Research on the evaluation method of whole process engineering consulting service modes based on uncertain multiple-attribute group decision-making.

With the continuous development of the economy and society, the engineering construction industry has experienced rapid growth, and higher requirements have been put forward for engineering consulting services. Currently, most engineering consulting service enterprises in China only provide relevant consulting services for engineering construction at a certain stage, lacking overall planning and overall control over the entire lifecycle of engineering construction. In order to improve the scientific level of fixed assets investment decision-making and construction management, it is of great value to explore professional engineering consulting services covering the whole process of project construction in the project decision-making stage and implementation stage to achieve the optimization of project quality and economic benefits. The whole process engineering consulting service modes (ECSM) evaluation is a multiple-attribute group decision-making (MAGDM). Recently, the TODIM technique and MACONT technique was created to put forward MAGDM. The interval neutrosophic sets (INSs) are created as a tool for managing fuzzy information during the whole process ECSM evaluation. In this work, the interval neutrosophic number TODIM-MACONT (INN-TODIM-MACONT) technique is created to put forward the MAGDM under INSs. Finally, a numerical analysis for whole process ECSM evaluation is given to validate the proposed technique. The main contributions are outlined: (1) the TODIM and MACONT technique was enhanced under INSs; (2) Information Entropy is created to conduct the weight information under INSs. (3) the INN-TODIM-MACONT technique is created to implement the MAGDM under INSs; (4) a numerical example for whole process ECSM evaluation and some comparative analysis is created to verify the INN-TODIM-MACONT technique.

LogTODIM-PROMETHEE technique for development evaluation of school-enterprise cooperation from the perspective of collaborative education based on the probabilistic linguistic group decision-making.

The integration of industry and education can be literally explained as the role of education in providing intellectual support and production services for the development of industries in a country or region, evolving from an auxiliary role in industrial development to a supporting role in industrial development. The government, enterprises, universities, and intermediaries are all the main bodies of industry education integration, and school enterprise cooperation is the core. The two basic functions of universities, namely "applied scientific research" and "social services", must be highlighted. How to strengthen the cultivation of applied talents and improve the quality of talent cultivation in universities is a problem that universities must face in their transformation. Strengthening school enterprise cooperation and promoting the integration of industry and education is an effective way to solve this problem. The development evaluation of school-enterprise cooperation from the perspective of collaborative education is a multiple-attribute group decision-making (MAGDM) problem. Recently, the Logarithmic TODIM (LogTODIM) and PROMETHEE technique was employed to put forward the MAGDM issues. The probabilistic linguistic term sets (PLTSs) are employed as a technique for characterizing uncertain information during the development evaluation of school-enterprise cooperation from the perspective of collaborative education. In this paper, the probabilistic linguistic LogTODIM-PROMETHEE (PL-LogTODIM-PROMETHEE) technique is constructed to put forward the MAGDM under PLTSs. The MEREC technique is employed to obtain the weight values under PLTSs. Finally, a numerical example for development evaluation of school-enterprise cooperation from the perspective of collaborative education is put forward to validate the LogTODIM-PROMETHEE technique.

Projection-driven optimization framework for risk assessment of "dual carbon" audit in power grid enterprises with q-rung orthopair fuzzy MAGDM.

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.

Enhancing breast cancer treatment selection through 2TLIVq-ROFS-based multi-attribute group decision making.

Introduction: Breast 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. Methods: The 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. Results: Then, 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. Discussion: To 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.

Group decision-making algorithm with sine trigonometric r,s,t-spherical fuzzy aggregation operators and their application.

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.

A MAGDM approach for evaluating the impact of artificial intelligence on education using 2-tuple linguistic q-rung orthopair fuzzy sets and Schweizer-Sklar weighted power average operator.

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.

A novel group decision making method based on CoCoSo and interval-valued Q-rung orthopair fuzzy sets.

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.

Enhanced LogTODIM-TOPSIS framework for interval-valued intuitionistic fuzzy MAGDM and applications to intangible assets operational management performance evaluation of commercial sporting events.

