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According to survey data released by the National Bureau of Statistics, from 2011 to 2022, the total output value of China's construction industry showed an increasing trend year by year. From 2018 to 2021, infrastructure investment has always maintained a positive growth, indicating that the current construction industry is in a rapid development stage. In order to improve the development quality of the construction industry as much as possible, it is of great significance to develop the whole Process engineering consulting service model. The quality evaluation of whole process engineering consulting service modes is MAGDM. The single-valued neutrosophic sets (SVNSs) is useful tool to cope with uncertain information during the quality evaluation of whole process engineering consulting service modes. In this paper, the single-valued neutrosophic number combined TOPSIS (SVNN-CTOPSIS) model based on single-valued neutrosophic number Hamming distances (SVNNHD) and single-valued neutrosophic number Euclidean distance (SVNNED) is formed to cope with the MAGDM. The CRITIC model is utilized to obtain the weight numbers in light with the SVNNHD and SVNNED under SVNSs. Finally, numerical example and comparative analysis for quality evaluation of whole process engineering consulting service modes is utilized to verify SVNN-CTOPSIS model. The main contributions of this study are formed: (1) the CRITIC model is formed to obtain the weight numbers in light with SVNNHD and SVNNED; (2) the SVNN-CTOPSIS model is formed in light with SVNNHD and SVNNED under SVNNs; (3) Finally, numerical example and comparative analysis for quality evaluation of whole process engineering consulting service modes is employed to verify SVNN-CTOPSIS model. [ABSTRACT FROM AUTHOR]

In order to conduct an in-depth study of Zhan’s methodology pertaining to the covering of multigranulation fuzzy rough sets ( C MG FRSs), we build two families: the family of fuzzy β -minimum descriptions and the family of β -maximum descriptions. Subsequently, utilizing these notions, we proceed to develop two variations of covering via optimistic (pessimistic) multigranuation rough set samples ( CO(P) MG FRS). The axiomatic properties are examined. In this study, we examine four models of covering using variable precision multigranulation fuzzy rough sets ( CVP MG FRSs). We proceed with analyzing the features of these models. Interconnections between these planned plans are also elucidated. This study explores algorithms that aim to identify innovative strategies for addressing multiattribute group decision-making problems (MAGDM) and multicriteria group decision-making problems (MCGDM). The test examples have been elucidated to provide an inclusive grasp of the efficacy of the offered samples. Ultimately, the distinctions between our methodologies and the preexisting research have been demonstrated. [ABSTRACT FROM AUTHOR]

Multi-attribute group decision making (MAGDM) is a pivotal tool in diverse evaluations. However, existing approaches often overlook attribute ambiguity and interrelationships, leading to unreliable outcomes. This article introduces a novel MAGDM support scheme that extends the widely accepted ORESTE (organísation, rangement et Synthese dèdonnees relarionnelles, in French) method to the context of Probabilistic Hesitant Interval-Value Sets (PHIVSs). PHIVSs integrate Hesitant Fuzzy Linguistic Terms (HFLTs) and Probabilistic Linguistic Term Sets (PLTSs) and transform conventional linguistic terms into interval-based expressions. This augmentation significantly extends their applicability in MAGDM scenarios, particularly those marked by elevated uncertainty. The conventional ORESTE model, a standard MAGDM tool, encounters limitations in intricate scenarios, resulting in data loss and necessitating more adaptive solutions. Our integrated PHIVS approach overcomes these challenges by incorporating fuzzy representation into ORESTE, enabling robust MAGDM solutions. Preferences are classified into three intensities based on likelihoods, establishing a structured Preference Intensity Relation (PIR). PIR effectively discerns among alternatives, elucidating preferences, indifference, or incomparability. This distinction proves invaluable in complex and uncertain decision-making across diverse domains. A key innovation of our approach lies in the unexplored application of PHIVS and ORESTE in MAGDM. Utilizing probability measures for PHIVSs, we establishes precise binary connections among alternatives for enhancing assessment and prioritization. The representation of evaluations with PHIVS and integration of likelihood measures offer an efficient solution for intricate MAGDM problems, particularly those laden with uncertainty. To illustrate the utility of our approach, we provide two comprehensive examples. These examples showcase the practicality and effectiveness of our approach in real-world assessments, highlighting its significance in advancing decision-making methodologies. [ABSTRACT FROM AUTHOR]

In the process of multi-attribute group decision-making (MAGDM), the cubic q-rung orthopair fuzzy sets (Cuq-ROFSs) are utilized to express membership and non-membership degrees in the form of interval values to efficiently cope with decision makers' (DMs') complex assessment values. To more efficiently capture DM evaluation results in the MAGDM procedure, we offer a novel tool called 2-tuple linguistic cubic q-rung orthopair fuzzy set (2TLCuq-ROFS), which extends Cuq-ROFS by using 2-tuple linguistic (2TL) terms. 2TLCuq-ROFS effectively incorporates the advantages of 2TL and Cuq-ROFS, making them attractive and versatile for depicting attribute values in an uncertain and complex decision-making environment. To effectively aggregate the attribute values in the form of 2-tuple linguistic cubic q-rung orthopair fuzzy numbers (2TLCuq-ROFNs), some Maclaurin symmetric mean (MSM) operators and their weighted forms are presented in this paper. The weight information for attributes is unknown. Therefore, the criteria importance through inter-criteria correlation (CRITIC) method is employed to determine the objective weight information. The purpose of this study is to incorporate a conventional multi-attributive border approximation area comparison (MABAC) framework based on 2TLCuq-ROFNs because it addresses problematic and imprecise decision-making problems by calculating the distance among each alternative and the border approximation area by using 2TLCuq-ROFNs and MSM aggregation operators. First, some basic concepts associated with 2TLCuq-ROFNs and the CRITIC-MABAC procedure are briefly explained. Moreover, an evaluation framework based on the improved CRITIC-MABAC method is established. An explanatory case study related to the risk investment problem in Belt and Road is used to verify the validity and practicality of the designed evaluation framework. In conclusion, by utilizing the CRITIC-MABAC methodology based on proposed operators, we find that Λ 7 is the optimal alternative for risk investment. Furthermore, comparison analysis emphasizes the integrity and prominent features of the proposed methodology and provides various complementary perspectives for investors. [ABSTRACT FROM AUTHOR]

Abstract r, s, t-spherical fuzzy (r, s, t-SPF) sets provide a robust framework for managing uncertainties in decision-making, surpassing other fuzzy sets in their ability to accommodate diverse uncertainties through the incorporation of flexible parameters r, s, and t. Considering these characteristics, this article explores sine trigonometric laws to enhance the applicability and theoretical foundation for r, s, t-SPF setting. Following these laws, several aggregation operators (AOs) are designed for aggregation of the r, s, t-SPF data. Meanwhile, the desired characteristics and relationships of these operators are studied under sine trigonometric functions. Furthermore, we build a group decision-making algorithm for addressing multiple attribute group decision-making (MAGDM) problems using the developed AOs. To exemplify the applicability of the proposed algorithm, we address a practical example regarding laptop selection. Finally, parameter analysis and a comprehensive comparison with existing operators are conducted to uncover the superiority and validity of the presented AOs.

