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Keywords = q-rung orthopair fuzzy sets

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27 pages, 1540 KB  
Article
Unraveling COVID-19’s Impact on Raw Material Supply Chains and Production in the Turkish Pipe Industry: A Critical ANOVA and Advanced MCDM Evaluation
by Hatef Javadi, Oguz Toragay, Mehmet Akif Yerlikaya, Marco Falagario and Nicola Epicoco
Appl. Sci. 2026, 16(2), 959; https://doi.org/10.3390/app16020959 - 16 Jan 2026
Viewed by 121
Abstract
This paper analyzes the impact of COVID-19 on the supply chain and production, investigating countermeasures for industrial recovery. In particular, the study examines how COVID-19 has affected the raw material supply chain, production, and outages on a real case study, that is, Turkey’s [...] Read more.
This paper analyzes the impact of COVID-19 on the supply chain and production, investigating countermeasures for industrial recovery. In particular, the study examines how COVID-19 has affected the raw material supply chain, production, and outages on a real case study, that is, Turkey’s Glass-Reinforced Plastic (GRP) pipe industry. Using two- and three-way analysis of variance (ANOVA), significant negative impacts on the raw material supply chain are identified with 95% confidence. To enhance decision-making, the fuzzy q-rung orthopair set (FQROPS) and entropy-based multi-criteria decision-making (MCDM) methods are integrated in the baseline method. Specifically, ANOVA-identified factors, such as cost, supply continuity, production capacity, and risk level, are used as criteria in the MCDM analysis. Entropy determined criteria weights and FQROPS evaluate alternatives based on their proximity to the ideal solution. Findings show that significant disruptions occurred due to the pandemic. In addition, the MCDM analysis reveals that pre-pandemic conditions for key materials, such as fiberglass and resin, were significantly more favorable in terms of cost, supply continuity, production capacity, and risk levels. This integrated approach provides strategic insights for managing supply chains and production in the GRP pipe industry during and after pandemic events. Full article
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44 pages, 642 KB  
Article
A Fractional q-Rung Orthopair Fuzzy Tensor Framework for Dynamic Group Decision-Making: Application to Smart City Renewable Energy Planning
by Muhammad Bilal, Chaoqian Li, A. K. Alzahrani and A. K. Aljahdali
Fractal Fract. 2026, 10(1), 52; https://doi.org/10.3390/fractalfract10010052 - 13 Jan 2026
Viewed by 108
Abstract
In complex decision-making scenarios, such as smart city renewable energy project selection, decision-makers must contend with multi-dimensional uncertainty, conflicting expert opinions, and evolving temporal dynamics. This study introduces a novel Fractional q-Rung Orthopair Fuzzy Tensor (Fq-ROFT)-based group decision-making methodology that integrates the flexibility [...] Read more.
In complex decision-making scenarios, such as smart city renewable energy project selection, decision-makers must contend with multi-dimensional uncertainty, conflicting expert opinions, and evolving temporal dynamics. This study introduces a novel Fractional q-Rung Orthopair Fuzzy Tensor (Fq-ROFT)-based group decision-making methodology that integrates the flexibility of q-rung orthopair fuzzy sets with tensorial representation and fractional-order dynamics. The proposed framework allows for the modeling of positive and negative membership degrees in a multi-dimensional, time-dependent structure while capturing memory effects inherent in expert evaluations. A detailed case study involving six renewable energy alternatives and six criteria demonstrates the method’s ability to aggregate expert opinions, compute fractional dynamic scores, and provide robust, reliable rankings. Comparative analysis with existing approaches, including classical q-ROFSs, intuitionistic fuzzy sets, and weighted sum methods, highlights the superior discriminative power, consistency, and dynamic sensitivity of the Fq-ROFT approach. Sensitivity analysis confirms the robustness of the top-ranked alternatives under variations in expert weights and fractional orders and membership perturbations. The study concludes by discussing the advantages, limitations, and future research directions of the proposed methodology, establishing Fq-ROFT as a powerful tool for dynamic, high-dimensional, and uncertain group decision-making applications. Full article
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29 pages, 943 KB  
Article
A Linguistic q-Rung Orthopair ELECTRE II Algorithm for Fuzzy Multi-Criteria Ontology Ranking
by Ameeth Sooklall and Jean Vincent Fonou-Dombeu
Big Data Cogn. Comput. 2025, 9(11), 277; https://doi.org/10.3390/bdcc9110277 - 3 Nov 2025
Viewed by 487
Abstract
In recent years, interest in the application of ontologies in various domains of knowledge has grown significantly. Ontologies are widely used in a myriad of areas, such as artificial intelligence, data integration, knowledge management, and the semantic web, to name but a few. [...] Read more.
