, and traditional fuzzy set components. This comprehensive set theory is designed to express all information provided by decision makers as interval-valued intuitionistic fuzzy decision matrices, addressing a broader range of demands than conventional fuzzy decision-making methods. Multi-criteria decision-making (MCDM) methods are essential tools for analyzing and evaluating alternatives across multiple dimensions, enabling informed decision making aligned with strategic objectives. In this study, we applied MCDM methods to octahedron sets for the first time, optimizing decision results by considering various constraints and preferences. By employing an MCDM algorithm, this study demonstrated how the integration of MCDM into octahedron sets can significantly enhance decision-making processes. The algorithm allowed for the systematic evaluation of alternatives, showcasing the practical utility and effectiveness of octahedron sets in real-world scenarios. This approach was validated through influential examples, underscoring the value of algorithms in leveraging the full potential of octahedron sets. Furthermore, the application of MCDM to octahedron sets revealed that this hybrid structure could handle a wider range of decision-making problems more effectively than traditional fuzzy set approaches. This study not only highlights the theoretical advancements brought by octahedron sets but also provides practical evidence of their application, proving their importance and usefulness in complex decision-making environments. Overall, the integration of octahedron sets and MCDM methods marks a significant step forward in decision science, offering a robust framework for addressing uncertainty and optimizing decision outcomes. This research paves the way for future studies to explore the full capabilities of octahedron sets, potentially transforming decision-making practices across various fields. Full article

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

27 pages, 1550 KiB

Open AccessArticle

An Integrated Bayesian Best–Worst Method and Consensus-Based Intuitionistic Fuzzy Evaluation Based on Distance from Average Solution Approach for Evaluating Alternative Aircraft Models from a Sustainability Perspective

by Ergun Arı and Mehtap Dursun

Symmetry 2024, 16(8), 1086; https://doi.org/10.3390/sym16081086 - 21 Aug 2024

Viewed by 890

Abstract

Sustainability in transportation is vital for lessening environmental effects and ensuring the long-term viability of the transportation industry. The aviation sector, a significant player in sustainable transport, has encountered obstacles in reducing its ecological footprint, especially in aircraft design and operation. Symmetry and [...] Read more.

Sustainability in transportation is vital for lessening environmental effects and ensuring the long-term viability of the transportation industry. The aviation sector, a significant player in sustainable transport, has encountered obstacles in reducing its ecological footprint, especially in aircraft design and operation. Symmetry and asymmetry exist widely in the aviation sector, as in other industrial applications. Multicriteria decision making (MCDM) is an important research topic that is widely applied to practical decision-making problems and is considered a complex tool with which to balance the symmetry between goals and conflicting criteria. This research assesses different airplane models in order to pinpoint the most environmentally friendly options using the Bayesian best–worst (BWM) method for evaluating criteria and the consensus-based intuitionistic fuzzy evaluation based on distance from average solution (IF EDAS) method for assessing alternatives. The Bayesian BWM approach facilitates group decision making on criteria evaluation and systematically evaluates factors like fuel efficiency, emissions, and noise levels, offering a holistic view of each airplane model’s sustainability performance. Conversely, consensus-based IF EDAS allows for the ranking of alternatives based on their distance to the average solution for a sustainable airplane model while concurrently considering multiple criteria, guiding decisionmakers to a consensus and eliminating the asymmetry between opinions before the final decision. This study reveals that technical features are the critical criteria for airplanes and significantly influence alternative rankings. The findings indicate that the chosen decision criteria greatly impact the selection of the most sustainable airplane model as part of a sustainable transportation system, potentially altering ranking orders. Full article

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

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29 pages, 4690 KiB

Open AccessArticle

A Study on Complex t-Neutrosophic Graph with Intention to Preserve Biodiversity

by Murugan Kaviyarasu, Luminița-Ioana Cotîrlă, Daniel Breaz, Murugesan Rajeshwari and Eleonora Rapeanu

Symmetry 2024, 16(8), 1033; https://doi.org/10.3390/sym16081033 - 12 Aug 2024

Viewed by 612

Abstract

This study introduces the notion of complex t-neutrosophic graphs (CTNGs) as a powerful tool for understanding and displaying complex interactions that are sometimes difficult to understand. It demonstrates that CTNGs may accurately reflect complicated interactions involving several components or dimensions within a particular [...] Read more.