The effective operation of intangible assets in commercial sports events can bring long-term, sustainable, and large-scale economic benefits to sports events. However, currently, in the operation of commercial sports events, the lack of experience in hosting events often hinders the development of intangible assets that should have created higher profits, and cannot achieve the expected value. The intangible assets operational management performance (IAOMP) evaluation of commercial sporting events is the multiple-attribute group decision-making (MAGDM). The Logarithmic TODIM (LogTODIM) and TOPSIS technique was brought forward the MAGDM. The interval-valued intuitionistic fuzzy sets (IVIFSs) are brought forward as the useful technique for coping with uncertain and fuzzy information during the IAOMP evaluation of commercial sporting events. In this study, the interval-valued intuitionistic fuzzy number Logarithmic TODIM-TOPSIS (IVIFN-LogTODIM-TOPSIS) technique is brought forward the MAGDM under IVIFSs circumstances. Finally, the numerical example for IAOMP evaluation of commercial sporting events is brought forward to verify the IVIFN-LogTODIM-TOPSIS technique. The main contribution of this study is brought forward: (1) the LogTODIM-TOPSIS was extended to IVIFSs in light with MEREC model; (2) the MEREC model is brought forward to derive weight in light with score information values under IVIFSs circumstances. (3) the IVIFN-LogTODIM-TOPSIS is brought forward for MAGDM under IVIFSs circumstances; (4) the numerical example for IAOMP evaluation of commercial sporting events and several different comparative analysis is brought forward to verify the IVIFN-LogTODIM-TOPSIS model.

Optimized multiple-attribute group decision-making through employing probabilistic hesitant fuzzy TODIM and EDAS technique and application to teaching quality evaluation of international Chinese course in higher vocational colleges.

With the construction and development of the "the Belt and Road", the international community has an increasing demand for high-quality technical and skilled talents who both understand Chinese and have an international perspective. Exploring a Chinese curriculum system suitable for the development of international students is conducive to promoting the international development of vocational education, improving the quality of international student training, providing talent support for Chinese and foreign enterprises, and promoting the "going out" of Chinese enterprises and international production capacity cooperation. The training of international students in higher vocational colleges starts late, has little experience, lacks theoretical innovation, and lacks the development characteristics of vocational education. The teaching quality evaluation of international Chinese course in higher vocational colleges is multiple-attributes group decision-making (MAGDM). Recently, the TODIM and EDAS technique has been employed to manage MAGDM. The probabilistic hesitant fuzzy sets (PHFSs) are employed as a useful tool for depicting uncertain information during the teaching quality evaluation of international Chinese course in higher vocational colleges. In this paper, the probabilistic hesitant fuzzy TODIM-EDAS (PHF-TODIM-EDAS) technique is built to manage the MAGDM under PHFSs. Finally, the numerical example for teaching quality evaluation of international Chinese course in higher vocational colleges is employed to show the PHF-TODIM-EDAS technique. The main contribution of this paper is outlined: (1) the TODIM technique based on EDAS technique has been extended to PHFSs based on CRITIC technique; (2) the CRITIC technique is employed to derive weight numbers under PHFSs. (3) the PHF-TODIM-EDAS technique is founded to manage the MAGDM under PHFSs; (4) a numerical case study for teaching quality evaluation of international Chinese course in higher vocational colleges and some comparative analysis is supplied to validate the proposed PHF-TODIM-EDAS technique.

Complex Fermatean fuzzy extended TOPSIS method and its applications in decision making.

The fuzzy set has its own limitations due to the membership function only. The fuzzy set does not describe the negative aspects of an object. The Fermatean fuzzy set covers the negative aspects of an object. The complex Fermatean fuzzy set is the most effective tool for handling ambiguous and uncertain information. The aim of this research work is to develop new techniques for complex decision-making based on complex Fermatean fuzzy numbers. First, we construct different aggregation operators for complex Fermatean fuzzy numbers, using Einstein t-norms. We define a series of aggregation operators named complex Fermatean fuzzy Einstein weighted average aggregation (CFFEWAA), complex Fermatean fuzzy Einstein ordered weighted average aggregation (CFFEOWAA), and complex Fermatean fuzzy Einstein hybrid average aggregation (CFFEHAA). The fundamental properties of the proposed aggregation operators are discussed here. The proposed aggregation operators are applied to the decision-making technique with the help of the score functions. We also construct different algorithms based on different aggregation operators. The extended TOPSIS method is described for the decision-making problem. We apply the proposed extended TOPSIS method to MAGDM problem "selection of an English language instructor". We also compare the proposed models with the existing models.

A novel approach based on similarity measure for the multiple attribute group decision-making problem in selecting a sustainable cryptocurrency.