In recent years, interest in the application of ontologies in various domains of knowledge has grown significantly. Ontologies are widely used in a myriad of areas, such as artificial intelligence, data integration, knowledge management, and the semantic web, to name but a few. However, despite the widespread adoption, there exist a range of problems associated with ontologies, such as the complexity and cognitive challenges associated with ontology engineering, design, and development. One of the solutions to these challenges is to reuse existing ontologies rather than developing new ontologies afresh for new applications. The reuse of ontologies that describe a knowledge domain is a complex task consisting of many aspects. One of the key aspects involves ranking ontologies to aid in their selection. Various techniques have been proposed for this task, but many of them fall short in their expressiveness and ability to capture the cognitive aspects of human-like decision-making processes. Furthermore, much of the existing research focuses on an objective approach to ontology ranking, but it is unquestionable that a wide range of aspects pertaining to the quality of an ontology simply cannot be captured in a quantitative manner. Existing ranking models fail to provide a robust and flexible canvas for facilitating qualitative ontology ranking and selection for reuse. To address the aforementioned shortcomings of existing ontology ranking approaches, this study proposes a novel algorithm for ranking ontologies that extends the Elimination and Choice Translating Reality (ELECTRE) multi-criteria decision-making method with the Linguistic q-Rung Orthopair Fuzzy Set (Lq-ROFS-ELECTRE II), allowing the expression of uncertainty in a more robust and precise manner. The new Lq-ROFS-ELECTRE II algorithm was applied to rank a set of 19 ontologies of the machine learning (ML) domain. The ML ontologies were evaluated using a set of seven qualitative criteria extracted from the Ontometric framework. The proposed Lq-ROFS-ELECTRE II algorithm was then applied to rank the 19 ontologies in light of the seven criteria. The ranking results obtained were compared against the quantitative rankings of the same 19 ontologies using the traditional ELECTRE II algorithm, and confirmed the validity of the ranking performed by the proposed Lq-ROFS-ELECTRE II algorithm and its effectiveness in the task of ontology ranking. Furthermore, a comparative analysis of the proposed Lq-ROFS-ELECTRE II against existing MCDM methods and other existing fuzzy ELECTRE II methods displayed its superior modeling capabilities that allow for more natural decision evaluation from subject experts in real-world applications and allow the decision-maker to have much flexibility in expressing their preferences. These capabilities of the Lq-ROFS-ELECTRE II algorithm make it applicable not only in ontology ranking, but in any domain where there exist decision-making scenarios that comprise multiple conflicting criteria under uncertainty. Full article
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17 pages, 1159 KB  
Article
Assessing Voluntary Guardianship and Personal Autonomy Using a Circular q-Rung Orthopair Fuzzy CoCoFISo Decision Framework
by Xin Li
Symmetry 2025, 17(10), 1658; https://doi.org/10.3390/sym17101658 - 5 Oct 2025
Viewed by 447
Abstract
A balance between support and independence in guardianship systems is of high concern, especially with those who need help in making decisions. The research presents a novel approach to evaluating voluntary models of guardianship, focusing on the preservation of individual autonomy and examining [...] Read more.