The development of sustainable supply chain finance (SSCF) promotes the improvement of the long-term production and operational performance of enterprises. It is significant to explore both environmentally friendly and cost-effective solutions, especially in the presence of uncertain information. The triangular neutrosophic number (TrNN) can enable decision-makers (DMs) to express their preferences in high uncertainty. This paper aims to provide a systematic multiple-attribute group decision-making (MAGDM) framework to support DMs in prioritizing sustainable development plannings by combining the best-worst method (BWM), optimization model of maximizing deviation method, and uniformity entropy theory. Moreover, a TrNN-based extended TOPSIS method is developed to measure the differences in DMs’ importance. We incorporate the cumulative prospect theory (CPT) method to account for DMs’ psychological behaviors in risk scenarios. The CPT-VIKOR methodology is employed to rank alternatives, enhancing the precision of decision-making. Finally, the proposed approach is successfully applied to the LNG industry to illustrate its applicability. [ABSTRACT FROM AUTHOR]

In this paper, we define the Quadripartition Neutrosophic Weighted Neutrality Aggregative (QNWNA) operator and Quadripartition Neutrosophic Ordered Weighted Neutrality Aggregative (QNOWNA) operator for solving Multi-Attribute Group Decision Making (MAGDM) problems. The basic properties of both operators are discussed thoroughly. A new MAGDM strategy is developed using these developed operators. A case study of e-commerce site selection in India is discussed to show the applicability of the proposed MADM strategy. Moreover, the performance of the QNWNA and QNOWNA operators are compared with Quadripartition Neutrosophic Weighted Arithmetic Aggregation (QNWAA) operator and Quadripartition Neutrosophic Weighted Geometric Aggregation (QNWGA), Quadripartition Single valued Neutrosophic Dombi Weighted Arithmetic Aggregation (QSVNDWAA) and QSVN Dombi Weighted Geometric Aggregation (QSVNDWAA) operator. [ABSTRACT FROM AUTHOR]

With the increasing uncertainty in information, fuzzy theory has become a crucial approach for solving Multiple Attribute Group Decision Making (MAGDM) problems. This paper proposes two methods for addressing MAGDM problems with interval-valued Fermatean fuzzy information. Firstly, a series of Hamacher operators on the interval-valued Fermatean fuzzy numbers (IVFFNs) are derived, based on the fundamental operational norms of IVFFNs and the definitions of Hamacher operators. Secondly, two decision-making methods are proposed in this paper, based on the newly introduced operators, and they are effectively applied to address the enterprise recruitment problem. Finally, we investigate the influence of parameters on the final decision and observe that variations in parameters have small impact on the outcome. This feature simplifies the decision-making process by eliminating the need for extensive parameter tuning. Furthermore, a comparative analysis is conducted between the proposed methods and the research of other scholars, demonstrating the effectiveness of our approach and validating its reliability. [ABSTRACT FROM AUTHOR]

The interval-valued intuitionistic fuzzy sets (IVIFSs), based on the intuitionistic fuzzy sets (IFSs), combine the classical decision method and its research and application is attracting attention. After a comparative analysis, it becomes clear that multiple classical methods with IVIFSs' information have been applied to many practical issues. In this paper, we extended the classical EDAS method based on the Cumulative Prospect Theory (CPT) considering the decision experts (DEs)' psychological factors under IVIFSs. Taking the fuzzy and uncertain character of the IVIFSs and the psychological preference into consideration, an original EDAS method, based on the CPT under IVIFSs (IVIF-CPT-EDAS) method, is created for multiple-attribute group decision making (MAGDM) issues. Meanwhile, the information entropy method is used to evaluate the attribute weight. Finally, a numerical example for Green Technology Venture Capital (GTVC) project selection is given, some comparisons are used to illustrate the advantages of the IVIF-CPT-EDAS method and a sensitivity analysis is applied to prove the effectiveness and stability of this new method. [ABSTRACT FROM AUTHOR]

In response to the growing maturation of technological level in the modern medical industry, this paper proposes the PZLMVF-VIKOR method to tackle uncertain multi-attribute group decision-making in smart healthcare. First, a novel Pythagorean Z-linguistic modified value function based on regret theory is defined to consider the impact of DMs' emotions on decision outcomes. Then, a combined weighting method is used to obtain the final attribute weight vector by the closeness degree, with the expert weight determination based on consensus measures. Subsequently, we propose an extended VIKOR method in Pythagorean Z-linguistic environment to solve the evaluation problem of the development in smart healthcare. Finally, a practical case and some comparative analysis is conducted to illustrate the justifiability and effectiveness of this method. [ABSTRACT FROM AUTHOR]

r, s, t-spherical fuzzy (r, s, t-SPF) sets provide a robust framework for managing uncertainties in decision-making, surpassing other fuzzy sets in their ability to accommodate diverse uncertainties through the incorporation of flexible parameters r, s, and t. Considering these characteristics, this article explores sine trigonometric laws to enhance the applicability and theoretical foundation for r, s, t-SPF setting. Following these laws, several aggregation operators (AOs) are designed for aggregation of the r, s, t-SPF data. Meanwhile, the desired characteristics and relationships of these operators are studied under sine trigonometric functions. Furthermore, we build a group decision-making algorithm for addressing multiple attribute group decision-making (MAGDM) problems using the developed AOs. To exemplify the applicability of the proposed algorithm, we address a practical example regarding laptop selection. Finally, parameter analysis and a comprehensive comparison with existing operators are conducted to uncover the superiority and validity of the presented AOs. [ABSTRACT FROM AUTHOR]

