2020 is the year of decisive victory in the comprehensive well-off society and the battle against poverty. While fully completing the task of poverty alleviation, consolidating the achievements of poverty alleviation, and researching and establishing a long-term mechanism to solve relative poverty, it is also necessary to do a good job in summarising poverty alleviation. The sorting and summary of China’s poverty alleviation theory is not only an important content of poverty alleviation summary, but also a need to study and consolidate the achievements of poverty alleviation. The risk assessment of poverty alleviation households’ return to poverty in Chongqing ethnic regions is the MAGDM. The MULTIMOORA approach is an efficient technique to solve the MAGDM, and CRITIC approach is an efficient technique to obtain the objective weight information. PDHLTS could excavate the uncertainty more effectively and deeply for risk assessment of poverty alleviation households’ return to poverty in Chongqing ethnic regions. In this study, CRITIC technique is put forward with weight numbers along with PDHLTSs and PDHL-MULTIMORA approach is administrated for MAGDM with PDHLTSs. At last, numerical example for risk assessment of poverty alleviation households’ return to poverty in Chongqing ethnic regions and some comparisons is put forward to illustrate the PDHL-MULTIMORA.

Probabilistic dual hesitant fuzzy set (PDHFS), as an extension of dual hesitant fuzzy set (DHFS) and probabilistic hesitant fuzzy set (PHS), can better describe the uncertainty and fuzziness in the real world through membership degree (MD) and non-membership degree (NMD) and their respective probability information. Therefore, it can collect more comprehensive fuzzy information in decision-making issues, which makes PDHFS has a wide range of applications in practice. The distance, similarity and entropy measures (EMs) of PDHFSs were studied. Due to the particularity of PDHFS, the length of MD and NMD of two probabilistic dual hesitation fuzzy elements (PDHFEs) are often different. To define the distance measure more expediently, many current studies need to add fresh elements to ensure that the length of corresponding elements in MD and NMD are the same, which will destroy the original information of the elements. In order to overcome this disadvantage, this paper defined some novel PDHF distance measures without adding elements. Some novel PDHF similarity measures were defined through the complementary relationship between distance and similarity measures based on the newly proposed PDHF distance measures. The fuzziness of a given PDHFS can be measured by the similarity measure between it and its complement. Based on the property, some novel PDHF EMs were proposed. Finally, three numerical examples are given to illustrate the effectiveness and rationality of these novel information measures.

With the rapid advancement of Internet technology, the number of online shopping platforms has been increasing. Poor online shopping platform causes all sorts of trouble among the people despite convenience. A comprehensive and reasonable evaluation of online shopping platforms is of great significance. Therefore, this study establishes an online shopping platform evaluation model based on probability double linguistic-combinative distance-based assessment (PDHL-CODAS). First, the notion of probabilistic double hierarchy linguistic term sets (PDHLTSs) is reviewed. Then the distance formulas of PDHLTS are defined. Thereafter, cumulative prospect theory is used to generate the cumulative weight of probabilistic double hierarchy linguistic information. Additionally, the integrated determination of objective criteria weights method is introduced to calculate the objective weight. PDHL-CODAS method is established and applied to the evaluation of online shopping platforms. Finally, unlike the available probabilistic double hierarchy linguistic multiple attribute decision making methods, the defined method is scientifically effective.

In multiattribute group decision-making (MAGDM), experts often articulate their preference information to support decision-making by applying the multigranular linguistic model. Thus, the present work aims to introduce a novel MAGDM model to manage multigranular generalized orthopair 2-tuple linguistic information (GO2TLI). To begin with, a generalized orthopair 2-tuple linguistic model is put forward with the attempt of taking advantages of both q-rung orthopair fuzzy set (q-ROFS) and the 2-tuple linguistic model, while a transformation approach is supplied to tackle the consistency of multigranular GO2TLI. In addition, the Archimedean Copula as well as the Co-Copula operators are extended to handle GO2TLI along with their operational laws, to comprehensively model the relationship among attributes and experts. The Banzhaf Choquet-Copula aggregation operators on the generalized orthopair 2-tuple linguistic (GO2TLBCCA) are introduced, also some of its properties discussed. Third, the algorithms for regulating and determining the fuzzy measure (FM) of attributes and experts sets are proposed, followed by the corresponding decision-making approaches based upon the proposed GO2TLBCCA. The proposed MAGDM model can not only accommodate effectively the FMs of attribute (and expert) sets which are given subjectively, but also effectively address some multigranular GO2TLI as well as the partially unknown or completely unknown weights of attribute and expert sets. Finally, a case study is provided to demonstrate the validity of the proposed approach along with relevant discussions, the merits of the proposed approach are also analyzed by comparing with some extant decision methods.