Environmental impact and sustainability challenges in the cryptocurrencies has become increasingly examined in the literature. However, studies of the multiple attribute group decision making (MAGDM) method for major selection of cryptocurrencies in advancing sustainability are still at an early stage. In particular, research on the fuzzy-MAGDM method in the evaluation of sustainability in cryptocurrencies is scarce. This paper adds contributions by developing a novel MAGDM approach to evaluate the sustainability development of major cryptocurrencies. It proposes a similarity measure for interval-valued Pythagorean fuzzy numbers (IVPFNs) based on whitenisation weight function and membership function in grey systems theory for IVPFNs. It further developed a novel generalised interval-valued Pythagorean fuzzy weighted grey similarity (GIPFWGS) measure approach to provide a more rigorous evaluation in complex decision marking problem with embedding ideal solution and membership degree. It also conducts a sustainability evaluation model of major cryptocurrencies as a numerical application and performs a robustness assessment with different variations of the expert's weight to test how different values of parameter θ can affect the ranking results of alternatives. The results suggest that Stellar is the most sustainable cryptocurrency, while Bitcoin with its intensive energy consumption, high mining cost and high computing power provides the least effective support for its sustainable development. A comparative analysis with the average value method and Euclidean distance method was performed to validate the reliability of the proposed decision-making model and provides evidence that the GIPFWGS has better fault tolerance.

TODIM-VIKOR method based on hybrid weighted distance under probabilistic uncertain linguistic information and its application in medical logistics center site selection.

At a time of global epidemic control, the location of the medical logistics distribution center (MLDC) has an important impact on the operation of the entire logistics system to reduce the operating costs of the company, enhance the service quality and effectively control the COVID-19 on the premise of increasing the company's profits. Thus, the research on the location of MLDC has important theoretical and practical application significance separately. Recently, the TODIM and VIKOR method has been used to solve multiple-attribute group decision-making (MAGDM) issues. The probabilistic uncertain linguistic term sets (PULTSs) are used as a tool for characterizing uncertain information. In this paper, we design the TODIM-VIKOR model to solve the MAGDM in PULT condition. Firstly, some basic concept of PULTSs is reviewed, and TODIM and VIKOR method are introduced. The extended TODIM-VIKOR model is proposed to tackle MAGDM problems under the PULTSs. At last, a numerical case study for medical logistics center site selection (MLCSS) is given to validate the proposed method.

Models for MAGDM with dual hesitant q-rung orthopair fuzzy 2-tuple linguistic MSM operators and their application to COVID-19 pandemic.

In this article, we introduce dual hesitant q -rung orthopair fuzzy 2-tuple linguistic set (DHq-ROFTLS), a new strategy for dealing with uncertainty that incorporates a 2-tuple linguistic term into dual hesitant q -rung orthopair fuzzy set (DHq-ROFS). DHq-ROFTLS is a better way to deal with uncertain and imprecise information in the decision-making environment. We elaborate the operational rules, based on which, the DHq-ROFTL weighted averaging (DHq-ROFTLWA) operator and the DHq-ROFTL weighted geometric (DHq-ROFTLWG) operator are presented to fuse the DHq-ROFTL numbers (DHq-ROFTLNs). As Maclaurin symmetric mean (MSM) aggregation operator is a useful tool to model the interrelationship between multi-input arguments, we generalize the traditional MSM to aggregate DHq-ROFTL information. Firstly, the DHq-ROFTL Maclaurin symmetric mean (DHq-ROFTLMSM) and the DHq-ROFTL weighted Maclaurin symmetric mean (DHq-ROFTLWMSM) operators are proposed along with some of their desirable properties and some special cases. Further, the DHq-ROFTL dual Maclaurin symmetric mean (DHq-ROFTLDMSM) and weighted dual Maclaurin symmetric mean (DHq-ROFTLWDMSM) operators with some properties and cases are presented. Moreover, the assessment and prioritizing of the most important aspects in multiple attribute group decision-making (MAGDM) problems is analysed by an extended novel approach based on the proposed aggregation operators under DHq-ROFTL framework. At long last, a numerical model is provided for the selection of adequate medication to control COVID-19 outbreaks to demonstrate the use of the generated technique and exhibit its adequacy. Finally, to analyse the advantages of the proposed method, a comparison analysis is conducted and the superiorities are illustrated.

Operational efficiency evaluation of urban and rural residents' basic pension insurance system by utilizing a picture fuzzy TOPSIS method based on the cumulative prospect theory.