Vietnam, a country in Southeast Asia, is anticipated to experience an increase in energy consumption due to the growth of its manufacturing and industrial sectors, which aims to establish Vietnam as the world's new production hub. Fossil fuels, which are ecologically unfriendly and quickly running out, are now Vietnam's primary energy source. Due to the detrimental effects of fossil fuels on the environment, we can apply strategic decision-making in the industrial sector to choose the best alternative for a renewable energy resource (RER). RERs such as solar energy, wind energy, solid waste energy, biomass energy, geothermal energy, biofuel energy, and hydropower energy are important for generating energy and will be crucial for the survival of humanity, the planet, and other living things in the future. The actions of RER-based industrial development must be encouraged since they will make a significant contribution to overcome environmental impact limitations. The 2-tuple linguistic q -rung orthopair fuzzy set (2TL q -ROFS) is a novel development in fuzzy set theory that presents a decision-making method for selecting the most appropriate alternative. In this paper, we develop a family of the 2TL q -ROF Maclaurin symmetric mean aggregation operators such as the 2TL q -ROF Maclaurin symmetric mean (2TL q -ROFMSM) operator, the 2TL q -ROF dual Maclaurin symmetric mean (2TL q -ROFDMSM) operator and its weighted forms. We also look into a few of the proposed operators' properties and special cases. Then based on 2TL q -ROFS, a new Decision Making Trial and Evaluation Laboratory (DEMATEL) model is constructed, which can use the decision makers' preferences to get the optimum objective weights for attributes. Next, we extend the Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS) method to 2TL q -ROF version which not only covers the uncertainty of human cognition but also gives decision makers a larger space to represent their decisions. Utilizing this model the best RER for Vietnam is selected. The outcomes of the hybrid 2TL q -ROF-DEMATEL-TOPSIS method reveal that among the energy resources, hydropower energy ranked highest, followed by biofuel energy. [ABSTRACT FROM AUTHOR]

Abstract Interval-valued q-rung orthopair fuzzy set (IVq-ROFS) is a powerful tool for dealing with uncertainty. In this paper, we first propose a new method for aggregating multiple IVq-ROFSs, which is easier to understand and implement in the multi-attribute group decision making process compared to current aggregation operators. Secondly, this paper introduces a new fuzzy entropy with parameters based on IVq-ROFS, which is highly flexible due to its adjustable parameters. Based on this, the IVq-ROFS-based attribute weight calculation method is proposed to obtain the objective weights of the attributes, which is more reasonable and objective than the existing methods. Then, for the dimensional differences between the three compromise scores in the original Combined Compromise Solution (CoCoSo) method, the enhanced compromise scores are proposed. These scores are obtained by normalizing the three dependent compromise scores, ensuring that they fall within the same range. Finally, a novel CoCoSo mothed on IVq-ROFS using the proposed fuzzy entropy and enhanced compromise scores is presented. The proposed method is highly adaptable and scalable, not limited to IVq-ROFS. The excellent performance and robustness of the proposed method are verified in sepsis diagnosis applications.

The information in the real world often contains many properties such as fuzziness, randomness, and approximation. Although existing linguistic collections attempt to solve these problems, with the emergence of more and more constraints and challenges, this information cannot fully express the problem, leading to an increasing demand for methods that can contain multiple uncertain information. In this paper, we comprehensively consider the various characteristics of information including membership degree, credibility and approximation based on rough sets, and propose the concept of χ -linguistic sets (χ LSs), which depend on original data rather than prior knowledge and effectively solve the problem of incomplete information representation. At the same time, the corresponding theories such as the comparison method and operational rules have also been proposed. Subsequently, we construct a new χ -linguistic VIKOR (χ LVIKOR) method for multi-attribute group decision making (MAGDM) problem with χ LSs, and apply it to the risk assessment of COVID-19. Through comparative analysis, we discuss the effectiveness and superiority of χ LSs. [ABSTRACT FROM AUTHOR]

One of the most significant and complete approaches to accommodate greater uncertainty than current fuzzy structures is the T-Spherical Fuzzy Set (TSPFS). The primary benefit of TSPFS is that current fuzzy structures are special cases of it. Firstly, some novel TSPF power Heronian mean (TSPFPHM) operators are initiated based on Aczel–Alsina operational laws. These aggregation operators (AOs) have the capacity to eliminate the impact of uncomfortable data and can simultaneously consider the relationships between any two input arguments. Secondly, some elementary properties and core cases with respect to parameters are investigated and found that some of the existing AOs are special cases of the newly initiated aggregation operators. Thirdly, based on these AOs and Aczel–Alsina operational laws a newly advanced technique for order of preference by similarity to ideal solution (TOPSIS)-based method for dealing with multi-attribute group decision-making (MAGDM) problems in a T-Spherical fuzzy framework is established, where the weights of both the decision makers (DMs) and the criteria are completely unknowable. Finally, an illustrative example is provided to evaluate and choose the pharmaceutical firms with the capacity for high-quality, sustainable development in the TSPF environment to demonstrate the usefulness and efficacy. After that, the comparison analysis with other techniques is utilized to demonstrate the coherence and superiority of the recommended approach. [ABSTRACT FROM AUTHOR]

The complex q-rung orthopair fuzzy 2-tuple linguistic set (Cq-ROFTLS), which merges the concepts of complex q-rung orthopair fuzzy sets (Cq-ROFS) and 2-tuple linguistic terms, offers significant advantages in dealing with uncertain and imprecise information during decision-making by effectively representing two-dimensional information within a single set. Notably, the Cq-ROFTLS introduces phase terms that empower experts to express their perspectives flexibly, particularly enhancing its capacity to address periodic elements. To address uncertainty, this approach employs complex values to quantify both membership and non-membership degrees within 2-tuple linguistic environment. Additionally, this research introduces the generalized Maclaurin symmetric mean (MSM) aggregation operator, specifically designed for Cq-ROFTL information. This introduces the Cq-ROFTLMSM and its dual form, the Cq-ROFTL Dual MSM (Cq-ROFTLDMSM), each carrying valuable properties. In cases where the importance of input factors varies, the study proposes the Cq-ROFTL weighted MSM (Cq-ROFTLWMSM) and its dual form, the Cq-ROFTL weighted dual MSM (Cq-ROFTLWDMSM). These operators not only make their debut but also showcase their properties and applications. They flexibly adjust to the significance of inputs, leading to a more refined decision-making process. The methodology extends to address multi-attribute group decision-making (MAGDM) within the Cq-ROFTL framework using the Complex Proportional Assessment (COPRAS) method. The introduction of new aggregation techniques further enhances this approach. A practical illustration involving the selection of the optimal bio-energy production technology (BPT) highlights the real-world effectiveness of the methodology. Through thorough comparisons and a focused exploration of advantages, the study effectively validates the merits of this approach. [ABSTRACT FROM AUTHOR]

A historic building is typically defined as a structure that possesses historical significance, meaning that it maintains a tangible connection to past events, thereby establishing a meaningful link between contemporary individuals and historical occurrences. The primary objective of this article is to investigate and analyze the most exceptional historical site worldwide for a visit. Our research provides a strategy framework to evaluate and select the best historical site worldwide to meet the visiting needs of individuals. The 2-tuple linguistic q-rung orthopair fuzzy set (2TLq-ROFS) is a novel type of fuzzy set that can provide decision makers more flexibility to express their preferences. In order to cope with multi-attribute group decision-making (MAGDM) problems, the 2TLq-ROF aggregation operators are efficient in merging the individual preferences of the decision makers into a collective one. We combine the merits of the power average (PA) and the power geometric (PJ) operators with the Heronian mean (HM) operator to build some new aggregation operators by taking into account the impact of extreme data on decision outcomes. Using the proposed aggregation operators, we also develop an innovative MAGDM approach for aggregating the 2TLq-ROF information. Finally, an illustrative example for the selection of the best historical site worldwide is used to demonstrate the applicability of the established methodology. The effectiveness and superiority of the proposed approach are demonstrated through parameter analysis of parameters q, κ , and ε , and further comparative analysis with existing aggregation operators is done. [ABSTRACT FROM AUTHOR]