This study introduces the notion of complex t-neutrosophic graphs (CTNGs) as a powerful tool for understanding and displaying complex interactions that are sometimes difficult to understand. It demonstrates that CTNGs may accurately reflect complicated interactions involving several components or dimensions within a particular scenario. It also instructs the basic set operations of CTNGs and analyzes notions like homomorphism and isomorphism within this framework. Furthermore, the research describes a practical application of CTNGs. It illustrates their value in addressing biodiversity conservation by taking into account a variety of relevant factors. The paper uses this application to highlight the flexibility and effectiveness of CTNGs as a tool for decision-makers to visualize and prioritize activities targeted at improving biodiversity conservation. Full article

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

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23 pages, 924 KiB

Open AccessArticle

Advancing Sustainable Urban Development: Navigating Complexity with Spherical Fuzzy Decision Making

by Mohd Anjum, Hong Min, Gaurav Sharma and Zubair Ahmed

Symmetry 2024, 16(6), 670; https://doi.org/10.3390/sym16060670 - 29 May 2024

Cited by 1 | Viewed by 985

Abstract

This study explores the complexities of urban planning and addresses major issues by carefully weighing four options for smart city technology, community-based development, green infrastructure investment, and transit-oriented development. Unlike traditional evaluations, our study applies the novel SWARA-WASPAS model to spherical fuzzy sets [...] Read more.

This study explores the complexities of urban planning and addresses major issues by carefully weighing four options for smart city technology, community-based development, green infrastructure investment, and transit-oriented development. Unlike traditional evaluations, our study applies the novel SWARA-WASPAS model to spherical fuzzy sets (SFSs), thus identifying and navigating the uncertainty present in decision making. This methodological approach improves the accuracy of our assessment by providing detailed information about the advantages and disadvantages of each option. Our study offers useful insights for urban policymakers and planners using carefully weighted criteria and employing a methodical ranking procedure. The aim is to provide insights for decisions that promote equity, environmental consciousness, resilience, and symmetry in urban environments. The application of the SWARA-WASPAS approach not only advances the field but also provides a strong basis for informed decision making. This improves the accuracy of our evaluations and provides detailed insights into each option’s pros and cons. Our study uses weighted criteria and systematic ranking to advise urban policymakers and planners. Our main goal is to help urban populations make resilient, environmentally responsible, equitable, and symmetrical decisions. Our research aims to further the conversation on sustainable urban development by offering a framework based on data that addresses the difficulties associated with dynamic urban environments. In the end, we want our humanized viewpoint to speak to a wider audience and inspire a shared dedication to creating cities that flourish in the face of changing urban environments. Full article

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

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19 pages, 493 KiB

Open AccessArticle

Novel Distance Measures of q-Rung Orthopair Fuzzy Sets and Their Applications

by Donglai Wang, Yige Yuan, Zhe Liu, Sijia Zhu and Zhifang Sun

Symmetry 2024, 16(5), 574; https://doi.org/10.3390/sym16050574 - 7 May 2024

Cited by 3 | Viewed by 1352

Abstract

The q-rung orthopair fuzzy sets (q-ROFSs), a novel concept for processing vague information, offer a more potent and all-encompassing method compared to traditional fuzzy sets, intuitionistic fuzzy sets, and Pythagorean fuzzy sets. The inclusion of the parameter q allows for [...] Read more.