A balance between support and independence in guardianship systems is of high concern, especially with those who need help in making decisions. The research presents a novel approach to evaluating voluntary models of guardianship, focusing on the preservation of individual autonomy and examining the underlying decision symmetry in assessing diverse guardianship options. The ultimate solution to the inherent uncertainty and lack of objectivity in expert evaluations is to apply the circular q-rung orthopair fuzzy (Cq-ROF) combined compromise for ideal solution (CoCoFISo) approach, an effective multi-criteria decision-making (MCDM) model that integrates ranking and sorting views using a Cq-ROF framework within a symmetry-oriented analytical perspective. These are five major assessment factors: how well autonomy is preserved, legal and ethical adherence, psychological health, social integration aid, and risk prevention. It explores ten alternative approaches to guardianship, ranging from complete legal guardianship to community-based self-management solutions, and the use of technology as an element of support. The suggested approach can facilitate more sophisticated modelling of expert opinions, rather than relying on simplistic and straightforward distinctions and diverse evaluations. The case study results indicate that the hybrid and supported forms of decision-making could offer opportunities to preserve a high degree of personal autonomy while ensuring safety and compliance. The research gives a coherent, adaptable, and explainable approach to managing ethical and policy-level judgment concerning voluntary guardianship systems. Full article
(This article belongs to the Section Mathematics)
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21 pages, 2681 KB  
Article
A Novel q-Type Semi-Dependent Neutrosophic Decision-Making Approach and Its Applications in Supplier Selection
by Jinbo Zhang and Minghua Shi
Information 2025, 16(9), 742; https://doi.org/10.3390/info16090742 - 28 Aug 2025
Viewed by 638
Abstract
The principles of least effort and the illusion of control may influence the decision-making process. It is challenging for a decision-maker to maintain complete independence when assessing the membership and non-membership degrees of indicators. However, existing neutrosophic sets and q-rung orthopair fuzzy sets [...] Read more.
The principles of least effort and the illusion of control may influence the decision-making process. It is challenging for a decision-maker to maintain complete independence when assessing the membership and non-membership degrees of indicators. However, existing neutrosophic sets and q-rung orthopair fuzzy sets assume full independence of such information. In view of this, this paper proposes a new neutrosophic set, namely the q-type semi-dependent neutrosophic set (QTSDNS), based on the classical neutrosophic set, whose membership and non-membership degrees are interrelated. QTSDNS is a generalized form of classical semi-dependent fuzzy sets, such as the intuitionistic neutrosophic set. It contains a regulatory parameter, which allows for decision-makers to flexibly adjust the model. Furthermore, a multi-attribute group decision-making (MAGDM) algorithm is proposed by integrating QTSDNS with evidence theory to solve the supplier selection problem. The algorithm first utilizes QTSDNS to represent the preference information of experts, then employs the q-TSDNWAA (or q-TSDNWGA) operator to aggregate the evaluation information of individual experts. Following the analysis of the mathematical relationship between QTSDNS and evidence theory, evidence theory is used to aggregate the evidence from each expert to obtain the group trust interval. Then, the best supplier is determined using interval number ranking methods. Finally, a numerical example is provided to demonstrate the feasibility of the proposed method. Full article
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15 pages, 1191 KB  
Article
Harnessing High-Altitude Advantages: Sustainable Data Center Site Selection in Ski Resort Regions for Optimized Energy Efficiency
by Sinan Öztaş
Sustainability 2025, 17(8), 3494; https://doi.org/10.3390/su17083494 - 14 Apr 2025
Viewed by 1369
Abstract
Data centers are a part of the digital economy, but they are great contributors to energy use and carbon emissions. The site selection for data centers can, therefore, be an important tool in the optimization of energy efficiency and sustainability, especially in those [...] Read more.