In this paper, we propose two multi-attribute group decision-making (MAGDM) algorithms that rely on ingenious linguistic intuitionistic fuzzy (LIF) weighted Maclaurin symmetric means. At the outset, the advanced LIF Maclaurin symmetric mean (ALIFMSM), advanced LIF weighted Maclaurin symmetric mean (ALIFWMSM), advanced LIF dual Maclaurin symmetric mean (ALIFDMSM) and advanced LIF weighted dual Maclaurin symmetric mean (ALIFWDMSM) are introduced in response to the effect of the extreme values on the available LIF correlation means. Then, we present a typical MAGDM algorithm based on the ALIFWMSM (resp. ALIFWDMSM) (Algorithm I), and a practical example shows that it overcomes the defects of a series of existing algorithms. Moreover, considering that the research on LIF numbers (LIFNs) as the attribute weights and the decision- maker (DM) weights has not been reported thus far, we devise an additional MAGDM algorithm relying on the ALIFWMSM (Algorithm II). Algorithm II is for such problems where each DM, according to their respective perceptions, not only provides the LIF evaluation values for the alternatives, but also assigns the LIF importance for the attributes; meanwhile, DMs' LIF importance is generated through negotiation and compromise among group members. Algorithm II consists of two main phases as follows: The 1st phase derives the combined attribute weights corresponding to each DM and the combined DM weights; the 2nd phase fuses evaluation information of the alternatives by the ALIFWMSM. Finally, Algorithm II is used to address a real-world case. Additionally, a comparative analysis with other similar works is performed to illustrate its novelty. [ABSTRACT FROM AUTHOR]

In multi-attribute group decision-making (MAGDM), the attributes can be placed into independent groups based on their properties through partitioning. First, the partitioned dual Hamy mean (PDHM) operator is introduced, along with its essential properties. This operator integrates these separate groups while preserving the relationships between the attributes within each group. Furthermore, the partitioned Hamy mean (PHM) and the PDHM operators are also constructed in the generalized orthopair fuzzy environment, namely the q-rung orthopair fuzzy PHM (q-ROFPHM), the q-rung orthopair fuzzy PDHM (q-ROFPDHM), and their weighted forms. Their essential properties are verified to ensure the validity of the proposed aggregation operators (AOs). Subsequently, a new MAGDM approach is developed, employing the proposed AOs. The MAGDM problem of selecting the best person is examined. Moreover, the research includes a sensitivity analysis in three directions and a comparative analysis of the proposed MAGDM approach with five different approaches. The findings indicate that applying attribute partitioning in the proposed approach mitigates the adverse impact of irrelevant attributes, leading to more feasible and reliable outcomes. Additionally, a practical case study focuses on selecting a suitable industry for investment among the five available options. This case study demonstrates the approach's effectiveness by considering five distinct qualities and results that make the Internet industry the best place to invest. Furthermore, a comparative analysis with four similar papers is also performed, indicating that the developed method's results are more reliable and consistent. [ABSTRACT FROM AUTHOR]

The choice of an optimal airport for local businesses for any traveling purpose due to the complexity of the access to the global market could be considered a group decision-making problem. To cope with this type of problem, the goal of this research is to introduce the power Muirhead mean operators into the environment of a 2-tuple linguistic q-rung orthopair fuzzy set (2TLq-ROFS). This paper proposes four novel aggregation operators: the 2TLq-ROF power Muirhead mean (2TLq-ROFPMM) operator, the 2TLq-ROF dual power Muirhead mean (2TLq-ROFDPMM) operator, the 2TLq-ROF weighted power Muirhead mean (2TLq-ROFWPMM) operator, and the 2TLq-ROF weighted dual power Muirhead mean (2TLq-ROFWDPMM) operator. Then, two new frameworks are constructed by employing the 2TLq-ROFWPMM and the 2TLq-ROFWDPMM aggregation operators to address challenges involving multi-attribute group decision-making. However, the decision-making process is complicated due to the ambiguity over the outcomes of airport choice. The constructed frameworks are being used to solve the problem of choosing the optimal airport in Pakistan for resolving the complexity of the access to the global market in local businesses. To demonstrate the superiority of our approach, parameter analysis with parameters q and ð is carried out. In addition, we compare our formulated approach with different aggregation operators in the literature to prove its effectiveness and efficiency. Finally, some research study conclusions are drawn, limitations are given, and future directions are revealed. [ABSTRACT FROM AUTHOR]

Power grid enterprises are the backbone of promoting clean and low-carbon energy transformation, playing an important role in achieving carbon peak and carbon neutrality. It is very necessary to audit the implementation of the “dual carbon” work of power grid enterprises, in order to better implement the national “dual carbon” policy and serve the development of the national economy. The risk assessment of “dual carbon” audit in power grid enterprises is multiple-attribute group decision-making (MAGDM). In this study, in light with projection measure technique and bidirectional projection measure technique, four forms of projection measure technique with q-rung orthopair fuzzy sets (q-ROFSs) are conducted. Then, two weighed projection techniques are conducted to manage the MAGDM. Finally, a numerical example for risk assessment of “dual carbon” audit in power grid enterprises and comparative analysis is utilized to verify the developed techniques. The major contribution of this research is constructed: (1) entropy technique is implemented to determine the weight values in line with score number (SN) and accuracy number (AN); (2) two weighed projection techniques are implemented to put forward MAGDM with q-ROFSs; (3) the numerical example for risk assessment of “dual carbon” audit in power grid enterprises is implemented to show the two weighed projection techniques under q-ROFSs; and (4) comparative studies are constructed with existing techniques.