On the basis of previous scholars’ research, we improve the traditional TOmada de Decisão Interativa e Multicritério (TODIM) along with Cumulative Prospect Theory (CPT) under the 2-tuple linguistic Pythagorean fuzzy sets (2TLPFSs) in this article. First of all, we give some definitions of Pythagorean fuzzy sets, 2TLPFSs, and the 2-tuple linguistic Pythagorean fuzzy weighted average as well as 2-tuple linguistic Pythagorean fuzzy weighted geometric operators. After that, according to the existing researches, we simply introduce the TODIM method and TODIM method under 2TLPFSs. Furthermore, we propose the TODIM method based on CPT (CPT–TODIM) for multiple attribute group decision-making (MAGDM) with 2TLPFSs. Finally, a numerical example about company credit risk assessment is used to explain the new proposed method. Comparing with other methods, there is no doubt that this new method has superiority. To be exact, because the new method fully considers the mental factors of decision makers, it can better solve the uncertainty of MAGDM and improve the rationality of decision-making.

Intuitionistic fuzzy sets are often employed to depict complex and uncertain environments. The purpose of this article is to construct a new approach for dealing with multiattribute group decision making (MAGDM) problems. In this paper, we introduce the concept of cumulative prospect theory (CPT) into the original multiattributive border approximation area comparison (MABAC) method and create the intuitionistic fuzzy MABAC method based on CPT (CPT-IF-MABAC method). The new CPT-IF-MABAC method not only has fairly strong operability, but also inherits the characteristic of CPT that considers the influence of decision makers' attitude. Furthermore, this new model mixes together the determination method of attribute weight and alternative. At the end, the stability and availability of this method are demonstrated through an application instance about cold chain and the comparison with the existing methods, such as IF-MULTIMOORA method and IF-VIKOR method. In the future, we devote ourselves to explore more applications of this new proposed method and other more effective solutions for MAGDM.

Network security is a very important issue in recent years. For many new or traditional enterprises, utilizing internet to store and analyze data has become an indivisible part of their production and operation. But many enterprises do not have enough ability to ensure the security of information, so the choice of the optimal network security service provider has become a practical problem faced by many ordinary companies. In this paper, we establish bipolar fuzzy interactive multi-criteria decision-making (TODIM) based on the cumulative prospect theory (CPT-TODIM) model for dealing with the problem of multi-attribute group decision making, and this special model is applied to the field of network security about the issue of network security service provider selection. The second and third parts of this paper introduce the knowledge of bipolar fuzzy and the initial CPT-TODIM method. In the fourth part, we discuss the bipolar fuzzy CPT-TODIM model in detail. In the last two parts of this article, the method proposed in this paper is applied to the field of network security provider selection and compared with other methods. The results show that bipolar fuzzy CPT-TODIM method with unique advantages in some aspects is reasonable and effective, and can be applied to more uncertain decision fields. It is hoped that this method can help enterprises make better decisions.

The 2-tuple linguistic neutrosophic set (2TLNS) does a good job in coping with vague and uncertain environments and has been widely used in numerous fields. In this article, we come up with a new solution of multiple attribute group decision-making (MAGDM) problems, named as the modified TODIM method based on cumulative prospect theory and 2-tuple linguistic neutrosophic sets (CPT-2TLN-TODIM method). To ensure relatively objective attribute weights, the CRITIC is integrated into this new model in this paper. The CPT-2TLN-TODIM method fully considers the psychological state of decision makers that makes it more realistic. What's more, we introduce the application of CPT-2TLN-TODIM method in the evaluation of network security assessment team for verifying the practicability of the CPT-2TLN-TODIM method. And finally, the reliability of CPT-2TLN-TODIM method is confirmed by comparing with other existed methods. In the immediate future, we will further explore the application of this method in other fields and keep trying to put forward more scientific and reasonable methods to solve MAGDM problems.

As the generalisation of intuitionistic fuzzy sets (IFSs) and Pythagorean fuzzy set (PFS), the q-rung orthopair fuzzy set (q-ROFS) is more useful to express fuzzy and ambiguous information. Meanwhile, to consider human’s hesitance, the concept of q-rung orthopair hesitant fuzzy set (q-ROHFS) is presented, which can be more valid for handling real multiple attribute decision-making (MADM) problems. To fuse the information in q-ROHFS more effectively, in this article, based on power average (PA) operator and generalised Heronian mean (GHM) operator, some q-rung orthopair hesitant fuzzy power generalised Heronian mean (q-ROHFPGHM) operators which can consider the relationships between being fused arguments are defined and studied. Evidently, the new proposed operators can obtain more exact results than other existing methods. In addition, some precious properties of these operators are discussed. Afterwards, the defined aggregation operators are used to MADM with q-rung orthopair hesitant fuzzy numbers (q-ROHFNs) and the MADM decision-making model is developed. In accordance with the defined operators and built model, the q-rung orthopair hesitant fuzzy weighted power generalised Heronian mean (q-ROHFWPGHM) operator and the q-rung orthopair hesitant fuzzy weighted power generalised geometric Heronian mean (q-ROHFWPGGHM) operator are applied to deal with green supplier selection in supply chain management, and the availability and superiority of the proposed operators are analysed by comparing with some existing approaches. The method presented in this paper can effectually solve the MADM problems which the decision-making information is expressed by q-ROHFNs and the attributes are interactive.