Data centers are a part of the digital economy, but they are great contributors to energy use and carbon emissions. The site selection for data centers can, therefore, be an important tool in the optimization of energy efficiency and sustainability, especially in those areas where climatic and infrastructural factors can keep environmental impacts as low as possible. This study will evaluate seven possible sites for a data center in Turkey, focusing on high-altitude ski resorts with natural cooling advantages. In the paper, the research uses q-Rung Orthopair Fuzzy Numbers (q-ROFs) in combination with methods like Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) and VIseKriterijumska Optimizacija I Kompromisno Resenje (VIKOR), taking environmental, technical, and socio-economic criteria into consideration, such as energy efficiency, disaster risk, infrastructure quality, and accessibility. To strengthen result reliability, a sensitivity analysis by varying the q parameter and a comprehensive study by performing different multi-criteria decision-making (MCDM) methods were employed. Analysis revealed that Erciyes and Uludağ consistently ranked among the top alternatives across all methods and q values, indicating their robustness. The results confirm the effectiveness of the proposed methodology in supporting sustainable and high-altitude-aware site selection decisions. This research presents a holistic and Sustainable Site Selection framework for data centers; therefore, it provides actionable insights into stakeholders who balance operational efficiency with environmental responsibility. Future studies should subsequently delve into dynamic modeling and global applications to enhance the versatility of the framework. Full article
(This article belongs to the Section Energy Sustainability)
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30 pages, 2972 KB  
Article
A Novel Approach for Multi-Criteria Decision-Making Problem with Linguistic q-Rung Orthopair Fuzzy Attribute Weight Information
by Minghua Shi and Jinbo Zhang
Symmetry 2024, 16(12), 1641; https://doi.org/10.3390/sym16121641 - 11 Dec 2024
Cited by 2 | Viewed by 1075
Abstract
Linguistic q-Rung orthopair fuzzy set is a new extension of the linguistic Pythagorean fuzzy set, which effectively represents the fuzzy and uncertain decision-making information based on qualitative modeling. However, its operational rules are unable to process pure linguistic exponential calculations, in which the [...] Read more.
Linguistic q-Rung orthopair fuzzy set is a new extension of the linguistic Pythagorean fuzzy set, which effectively represents the fuzzy and uncertain decision-making information based on qualitative modeling. However, its operational rules are unable to process pure linguistic exponential calculations, in which the exponents are represented using linguistic q-Rung orthopair fuzzy values and the bases are represented as linguistic terms or interval linguistic numbers. This greatly restricts its application in decision making under complex environments. As the complement of the existing linguistic q-Rung orthopair fuzzy operational rules, this paper defines linguistic q-Rung orthopair fuzzy calculation rules, including division, subtraction, and exponent operations. Based on theorem-based proofs, the relevant properties of the calculation rules have been analyzed, such as commutative law, distributive law, symmetry, and so on. Moreover, in order to facilitate the application of linguistic q-Rung orthopair fuzzy theory, this paper introduces the concept of dual linguistic q-Rung orthopair fuzzy value. Building on this foundation, a series of weighted aggregation operators for the calculations involving linguistic q-Rung orthopair fuzzy values and dual linguistic q-Rung orthopair fuzzy values have been designed. In conclusion, a novel pure linguistic multi criteria decision-making methodology is introduced in this work. The validity and utility of the proposed method are demonstrated via a real-world application in the decision process of energy resource exploitation. Full article
(This article belongs to the Section Mathematics)
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40 pages, 475 KB  
Article
Decision Analysis Algorithm Using Frank Aggregation in the SWARA Framework with p,qRung Orthopair Fuzzy Information
by Jawad Ali, Suhad Ali Osman Abdallah and N. S. Abd EL-Gawaad
Symmetry 2024, 16(10), 1352; https://doi.org/10.3390/sym16101352 - 12 Oct 2024
Cited by 11 | Viewed by 1093
Abstract
The present study introduces an innovative approach to multi-criteria decision making (MCDM) aimed at handling decision analysis involving p,qrung orthopair fuzzy (p,qROF) data, where the criteria weights are completely unknown. To achieve this objective, we formulate [...] Read more.