The q-rung orthopair fuzzy sets (q-ROFSs), a novel concept for processing vague information, offer a more potent and all-encompassing method compared to traditional fuzzy sets, intuitionistic fuzzy sets, and Pythagorean fuzzy sets. The inclusion of the parameter q allows for the q-rung orthopair fuzzy sets to capture a broader range of uncertainty of information. In this paper, we present two novel distance measures for q-ROFSs inspired by the Jensen–Shannon divergence, called

D_{J S_2 D}

and

D_{J S_3 D}

, and we analyze some properties they satisfy, such as non-degeneracy, symmetry, boundedness, and triangular inequality. Then, the normalized distance measures, called

D_{\tilde{J S_2 D}}

and

D_{\tilde{J S_3 D}}

, are proposed and we verify their rationality through numerical experiments. Finally, we apply the proposed distance measures to practical scenarios, including pattern recognition and multicriteria decision-making, and the results demonstrate the effectiveness of the proposed distance measures. Full article

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

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30 pages, 598 KiB

Open AccessArticle

A Nonlinear Programming Approach to Solving Interval-Valued Intuitionistic Hesitant Noncooperative Fuzzy Matrix Games

by Shuvasree Karmakar and Mijanur Rahaman Seikh

Symmetry 2024, 16(5), 573; https://doi.org/10.3390/sym16050573 - 7 May 2024

Viewed by 773

Abstract

Initially, fuzzy sets and intuitionistic fuzzy sets were used to address real-world problems with imprecise data. Eventually, the notion of the hesitant fuzzy set was formulated to handle decision makers’ reluctance to accept asymmetric information. However, in certain scenarios, asymmetric information is gathered [...] Read more.

Initially, fuzzy sets and intuitionistic fuzzy sets were used to address real-world problems with imprecise data. Eventually, the notion of the hesitant fuzzy set was formulated to handle decision makers’ reluctance to accept asymmetric information. However, in certain scenarios, asymmetric information is gathered in terms of a possible range of acceptance and nonacceptance by players rather than specific values. Furthermore, decision makers exhibit some hesitancy regarding this information. In such a situation, all the aforementioned expansions of fuzzy sets are unable to accurately represent the scenario. The purpose of this article is to present asymmetric information situations in which the range of choices takes into account the hesitancy of players in accepting or not accepting information. To illustrate these problems, we develop matrix games that consider the payoffs of interval-valued intuitionistic hesitant fuzzy elements (IIHFEs). Dealing with these types of fuzzy programming problems requires a significant amount of effort. To solve these matrix games, we formulate two interval-valued intuitionistic hesitant fuzzy programming problems. Preserving the hesitant nature of the payoffs to determine the optimal strategies, these two problems are transformed into two nonlinear programming problems. This transformation involves using mathematical operations for IIHFEs. Here, we construct a novel aggregation operator of IIHFEs, viz., min-max operators of IIHFEs. This operator is suitable for applying the developed methodology. The cogency and applicability of the proposed methodology are verified through a numerical example based on the situation of conflict between hackers and defenders to prevent damage to cybersecurity. To validate the superiority of the proposed model along with the computed results, we provide comparisons with the existing models. Full article

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

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23 pages, 3731 KiB

Open AccessArticle

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 - 6 Apr 2024

Viewed by 961

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)

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24 pages, 774 KiB

Open AccessArticle

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

Cited by 4 | Viewed by 1509

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)

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12 pages, 2666 KiB

Open AccessArticle

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

Cited by 5 | Viewed by 1648

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)

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19 pages, 665 KiB

Open AccessArticle

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 - 5 Oct 2023

Cited by 4 | Viewed by 1216

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)

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21 pages, 3503 KiB

Open AccessArticle

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 4 | Viewed by 1703

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)

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23 pages, 1891 KiB

Open AccessArticle

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 5 | Viewed by 1547

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)

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23 pages, 1842 KiB

Open AccessArticle

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 17 | Viewed by 1822

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

Open AccessArticle

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 19 | Viewed by 1653

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

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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21 pages, 760 KiB

Open AccessArticle

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 - 9 Feb 2023

Cited by 6 | Viewed by 1608

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)

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21 pages, 3261 KiB

Open AccessArticle

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 4 | Viewed by 2124

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)

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