IntroductionBreast cancer is an extremely common and potentially fatal illness that impacts millions of women worldwide. Multiple criteria and inclinations must be taken into account when selecting the optimal treatment option for each patient.MethodsThe selection of breast cancer treatments can be modeled as a multi-attribute group decision-making (MAGDM) problem, in which a group of experts evaluate and rank alternative treatments based on multiple attributes. MAGDM methods can aid in enhancing the quality and efficacy of breast cancer treatment selection decisions. For this purpose, we introduce the concept of a 2-tuple linguistic interval-valued q-rung orthopair fuzzy set (2TLIVq-ROFS), a new development in fuzzy set theory that incorporates the characteristics of interval-valued q-rung orthopair fuzzy set (IVq-ROFS) and 2-tuple linguistic terms. It can express the quantitative and qualitative aspects of uncertain information, as well as the decision-makers' level of satisfaction and dissatisfaction.ResultsThen, the 2TLIVq-ROF weighted average (2TLIVq-ROFWA) operator and the 2TLIVq-ROF weighted geometric (2TLIVq-ROFWJ) operator are introduced as two new aggregation operators. In addition, the multi-attribute border approximation area comparison (MABAC) method is extended to solve the MAGDM problem with 2TLIVq-ROF information.DiscussionTo demonstrate the efficacy and applicability of the suggested model, a case study of selecting the optimal breast cancer treatment is presented. The results of the computations show that the suggested MAGDM model is able to handle imprecision and subjectivity in complicated decision-making scenarios and opens new research scenarios for scholars.

The term “cloud security (CS)” describes the collection of procedures and tools intended to defend networks, data, apps, and systems used in cloud computing from possible security risks and unauthorized access. Data breaches, identity and access management, network security, adherence to industry and governmental standards, and the security of third-party services and apps are a few of the major issues with CS. Selecting the best CS becomes critical for resolving all these problems. Within the context of hesitant bipolar complex fuzzy sets (HBCFSs) theory, we address in this study optimal selection utilizing various conceptions of aggregation operators (AOs). The notion of HBCFSs gives us a valuable framework by providing the hesitancy nature of any object along with its positive and negative aspects. Moreover, HBCFSs are a valuable tool to eliminate the vagueness and uncertainty of any given information. In this manuscript, by utilizing the framework of HBCFSs we developed some new AOs which are obliging to convert the set of information into a singleton value. Then by utilizing these AOs we calculate and aggregate all the numerical significance of CS. To handle our supposed problem of CS the mainly developed AOs are hesitant bipolar complex fuzzy (HBCF) weighted averaging (HBCFWA), HBCF ordered weighted averaging (HBCFOWA), HBCF weighted geometric (HBCFWG), HBCF ordered weighted geometric (HBCFOWG), generalized HBCF weighted averaging (GHBCFWA), generalized HBCF weighted geometric (GHBCFWG) operators. Furthermore, we develop the multi-attributive border approximation area comparison (MABAC) method to address our multi-attribute group decision-making (MAGDM) problem of CS. Moreover, in this manuscript, we propose and analyze a CS-related numerical case study to identify the optimal CS. Lastly; to demonstrate the advantages and superiority of the interpretive work, we compared our suggested methodology with other extant ideas.

The main objective of water purification processes is to remove harmful chemical compounds and microorganisms from water sources to produce suitable water for human consumption. Water purification plays a pivotal role in meeting the critical demand for clean drinking water across diverse industries, including medical, pharmaceutical, and chemical sectors. Its significance extends beyond industry needs, impacting the resilience and prosperity of nations. As a result, experts around the world are studying several potential technologies to increase and maintain water supplies. In regions susceptible to drought, the need for innovative water purification strategies is even more critical. This article presents a novel approach, the “Extended MULTIMOORA” method utilizing $ff^{\prime }$ -fractional linguistic term sets ( $ff^{\prime }$ -FLTSs), to address the challenge of selecting the most effective water purification process. This article introduces the concepts of arithmetic mean, geometric mean, weighted averaging, and weighted geometric operators for $ff^{\prime }$ -FLTSs and investigate its several important key features. In decision-making problems, when the weights of the decision makers are unknown, the decision-making process is more difficult, we introduce an entropy measure and a distance measure to find the weight information. Furthermore, we effectively apply the proposed technique and newly defined operators to select the best technique for purifying water at a commercial scale. At last, we establish a comparative analysis to show the validity and feasibility of the proposed techniques compared to existing methods.

Abstract One of the most significant and complete approaches to accommodate greater uncertainty than current fuzzy structures is the T-Spherical Fuzzy Set (TSPFS). The primary benefit of TSPFS is that current fuzzy structures are special cases of it. Firstly, some novel TSPF power Heronian mean (TSPFPHM) operators are initiated based on Aczel–Alsina operational laws. These aggregation operators (AOs) have the capacity to eliminate the impact of uncomfortable data and can simultaneously consider the relationships between any two input arguments. Secondly, some elementary properties and core cases with respect to parameters are investigated and found that some of the existing AOs are special cases of the newly initiated aggregation operators. Thirdly, based on these AOs and Aczel–Alsina operational laws a newly advanced technique for order of preference by similarity to ideal solution (TOPSIS)-based method for dealing with multi-attribute group decision-making (MAGDM) problems in a T-Spherical fuzzy framework is established, where the weights of both the decision makers (DMs) and the criteria are completely unknowable. Finally, an illustrative example is provided to evaluate and choose the pharmaceutical firms with the capacity for high-quality, sustainable development in the TSPF environment to demonstrate the usefulness and efficacy. After that, the comparison analysis with other techniques is utilized to demonstrate the coherence and superiority of the recommended approach.

As the rapidly progressing applications of uncertainty theories, the need for modifications to some of their existing mathematical tools or creating new tools to deal correctly with them in various environments is also exposed. Hesitant fuzzy numbers (HFNs), as a particular case of fuzzy numbers, are not an exception to this rule. Considering the necessity of determining the distance between given HFNs in many of their practical applications, this article shows that the existing methods either do not provide correct results or are not able to meet the needs of users. This paper aims to present new methods for distance measures of hesitant fuzzy numbers. To do them, three prevalent distance measures, i.e., the generalized distance measure, the Hamming distance measure, and the Euclidean distance measure, will be optimized into three distinct trinal categories. With the approach of reducing error propagation via reducing some unnecessary mathematical computations, new distance measures on HFNs will be introduced, first. The middle is the modification of the first category, which is more suitable when the given HFNs are equal-distance by the previous formula. Also, as the third category, the weighted form of these distance measures has been proposed, to be used where the real and membership parts of HFNs are not of equal importance. As an application of these, a TOPSIS-based technique for solving multi-attribute group decision-making problems with HFNs has been proposed. A numerical example will be implemented to describe the presented method. Finally, along with the validation of the proposed method, its numerical comparison with some other existing methods will be discussed in detail. [ABSTRACT FROM AUTHOR]