The present study introduces an innovative approach to multi-criteria decision making (MCDM) aimed at handling decision analysis involving p,qrung orthopair fuzzy (p,qROF) data, where the criteria weights are completely unknown. To achieve this objective, we formulate generalized operational rules referred to as Frank operational rules, tailored for p,qROF numbers (p,qROFNs) utilizing the Frank t-norm and t-conorm. With these newly devised operations as a foundation, we create a variety of p,qROF aggregation operators (AOs) to effectively aggregate p,qROF information. Furthermore, we examine specific instances of these operators and rigorously establish their desirable properties, including idempotency, monotonicity, boundedness, and symmetry. Subsequently, we adapt the SWARA technique to the realm of p,qROF fuzzy data and this adapted technique becomes instrumental in determining criteria weights within the proposed MCDM framework centered around proposed AOs. We furnish a descriptive example to exemplify the practicality of the developed approach. Lastly, the effectiveness and soundness of our approach are underscored through both parameter analysis and a comparative evaluation. Full article
(This article belongs to the Section Engineering and Materials)
14 pages, 300 KB  
Article
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
Cited by 1 | Viewed by 1645
Abstract
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)
24 pages, 1614 KB  
Review
Review of Intelligent Methods and Their Potential Use towards a Smart Grid Negotiation Framework
by Dimitrios K. Panagiotou and Anastasios I. Dounis
Appl. Sci. 2024, 14(12), 5196; https://doi.org/10.3390/app14125196 - 14 Jun 2024
Cited by 2 | Viewed by 1662
Abstract
The integration of Distributed Energy Resources utilizing Renewable Energy Sources, Energy Storage Systems, and Information and Communication Technologies is transforming traditional energy systems into adaptable, flexible, and sustainable systems, with the Smart Grid concept playing a pivotal role. This paper surveys intelligent techniques [...] Read more.
The integration of Distributed Energy Resources utilizing Renewable Energy Sources, Energy Storage Systems, and Information and Communication Technologies is transforming traditional energy systems into adaptable, flexible, and sustainable systems, with the Smart Grid concept playing a pivotal role. This paper surveys intelligent techniques and methods applied in various markets and applications, particularly focusing on their potential adaptation for negotiation processes in Smart Grid contexts. The negotiation mechanisms, crucial for prosumers who engage in real-time transactions, are analyzed with a focus on fuzzy logic tools, specifically q-Rung Orthopair Fuzzy Sets. These tools are evaluated for their capability to handle negotiation tasks and Multi-Criteria Decision-Making problems. The paper proposes a negotiation schema for healthcare buildings, especially hospitals, given their significant environmental impact, providing insight for future research. Full article
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21 pages, 1119 KB  
Article
An Integrated Q-Rung Orthopair Fuzzy (Q-ROF) for the Selection of Supply-Chain Management
by Babek Erdebilli and Çiğdem Sıcakyüz
Sustainability 2024, 16(12), 4901; https://doi.org/10.3390/su16124901 - 7 Jun 2024
Cited by 10 | Viewed by 2738
Abstract
The integration of sustainable indicators into supply-chain management (SCM), including cost, innovation capability, quality, service capability, long-term cooperation, environmental management system, pollution reduction, green image, social responsibility, and employment practices, has become essential for conducting strategic analyses of the entire supply-chain process competitive [...] Read more.