In this paper, we utilize Hamacher operations and power aggregation operators to develop some Pythagorean fuzzy Hamacher power aggregation operators: Pythagorean fuzzy Hamacher power average (PFHPA) operator, Pythagorean fuzzy Hamacher power geometric (PFHPG) operator, Pythagorean fuzzy Hamacher power weighted average (PFHPWA) operator, Pythagorean fuzzy Hamacher power weighted geometric (PFHPWG) operator, Pythagorean fuzzy Hamacher power ordered weighted average (PFHPOWA) operator, Pythagorean fuzzy Hamacher power ordered weighted geometric (PFHPOWG) operator, Pythagorean fuzzy Hamacher power hybrid average (PFHPHA) operator and Pythagorean fuzzy Hamacher power hybrid geometric (PFHPHG) operator. The prominent characteristic of these proposed operators are studied. Then, we utilize these operators to develop some approaches to solve the multiple attribute decision making problems with Pythagorean fuzzy numbers (PFNs). Finally, a practical example is given to verify the developed approach and deliver a comparative analysis.

The dual hesitant Pythagorean fuzzy set (DHPFS) consists of two parts, that is, the membership hesitancy function and the nonmembership hesitancy function, supporting a more exemplary and flexible access to assign values for each element in the domain. It is very suitable to handle the situation that there are various possible values in membership and nonmembership degrees to depict the true circumstance. The bidirectional project method of DHPFS calculates method considered not only the bidirectional projection magnitudes and the distance but also includes angle between objects evaluated. Therefore, this paper proposes a bidirectional project method of DHPFS to handle the multiple attribute decision-making (MADM) problem under the dual hesitant Pythagorean fuzzy environment. Through the measure between each alternative decision matrix and the positive and negative ideal alternative matrix, the ranking order all alternatives can be used to select the best alternative. Furthermore, a model for MADM has been given. Finally, a numerical example for performance assessment of new rural construction has been given to demonstrate the application of bidirectional project method of DHPFS, and we used the dual hesitant Pythagorean weighted Bonferroni mean to compare its reasonable and effectiveness.

The Pythagorean fuzzy set (PFS) is characterized by two functions expressing the degree of membership and the degree of nonmembership, which square sum of them is equal or less than 1. It was proposed as a generalization of a fuzzy set to deal with indeterminate and inconsistent information. In this study, we shall present some novel Dice similarity measures of PFSs and the generalized Dice similarity measures of PFSs and indicates that the Dice similarity measures and asymmetric measures (projection measures) are the special cases of the generalized Dice similarity measures in some parameter values. Then, we propose the generalized Dice similarity measures-based multiple attribute group decision-making models with Pythagorean fuzzy information. Then, we apply the generalized Dice similarity measures between PFSs to multiple attribute group decision making. Finally, an illustrative example is given to demonstrate the efficiency of the similarity measures for selecting the desirable ERP system.

In this paper, the Hamy mean (HM) operator, weighted HM (WHM), dual HM (DHM) operator, and dual WHM (WDHM) operator under the q-rung orthopair fuzzy sets (q-ROFSs) is studied to propose the q-rung orthopair fuzzy HM (q-ROFHM) operator, q-rung orthopair fuzzy WHM (q-ROFWHM) operator, q-rung orthopair fuzzy DHM (q-ROFDHM) operator, and q-rung orthopair fuzzy weighted DHM (q-ROFWDHM) operator and some of their desirable properties are investigated in detail. Then, we apply these operators to multiple attribute decision-making problems. Finally, a practical example for enterprise resource planning system selection is given to verify the developed approach and to demonstrate its practicality and effectiveness.

In this paper, according to the Maclaurin symmetric mean (MSM) operator, the dual MSM (DMSM) operator and the q-rung interval-valued orthopair fuzzy set (q-RIVOFS), we develop some novel MSM operators under the q-rung interval-valued orthopair fuzzy environment, such as, the q-rung interval-valued orthopair fuzzy MSM operator, the q-rung interval-valued orthopair fuzzy weighted MSM (q-RIVOFWMSM) operator, the q-rung interval-valued orthopair fuzzy DMSM operator, and the q-rung interval-valued orthopair fuzzy weighted DMSM operator. In addition, some precious properties and numerical examples of these new operators are given in detail. These new operators have the advantages of considering the interrelationship of arguments and can deal with multiple attribute group decision-making problems with q-rung interval-valued orthopair fuzzy information. Finally, a reality example for green suppliers selection in green supply chain management is provided to demonstrate the proposed approach and to verify its rationality and scientific.