With the rapid development and application of internet technology, cross-border e-commerce (CBEC) has begun to popularize globally and play an important role in China's foreign trade. The Chinese government has successively introduced multiple policies and regulations to strongly support its rapid development. Compared to the booming trend of CBEC, the development of its supply chain is slightly lacking in momentum, which has formed a certain obstacle to the overall development of CBEC. The supply chain is the foundation of successful CBEC transactions, and the foundation of the supply chain is logistics. The primary task to improve the backwardness of supply chain development is to solve logistics problems. Therefore, while enjoying the dividends brought by the rapid development of CBEC, international logistics enterprises should continuously improve their logistics service capabilities, effectively evaluate their service quality, and then identify problems based on the evaluation results, analyze and improve them. The service quality evaluation of international logistics enterprises from the perspective of CBEC supply chain is a classical multiple attribute group decision making (MAGDM). The Spherical fuzzy sets (SFSs) provide more free space for DMs to portray uncertain information during the service quality evaluation of international logistics enterprises from the perspective of CBEC supply chain. Therefore, this paper expands the partitioned Maclaurin symmetric mean (PPMSM) operator and IOWA operator to SFSs based on the power average (PA) technique and construct induced spherical fuzzy weighted power partitioned MSM (I-SFWPPMSM) technique. Subsequently, a novel MAGDM method is constructed based on I-SFWPPMSM technique and SFNWG technique under SFSs. Finally, a numerical example for service quality evaluation of international logistics enterprises from the perspective of CBEC supply chain is employed to verify the constructed method, and comparative analysis with some existing techniques to testy the validity and superiority of the I-SFWPPMSM technique. [ABSTRACT FROM AUTHOR]

Precision agriculture refers to the use of advanced technologies and data analytics to optimize farming practices, maximize crop yields, and reduce resource wastage. In precision agriculture monitoring, unmanned aerial vehicles (UAVs) have emerged as a valuable tool for large-scale implementation. The selection of suitable UAVs is a critical aspect of precision agriculture and is deliberated as significant multi-attribute group decision-making (MAGDM) problem. In decision issues, the evaluation of experts about any available options plays an important role. In this context, interval-valued q-rung orthopair fuzzy set (IVq-ROFS) is a useful tool allowing experts to provide their evaluations in a wider space and better deal with incomplete information. This paper aims to develop a new approach to determining expert weights using distance and similarity measures for interval-valued q-rung orthopair fuzzy numbers (IVq-ROFNs). To achieve this, an average group assessment based on individual assessments is constructed. The experts' weights were then established by computing similarity measures between the individual evaluations and the average group assessment. Moreover, the technique for order of preference by similarity to the ideal solution (TOPSIS) method is extended to address the MAGDM problem under IVq-ROF information. An example involving UAV selection for precision agriculture is provided to demonstrate the validity of the suggested method, and the impact of parameters on decision results is discussed. Finally, a comparative analysis with existing approaches demonstrates the superiority and advantages of the proposed technique. [ABSTRACT FROM AUTHOR]

The impact of artificial intelligence (AI) in education can be viewed as a multi-attribute group decision-making (MAGDM) problem, in which several stakeholders evaluate the advantages and disadvantages of AI applications in educational settings according to distinct preferences and criteria. A MAGDM framework can assist in providing transparent and logical recommendations for implementing AI in education by methodically analyzing the trade-offs and conflicts among many components, including ethical, social, pedagogical, and technical concerns. A novel development in fuzzy set theory is the 2-tuple linguistic q-rung orthopair fuzzy set (2TLq-ROFS), which is not only a generalized form but also can integrate decision-makers quantitative evaluation ideas and qualitative evaluation information. The 2TLq-ROF Schweizer-Sklar weighted power average operator (2TLq-ROFSSWPA) and the 2TLq-ROF Schweizer-Sklar weighted power geometric (2TLq-ROFSSWPG) operator are two of the aggregation operators we create in this article. We also investigate some of the unique instances and features of the proposed operators. Next, a new Entropy model is built based on 2TLq-ROFS, which may exploit the preferences of the decision-makers to obtain the ideal objective weights for attributes. Next, we extend the VIseKriterijumska Optimizacija I Kompromisno Resenje (VIKOR) technique to the 2TLq-ROF version, which provides decision-makers with a greater space to represent their decisions, while also accounting for the uncertainty inherent in human cognition. Finally, a case study of how artificial intelligence has impacted education is given to show the applicability and value of the established methodology. A comparative study is carried out to examine the benefits and improvements of the developed approach.

Abstract In multi-attribute group decision-making (MAGDM), the attributes can be placed into independent groups based on their properties through partitioning. First, the partitioned dual Hamy mean (PDHM) operator is introduced, along with its essential properties. This operator integrates these separate groups while preserving the relationships between the attributes within each group. Furthermore, the partitioned Hamy mean (PHM) and the PDHM operators are also constructed in the generalized orthopair fuzzy environment, namely the q-rung orthopair fuzzy PHM (q-ROFPHM), the q-rung orthopair fuzzy PDHM (q-ROFPDHM), and their weighted forms. Their essential properties are verified to ensure the validity of the proposed aggregation operators (AOs). Subsequently, a new MAGDM approach is developed, employing the proposed AOs. The MAGDM problem of selecting the best person is examined. Moreover, the research includes a sensitivity analysis in three directions and a comparative analysis of the proposed MAGDM approach with five different approaches. The findings indicate that applying attribute partitioning in the proposed approach mitigates the adverse impact of irrelevant attributes, leading to more feasible and reliable outcomes. Additionally, a practical case study focuses on selecting a suitable industry for investment among the five available options. This case study demonstrates the approach’s effectiveness by considering five distinct qualities and results that make the Internet industry the best place to invest. Furthermore, a comparative analysis with four similar papers is also performed, indicating that the developed method’s results are more reliable and consistent.

In the 40 years of global microcredit practice, loan technology has played a positive role in microcredit as one of the most important supporting elements. The development and evolution of microcredit institution lending technology is the result of comprehensive consideration of specific regional economic, social, cultural, and geographical factors. In the context of the diversified trend of microcredit technology, choosing loan technology reasonably, exploring flexible guarantee conditions, and innovating diversified loan technology combinations will become practical problems faced by microcredit institutions, and also the direction of theoretical research. The timely innovation of group loan technology in microcredit has practical value and theoretical significance for promoting the innovation of financial agricultural products in the implementation of China's rural revitalization strategy, as well as bridging the theoretical controversy of microcredit loan technology. The performance evaluation of microfinance groups lending is a MAGDM issues. In this paper, the distances measures of single-valued neutrosophic sets (SVNSs) and maximizing deviation method (MDM) is used to obtain the attribute weight values. Based on the classical Multi-Attributive Border Approximation area Comparison (MABAC) method, the single-valued neutrosophic numbers MABAC (SVNN-MABAC) method is constructed for MAGDM under SVNSs. Finally, an example for performance evaluation of microfinance groups lending and some comparative decision analysis are constructed to verify the SVNN-MABAC model. [ABSTRACT FROM AUTHOR]