The integration of sustainable indicators into supply-chain management (SCM), including cost, innovation capability, quality, service capability, long-term cooperation, environmental management system, pollution reduction, green image, social responsibility, and employment practices, has become essential for conducting strategic analyses of the entire supply-chain process competitive advantage. This study proposes a fuzzy integration multi-criteria decision-making (MCDM) method to solve SCM issues. To navigate this complexity, a multi-criterion decision-making (MCDM) framework is employed, integrating MCDM methods with fuzzy logic to effectively address subjective environmental criteria. This innovative approach not only enhances supply-chain management (SCM) but also emphasizes the necessity for ongoing innovation in tackling contemporary supply-chain challenges. It serves as a cornerstone for sustainable supplier selection practices and optimizing SCM processes. In this study, a hybrid fuzzy MCDM method is proposed for supplier selection. The method addresses supplier selection by utilizing evaluations from expert decision-makers based on predetermined criteria. This comprehensive approach ensures that all relevant factors are considered, promoting sustainable and efficient supply-chain management. Full article
(This article belongs to the Special Issue Sustainable Supply Chain and Operations Management: 2nd Edition)
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19 pages, 493 KB  
Article
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 14 | Viewed by 2846
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 DJS_2D and DJS_3D, and we analyze some properties they satisfy, such as non-degeneracy, symmetry, boundedness, and triangular inequality. Then, the normalized distance measures, called DJS_2D˜ and DJS_3D˜, 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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28 pages, 337 KB  
Article
On Circular q-Rung Orthopair Fuzzy Sets with Dombi Aggregation Operators and Application to Symmetry Analysis in Artificial Intelligence
by Zeeshan Ali and Miin-Shen Yang
Symmetry 2024, 16(3), 260; https://doi.org/10.3390/sym16030260 - 20 Feb 2024
Cited by 25 | Viewed by 2607
Abstract
Circular q-rung orthopair fuzzy sets (FSs) were recently considered as an extension of q-rung orthopair FSs (q-ROFSs), circular intuitionistic FSs (Cir-IFSs), and circular Pythagorean FSs (Cir-PFSs). However, they are only considered for some simple algebraic properties. In this paper, we advance the work [...] Read more.
Circular q-rung orthopair fuzzy sets (FSs) were recently considered as an extension of q-rung orthopair FSs (q-ROFSs), circular intuitionistic FSs (Cir-IFSs), and circular Pythagorean FSs (Cir-PFSs). However, they are only considered for some simple algebraic properties. In this paper, we advance the work on circular q-ROFSs (Cirq-ROFSs) in Dombi aggregation operators (AOs) with more mathematical properties of algebraic laws. These include the circular q-rung orthopair fuzzy (Cirq-ROF) Dombi weighted averaging (Cirq-ROFDWA), Cirq-ROF Dombi ordered weighted averaging (Cirq-ROFDOWA), Cirq-ROF Dombi weighted geometric (Cirq-ROFDWG), and Cirq-ROF Dombi ordered weighted geometric (Cirq-ROFDOWG) operators. Additionally, we present the properties of idempotency, monotonicity, and boundedness for the proposed operators. In the context of artificial intelligence, symmetry analysis plays a significant and efficient role that can refer to several aspects. Thus, to compute the major aspect, we identify the multi-attribute decision-making (MADM) technique based on the proposed operators for Cirq-ROF numbers (Cirq-ROFNs) to enhance the worth of the evaluated operators. Finally, we use some existing techniques for comparison to our results to show the validity and supremacy of the proposed method. Full article
46 pages, 7408 KB  
Article
Hamacher Operations for Complex Cubic q-Rung Orthopair Fuzzy Sets and Their Application to Multiple-Attribute Group Decision Making
by Qian Yu
Symmetry 2023, 15(12), 2118; https://doi.org/10.3390/sym15122118 - 27 Nov 2023
Cited by 4 | Viewed by 1578
Abstract
In this paper, based on the advantages of q-rung orthopair fuzzy sets (q-ROFSs), complex fuzzy sets (CFSs) and cubic sets (CSs), the concept of complex cubic q-rung orthopair fuzzy sets (CCuq-ROFSs) is introduced and their operation rules and properties are discussed. The objective [...] Read more.