Population aging is the most serious challenge facing the pension insurance system in China in the next few decades. Compared with the employees of civil servants and enterprises and institutions, urban and rural residents are unstable vulnerable groups with less income. In order to deal with the pension risks caused by the growing aging population and solve the security problems of urban and rural residents, our government has carried out a series of constructive works in the pension insurance system: in view of the rural and urban residents, new rural social endowment insurance system and the social endowment insurance system for urban residents have been set up and combined into a unified basic old-age insurance system for urban and rural residents in 2014. With the continuous expansion in the scale of income and expenditure of urban and rural living insurance funds and the size of the insured number, it is of great necessity to evaluate the efficiency of this system. The operational efficiency evaluation of urban and rural residents' basic pension insurance systems is viewed as multi-attribute group decision-making (MAGDM). In this paper, we propose an approach by combining the traditional Technique for Order Preference by Similarity to an Ideal Solution (TOPSIS) with cumulative prospect theory (CPT) which can be widely used with vague information. Thus, the main contribution of this study is as follows: (1) the TOPSIS method is extended by picture fuzzy sets (PFSs) with unknown weight information; (2) entropy method to obtain the original weights of attributes; (3) the picture fuzzy-CPT-TOPSIS (PF-CPT-TOPSIS) method is used to deal with the MAGDM problems under PFSs; (4) a numerical instance for operational efficiency evaluation of urban and rural residents' basic pension insurance systems is proposed to testify the effectiveness of new method; and (5) some comparative studies are provided to give effect to the rationality of PF-CPT-TOPSIS approach.

A new MAGDM method with 2-tuple linguistic bipolar fuzzy Heronian mean operators.

In this article, we introduce the 2-tuple linguistic bipolar fuzzy set (2TLBFS), a new strategy for dealing with uncertainty that incorporates a 2-tuple linguistic term into bipolar fuzzy set. The 2TLBFS is a better way to deal with uncertain and imprecise information in the decision-making environment. We elaborate the operational rules, based on which, the 2-tuple linguistic bipolar fuzzy weighted averaging (2TLBFWA) operator and the 2-tuple linguistic bipolar fuzzy weighted geometric (2TLBFWG) operator are presented to fuse the 2TLBF numbers (2TLBFNs). The Heronian mean (HM) operator, which can reflect the internal correlation between attributes and their influence on decision results, is integrated into the 2TLBF environment to analyze the effect of the correlation between decision factors on decision results. Initially, the generalized 2-tuple linguistic bipolar fuzzy Heronian mean (G2TLBFHM) operator and generalized 2-tuple linguistic bipolar fuzzy weighted Heronian mean (G2TLBFWHM) operator are proposed and properties are explained. Further, 2-tuple linguistic bipolar fuzzy geometric Heronian mean (2TLBFGHM) operator and 2-tuple linguistic bipolar weighted geometric Heronian mean (2TLBFWGHM) operator are proposed along with some of their desirable properties. Then, an approach to multi-attribute group decision-making (MAGDM) based on the proposed aggregation operators under the 2TLBF framework is developed. At last, a numerical illustration is provided for the selection of the best photovoltaic cell to demonstrate the use of the generated technique and exhibit its adequacy.

A Novel MAGDM Method Based on Hesitant Picture Fuzzy Schweizer-Sklar Maclaurin Symmetric Mean Operators and Their Application.

Multiple attribute group decision making (MAGDM) issues play important roles in our daily life. In order to solve the problem that decision makers (DMs) may feel hesitant to select the appropriate evaluation values from several possible values in the process of providing evaluations, fuzzy theory and its extensions are widely applied in MAGDM problems. In this study, we first proposed hesitant picture fuzzy sets (HPFSs), which is a combination of the hesitant fuzzy set and picture fuzzy set. Subsequently, we introduced a novel Schweizer-Sklar t-norm and t-conorm operation rules of HPFSs and proposed a family of hesitant picture fuzzy Schweizer-Sklar Maclaurin symmetric mean operators. To show the application procedure of the proposed method to practical MAGDM issues, a numerical example about enterprise informatization level evaluation was employed to elaborate the calculation process with the proposed method. Finally, through the parameter analysis, validity analysis, and comparative analysis with some existing methods, we found that our method is more superior in providing DMs a greater decision-making freedom and relaxing the constraints on expressing personal preferences. This study provides a general framework of the proposed method to MAGDM problems under hesitant picture fuzzy environment, which enriches the fuzzy theory and its applications.

Entropy-Based GLDS Method for Social Capital Selection of a PPP Project with q-Rung Orthopair Fuzzy Information.