Due to the complexity and uncertainty of decision-making, probabilistic linguistic term sets (PLTSs) are currently important tools for qualitative evaluation of decision-makers. The asymmetry of evaluation information can easily lead to the loss of subjective preference information for decision-makers, and the existing operation of decision-maker evaluation information fusion operators is difficult to solve this problem. To solve such problems, this paper proposes some new operational methods for PLTSs based on Dombi T-conorm and T-norm. Considering the interrelationships between the input independent variables of PLTSs, the probabilistic linguistic weighted Dombi Bonferroni mean Power average (PLWDBMPA) operators are extended and the properties of these aggregation operators are proposed. Secondly, the PLWDBMPA operator is used to fuse the evaluation information of decision-makers, avoiding the loss of decision information as much as possible. This paper uses social media platforms and web crawler technology to obtain online comments from users on decision-making to obtain the public's attitude towards decision events. TF-IDF and Word2Vec are used to calculate the weight of alternatives on each attribute. Under traditional group decision-making methods and integrating the wisdom of the public, a novel multi-attribute group decision-making method based on TODIM method is proposed. Finally, the case study of Turkey earthquake shelter selection proves this method is scientific and effective. Meanwhile, the superiority of this method was further verified through comparisons with the PL-TOPSIS, PLWA, SPOTIS and PROMETHEE method. [ABSTRACT FROM AUTHOR]

Nowadays career choosing is a very difficult job for many students. This paper primarily addresses the concerns of those students who face difficulty in choosing the right career option for themselves, using multi-attribute group decision-making (MAGDM) methodologies based on CRITIC (Criteria Importance Through Inter criteria Correlation) and EDAS (Evaluation based on Distance from Average Solution) strategies under the single-valued neutrosophic set (SVNS) environment. First, the CRITIC strategy is used to calculate the weights of the attributes and then these weights are used to develop EDAS strategy in the SVNS environment. Since the usage of the geometric operator CRITIC-EDAS has not before been documented in the literature, this study is distinctive. A realistic example of commerce students' career selection problem is discussed. [ABSTRACT FROM AUTHOR]

In the field of multi-attribute group decision-making (MAGDM), "decision-making trial and evaluation laboratory" (DEMATEL) is a popular method that has been deployed to discover hidden relationships among many inter-twined factors of numerous real-world problems. This paper discusses several limitations of the DEMATEL method in mining the causal relationships and ranking the factors. Also, in this paper, we develop a novel decision-making framework that will be able to overcome the issues found in the DEMATEL method and tackle both formal and informal decisions. This model, which we call "Causal Relationship and Ranking Technique (CRRT)", uses a data-deterministic expert weighing setup rather than assigning equal weights or pre-defined weights to each expert. The model proposes a better technique to mine factor inter-relations and proposes two new types of digraphs portraying the causal inter-relationships among the factors, and also proposes a new two-step factor ranking method based on the derived causal relationships. The intuitionistic fuzzy setting is considered in this work in order to capture the uncertainty of expert opinions. Furthermore, our proposed framework is applied to a real-life case study on discovering various factors of a high school administration, that have a significant influence on students' performance. Comparison with standard methods such as TOPSIS and VIKOR for student performance data and also some other datasets such as supplier selection data, and sustainability data proves that the model is able to rank the factors better than the existing models. [ABSTRACT FROM AUTHOR]

• A novel group decision methods classification framework has been presented. • A review of existing multiple-source aggregation methods has been carried out. • Existing methods have been compared with current needs in the scientific field. • Future research pathways are provided to enhance upcoming techniques. • A multiple-source aggregation methods guide is provided. Interest in group decision-making (GDM) has been increasing prominently over the last decade. Access to global databases, sophisticated sensors which can obtain multiple inputs or complex problems requiring opinions from several experts have driven interest in data aggregation. Consequently, the field has been widely studied from several viewpoints and multiple approaches have been proposed. Nevertheless, there is a lack of general framework. Moreover, this problem is exacerbated in the case of experts' weighting methods, one of the most widely-used techniques to deal with multiple source aggregation. This lack of general classification scheme, or a guide to assist expert knowledge, leads to ambiguity or misreading for readers, who may be overwhelmed by the large amount of unclassified information currently available. To invert this situation, a general GDM framework is presented which divides and classifies all data aggregation techniques, focusing on and expanding the classification of experts' weighting methods in terms of analysis type by carrying out an in-depth literature review. Results are not only classified but analysed and discussed regarding multiple characteristics, such as MCDMs in which they are applied, type of data used, ideal solutions considered or when they are applied. Furthermore, general requirements supplement this analysis such as initial influence, or component division considerations. As a result, this paper provides not only a general classification scheme and a detailed analysis of experts' weighting methods but also a road map for researchers working on GDM topics or a guide for experts who use these methods. Furthermore, six significant contributions for future research pathways are provided in the conclusions. [ABSTRACT FROM AUTHOR]

In recent years, fossil fuel resources have become increasingly rare and caused a variety of problems, with a global impact on economy, society and environment. To tackle this challenge, we must promote the development and diffusion of alternative fuel technologies. The use of cleaner fuels can reduce not only economic cost but also the emission of gaseous pollutants that deplete the ozone layer and accelerate global warming. To select an optimal alternative fuel, different fuzzy decision analysis methodologies can be utilized. In comparison to other extensions of fuzzy sets, the T-spherical fuzzy set is an emerging tool to cope with uncertainty by quantifying acceptance, abstention and rejection jointly. It provides a general framework to unify various fuzzy models including fuzzy sets, picture fuzzy sets, spherical fuzzy sets, intuitionistic fuzzy sets, Pythagorean fuzzy sets and generalized orthopair fuzzy sets. Meanwhile, decision makers prefer to employ linguistic terms when expressing qualitative evaluation in real-life applications. In view of these facts, we develop an extended multi-attributive border approximation area comparison (MABAC) method for solving multiple attribute group decision-making problems in this study. Firstly, the combination of T-spherical fuzzy sets with 2-tuple linguistic representation is presented, which provides a general framework for expressing and computing qualitative evaluation. Secondly, we put forward four kinds of 2-tuple linguistic T-spherical fuzzy aggregation operators by considering the Heronian mean operator. We investigate some fundamental properties of the proposed 2-tuple linguistic T-spherical fuzzy aggregation operators. Lastly, an extended MABAC method based on the 2-tuple linguistic T-spherical fuzzy generalized weighted Heronian mean and the 2-tuple linguistic T-spherical fuzzy weighted geometric Heronian mean operators is developed. For illustration, a case study on fuel technology selection with 2-tuple linguistic T-spherical fuzzy information is also conducted. Moreover, we show the validity and feasibility of our approach by comparing it with several existing approaches.

A concept of intuitionistic fuzzy rough set based on approximations plays a vital role in coping with uncertainty. Aczel-Alsina t-norm and t-conorm are the most flexible operational laws based on the parameter for fuzzy frameworks. In multi-attribute group decision-making (MAGDM), the aim of this article is to develop some tools based on norm operations for the information fusion. In this article, intuitionistic fuzzy rough Aczel-Alsina weighted geometric operators are developed and studied their properties. Based on these operators, MAGDM algorithm is presented. The developed aggregation operators (AOs) are compared with some existing AOs, and their significance is discussed.