In this paper, based on the advantages of q-rung orthopair fuzzy sets (q-ROFSs), complex fuzzy sets (CFSs) and cubic sets (CSs), the concept of complex cubic q-rung orthopair fuzzy sets (CCuq-ROFSs) is introduced and their operation rules and properties are discussed. The objective of this paper was to develop some novel Maclaurin symmetric mean (MSM) operators for any complex cubic q-rung orthopair fuzzy numbers (CCuq-ROFNs) using Hamacher t-norm and t-conorm inspired arithmetic operations. The advantage of employing Hamacher t-norm and t-conorm based arithmetic operations with the MSM operator lies in their ability to take into account not only the interrelationships among multiple attributes but also to provide flexibility in the aggregation process due to the involvement of additional parameters. Also, the prominent characteristic of the MSM is that it can capture the interrelationship among the multi-input arguments and can provide more flexible and robust information fusion. Thus, based on the CCuq-ROF environment, we develop some new Hamacher operations for CCuq-ROFSs, such as the complex cubic q-rung orthopair fuzzy Hamacher average (CCuq-ROFHA) operator, the weighted complex cubic q-rung orthopair fuzzy Hamacher average (WCCuq-ROFHA) operator, the complex cubic q-rung orthopair fuzzy Hamacher Maclaurin symmetric mean (CCuq-ROFHMSM) operator and the weighted complex cubic q-rung orthopair fuzzy Hamacher Maclaurin symmetric mean (WCCuq-ROFHMSM) operator. Further, we develop a novel multi-attribute group decision-making (MAGDM) approach based on the proposed operators in a complex cubic q-rung orthopair fuzzy environment. Finally, a numerical example is provided to demonstrate the effectiveness and superiority of the proposed method through a detailed comparison with existing methods. Full article
(This article belongs to the Section Mathematics)
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36 pages, 811 KB  
Article
Interval-Valued p,q-Rung Orthopair Fuzzy Exponential TODIM Approach and Its Application to Green Supplier Selection
by Jawad Ali and Zareen A. Khan
Symmetry 2023, 15(12), 2115; https://doi.org/10.3390/sym15122115 - 27 Nov 2023
Cited by 16 | Viewed by 2723
Abstract
An interval-valued q-rung orthopair fuzzy set (IVqrOFS) is a robust and esteemed model in managing imprecise information, utilizing a controllable parameter q1. Expanding its applicability, we propose a refinement to it, termed [...] Read more.
An interval-valued q-rung orthopair fuzzy set (IVqrOFS) is a robust and esteemed model in managing imprecise information, utilizing a controllable parameter q1. Expanding its applicability, we propose a refinement to it, termed the interval-valued p,q-rung orthopair fuzzy set, denoted IVp,qrOFS. This advancement enables the handling of scenarios where varied assessment levels for membership and non-membership grades are necessary, a challenge unaddressed by existing extensions of interval-valued intuitionistic fuzzy sets. We establish the fundamental mathematical operations for the IVp,qrOFS and explore their key properties. To compare interval-valued p,q-rung orthopair fuzzy (IVp,qrOF) numbers, a novel score function is put forward and compared to the known IVqrOFS-based score functions to determine its viability. Moreover, we present IVp,qrOF aggregation operators (AOs), accompanied by rigorous proof of their essential characteristics, including boundedness, monotonicity, and symmetry. This study introduces the interaction of IVp,qrOF criteria through the inter-criteria correlation (CRITIC) approach. This method determines criteria weights based on the proposed distance measurements and the score function. The CRITIC method is integrated with the exponential TODIM approach (exp-TODIM), resulting in an innovative decision-making framework that is less susceptible to parameter fluctuations and showcases a high stability. An illustrative example of selecting a suitable supplier is provided to demonstrate the practical application of the developed exp-TODIM approach. Finally, a sensitivity analysis is conducted to exhibit the method’s stability, and a comparative analysis is performed to elucidate its strengths and advantages. Full article
(This article belongs to the Section Engineering and Materials)
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