The social capital selection of a public-private-partnership (PPP) project could be regarded as a classical multiple attribute group decision-making (MAGDM) issue. In this paper, based on the traditional gained and lost dominance score (GLDS) method, the q-rung orthopair fuzzy entropy-based GLDS method was used to solve MAGDM problems. First, some basic theories related to the q-rung orthopair fuzzy sets (q-ROFSs) are briefly reviewed. Then, to fuse the q-rung orthopair fuzzy information effectively, the q-rung orthopair fuzzy Hamacher weighting average (q-ROFHWA) operator and q-rung orthopair fuzzy Hamacher weighting geometric (q-ROFHWG) operator based on the Hamacher operation laws are proposed. Moreover, to determine the attribute weights, the q-rung orthopair fuzzy entropy (q-ROFE) is proposed and some significant merits of it are discussed. Next, based on the q-ROFHWA operator, q-ROFE, and the traditional GLDS method, a MAGDM model with q-rung orthopair fuzzy information is built. In the end, a numerical example for social capital selection of PPP projects is provided to testify the proposed method and deliver a comparative analysis.

Cumulative Prospect Theory: Performance Evaluation of Government Purchases of Home-Based Elderly-Care Services Using the Pythagorean 2-tuple Linguistic TODIM Method.

The aging trend of China's population is increasing, and the pension problem is becoming increasingly prominent. The pension mode provided by the government alone can no longer meet the social demand, and the government's purchase of home-based care services from social organizations has become a new trend. In order to improve the efficiency and quality of pension services, a reasonable performance evaluation model needs to be established. Performance evaluations of home-based elderly-care services purchased by the government are problematic as a result of multiple-attribute group decision-making (MAGDM), as the problems are not single-attribute or single-expert issues. The extended TODIM not only integrates the advantages of cumulative prospect theory (CPT) into a consideration of the psychological factors of DMs, but also retains the superiority of the classical TODIM in relative dominance. The Pythagorean 2-tuple linguistic sets (P2TLSs) could easily depict qualitative assessment information related to the government's purchase of home-based care services. Thus, in this paper, we extend the TODIM method based on the cumulative prospect theory (CPT) to the Pythagorean 2-tuple linguistic sets (P2TLSs) and propose a Pythagorean 2-tuple linguistic CPT-TODIM (P2TL-CPT-TODIM) method for MAGDM. The P2TL-CPT-TODIM method was proven superior to the classical one through a case study that included a performance evaluation of a home-based elderly-care service purchased by the government. Meanwhile, a comparison with the P2TL-CPT-TODIM method was performed to demonstrate the stability and effectiveness of the designed method.

VIKOR Method for MAGDM Based on Q-Rung Interval-Valued Orthopair Fuzzy Information and Its Application to Supplier Selection of Medical Consumption Products.

The VIKOR model has been considered a viable tool for many decision-making applications in the past few years, given the advantages of considering the compromise between maximizing the utility of group and minimizing personal regrets. The q-rung interval-valued orthopair fuzzy set (q-RIVOFS) is a generalization of intuitionistic fuzzy set (IFS) and Pythagorean fuzzy set (PFS) and has emerged to solve more complex and uncertain decision making problems which IFS and PFS cannot handle. In this manuscript, the key innovation is to combine the traditional VIKOR model with q-RIVOFS to develop the q-rung interval-valued orthopair fuzzy VIKOR model. In the new developed model, to express more information, the attribute's values in MAGDM problems are depicted by q-RIVOFNs. First of all, some basic theories and aggregation operators of q-RIVOFNs are simply introduced. Then we develop the origin VIKOR model to q-RIVOFS environment and briefly express the computing steps of this new established model. Thereafter, the effectiveness of the model is verified by an example of supplier selection of medical consumer products and through comparative analysis, the superiority of the new method is further illustrated.

Pythagorean 2-Tuple Linguistic Taxonomy Method for Supplier Selection in Medical Instrument Industries.

Supplier selection in medical instrument industries is a classical multiple attribute group decision making (MAGDM) problem. The Pythagorean 2-tuple linguistic sets (P2TLSs) can reflect uncertain or fuzzy information well and solve the supplier selection in medical instrument industries, and the original Taxonomy is very appropriate for comparing different alternatives with respect to their advantages from studied attributes. In this study, we present an algorithm that combines Pythagorean 2-tuple linguistic numbers (P2TLNs) with the Taxonomy method, where P2TLNs are applied to express the evaluation of decision makers on alternatives. Relying on the Pythagorean 2-tuple linguistic weighted average (P2TLWA) operator or Pythagorean 2-tuple linguistic weighted geometric (P2TLWG) operator to fuse P2TLNs, the new general framework is established for Pythagorean 2-tuple linguistic multiple attribute group decision making (MAGDM) under the classical Taxonomy method. Ultimately, an application case for supplier selection in medical instrument industries is designed to test the novel method's applicability and practicality and a comparative analysis with three other methods is used to elaborate further.