Evaluation and selection problems are becoming increasingly difficult due to human judgment and unknown evaluation risks. These circumstances mean that contractor selection is impacted by a number of factors, many of which have a hybrid uncertainty of fuzziness and probability. The objective of this paper is to propose a multi-attribute group decision-making (MAGDM) model for the selection of the most suitable construction company. A decision problem based on the decisions of many experts, with multiple conflicting criterion, should be taken into account to evaluate multiple companies. For this purpose, we propose the notion of a linguistic interval-valued T-spherical fuzzy set (LIVt-SFS) to allow decision-makers to provide their evaluations in a wider space and to better deal with vague information. In this study, we developed some basic operations and score and accuracy functions to compare LIVt-SF numbers (LIVt-SFNs). Based on these operations, two aggregation operators: LIVt-SF weighted averaging and LIVt-SF weighted geometric operators, are established. Moreover, the technique for order of preference by similarity to ideal solution (TOPSIS) method is extended to solve the MAGDM problem under LIVt-SFS information. Furthermore, an example of the selection of the best construction company is given to demonstrate the effectiveness and feasibility of the proposed model. The computational results demonstrate that the suggested MAGDM model is capable of dealing with imprecision and subjectivity in complex decision-making situations. In addition, a sensitivity analysis is conducted to observe the influence of the parameter 'q' on the decision results. Finally, a comparison with existing decision-making methods is presented for the authentication of our proposed approach. [ABSTRACT FROM AUTHOR]

In the study of group decision-making, the most important issue is how to coordinate opinions from different decision experts (DEs) to reach a consensus under uncertainty. To tackle uncertainties surrounding multi-attribute group decision-making (MAGDM) problems in real-life scenes, we introduce 2-tuple linguistic T-spherical fuzzy sets (2TLT-SFSs) which generalize T-spherical fuzzy sets by means of 2-tuple linguistic terms. The 2TLT-SFS model enables the degrees of membership, abstention, and non-membership to be expressed by linguistic terms. This makes it more flexible and descriptive to model the attitudes of DEs in MAGDM applications. Due to the fact that multi-input arguments are interconnected and DEs have a lot of options perception, we also define Muirhead mean (MM) aggregation operators (AOs) to facilitate the fusion of 2TLT-SF information. With the aid of 2TLT-SFSs and MM AOs, the main goal of this research is to present a general MAGDM framework by integrating the step-wise weight assessment ratio analysis (SWARA) with the complex proportional assessment (COPRAS). Firstly, the MM, weighted MM, dual MM, and weighted dual MM operators are adapted to the 2TLT-SF environment, which put forward several new notions such as the 2-tuple linguistic T-spherical fuzzy Muirhead mean (2TLT-SFMM), 2-tuple linguistic T-spherical fuzzy weighted Muirhead mean (2TLT-SFWMM), 2-tuple linguistic T-spherical fuzzy dual Muirhead mean (2TLT-SFDMM), and 2-tuple linguistic T-spherical fuzzy weighted dual Muirhead mean (2TLT-SFWDMM) operators. Meanwhile, some properties regarding idempotency, monotonicity, boundedness, and specializations of the proposed operators are analyzed. Secondly, an integrated 2TLT-SF-MAGDM framework is established. In the proposed decision framework, the 2TLT-SF-SWARA method is utilized to identify the subjective weights of decision attributes, and the 2TLT-SF-COPRAS approach is used to rank alternatives. Lastly, a case study concerning hydropower plants assessment is presented to demonstrate that the suggested scheme is feasible and effective. Furthermore, sensitivity and comparison analyses are conducted to show the robustness and superiority of the proposed method. [ABSTRACT FROM AUTHOR]

In recent years, fossil fuel resources have become increasingly rare and caused a variety of problems, with a global impact on economy, society and environment. To tackle this challenge, we must promote the development and diffusion of alternative fuel technologies. The use of cleaner fuels can reduce not only economic cost but also the emission of gaseous pollutants that deplete the ozone layer and accelerate global warming. To select an optimal alternative fuel, different fuzzy decision analysis methodologies can be utilized. In comparison to other extensions of fuzzy sets, the T-spherical fuzzy set is an emerging tool to cope with uncertainty by quantifying acceptance, abstention and rejection jointly. It provides a general framework to unify various fuzzy models including fuzzy sets, picture fuzzy sets, spherical fuzzy sets, intuitionistic fuzzy sets, Pythagorean fuzzy sets and generalized orthopair fuzzy sets. Meanwhile, decision makers prefer to employ linguistic terms when expressing qualitative evaluation in real-life applications. In view of these facts, we develop an extended multi-attributive border approximation area comparison (MABAC) method for solving multiple attribute group decision-making problems in this study. Firstly, the combination of T-spherical fuzzy sets with 2-tuple linguistic representation is presented, which provides a general framework for expressing and computing qualitative evaluation. Secondly, we put forward four kinds of 2-tuple linguistic T-spherical fuzzy aggregation operators by considering the Heronian mean operator. We investigate some fundamental properties of the proposed 2-tuple linguistic T-spherical fuzzy aggregation operators. Lastly, an extended MABAC method based on the 2-tuple linguistic T-spherical fuzzy generalized weighted Heronian mean and the 2-tuple linguistic T-spherical fuzzy weighted geometric Heronian mean operators is developed. For illustration, a case study on fuel technology selection with 2-tuple linguistic T-spherical fuzzy information is also conducted. Moreover, we show the validity and feasibility of our approach by comparing it with several existing approaches. [ABSTRACT FROM AUTHOR]

This article elaborates the enormous theory of MULTIMOORA (multi-objective optimization ratio analysis plus full multiplicative form) method to build up a new outranking approach for the innovative extension of fuzzy set theory, namely, 2-tuple linguistic Fermatean fuzzy sets (2TLFFSs). The main objective of the proposed work is to expand and present the components of MULTIMOORA method in 2-tuple linguistic Fermatean fuzzy framework. The resulted technique is named as 2-tuple linguistic Fermatean fuzzy MULTIMOORA method. This technique is designed to tackle the unclear information using 2-tuple linguistic Fermatean fuzzy numbers (2TLFFNs). The proposed model is intrinsically superior to deal with one-dimensional linguistic data. The 2TLFF-MULTIMOORA method takes into account standard relative correlations. Also, it handles the rank inversion problem when changing the rank of alternatives by adding one or more alternatives. The algorithm designed for the proposed methodology is elaborated with a numerical example (to opt for the most favorable city for the selection of quality of life). The accuracy and precision of the proposed strategy is determined by narrating a comparative study. Finally, the advantages of the developed technique over existing methods are discussed briefly.