The Maclaurin symmetric mean (MSM) operator is a classical mean type aggregation operator used in modern information fusion theory, which is suitable to aggregate numerical values. The prominent characteristic of the MSM operator is that it can capture the interrelationship among the multi-input arguments. In this paper, we extend the MSM operator and dual MSM operator to q-rung orthopair fuzzy sets to propose the q-rung orthopair fuzzy MSM operator, q-rung orthopair fuzzy dual MSM operator, q-rung orthopair fuzzy weighted MSM operator, and q-rung orthopair fuzzy weighted dual MSM operator. Then, some desirable properties and special cases of these operators are discussed in detail. Finally, a numerical example is provided to illustrate the feasibility of the proposed methods and deliver the sensitivity analysis and comparative analysis.

In this paper, we expand the generalised Heronian mean (GHM) operator, generalised weighted Heronian mean (GWHM), geometric Heronian mean (GHM) operator, and weighted geometric Heronian mean (WGHM) operator with 2-tuple linguistic Pythagorean fuzzy numbers (2TLPFNs) to propose generalised 2-tuple linguistic Pythagorean fuzzy Heronian mean (G2TLPFHM) operator, generalised 2-tuple linguistic Pythagorean fuzzy weighted Heronian mean (G2TLPFWHM) operator, 2-tuple linguistic Pythagorean fuzzy geometric Heronian mean (2TLPFGHM) operator, 2-tuple linguistic Pythagorean fuzzy weighted geometric Heronian mean (2TLPFWGHM) operator. Then, the MADM methods are proposed with these operators. In the end, we utilise an applicable example for green supplier selection to prove the proposed methods.

In this paper, we expand the Muirhead mean (MM) operator and dual MM (DMM) operator with 2-tuple linguistic neutrosophic numbers (2TLNNs) to propose the 2-tuple linguistic neutrosophic numbers MM (2TLNNMM) operator, 2-tuple linguistic neutrosophic numbers weighted MM (2TLNNWMM) operator, 2-tuple linguistic neutrosophic numbers DMM (2TLNNDMM) operator and 2-tuple linguistic neutrosophic numbers weighted DMM (2TLNNWDMM) operator. Then, the MADM methods are proposed with these two operators. Finally, an example for green supplier selection is used to show the proposed methods.

In this paper, we investigate the multiple attribute decision making problems with Pythagorean fuzzy information. Then, we utilize arithmetic and geometric operations to develop some Pythagorean fuzzy interaction aggregation operators: Pythagorean fuzzy interaction weighted average (PFIWA) operator, Pythagorean fuzzy interaction weighted geometric (PFIWG) operator, Pythagorean fuzzy interaction ordered weighted average (PFIOWA) operator, Pythagorean fuzzy interaction ordered weighted geometric (PFIOWG) operator, Pythagorean fuzzy interaction hybrid average (PFIHA) operator, Pythagorean fuzzy interaction hybrid geometric (PFIHG) operator, Pythagorean fuzzy interaction correlate aggregation operators, Pythagorean fuzzy interaction induced aggregation operators, Pythagorean fuzzy interaction induced correlate aggregation operators, Pythagorean fuzzy interactive power arithmetic and geometric aggregation operators. The prominent characteristic of these proposed operators are studied. Then, we have utilized these operators to develop some approaches to solve the Pythagorean fuzzy multiple attribute decision making problems. Finally, a practical example for selecting the service outsourcing provider of communications industry is given to verify the developed approach and to demonstrate its practicality and effectiveness.

In this paper, we investigate the multiple attribute decision making (MADM) problem based on the arithmetic, geometric aggregation operators and Hamacher operations with picture fuzzy information. Then, motivated by the ideal of traditional arithmetic, geometric aggregation operators and Hamacher operations, we have developed some aggregation operators for aggregating picture fuzzy information: picture fuzzy Hamacher aggregation operators, picture fuzzy Hamacher geometric aggregation operators, picture fuzzy Hamacher correlated aggregation operators, induced picture fuzzy Hamacher aggregation operators, induced picture fuzzy Hamacher correlated aggregation operators, picture fuzzy Hamacher prioritized aggregation operators, picture fuzzy Hamacher power aggregation operators. Then, we have utilized these operators to develop some approaches to solve the picture fuzzy multiple attribute decision making problems. Finally, a practical example for enterprise resource planning (ERP) system selection is given to verify the developed approach and to demonstrate its practicality and effectiveness.

The generalized Heronian mean and geometric Heronian mean operators provide two aggregation operators that consider the interdependent phenomena among the aggregated arguments. In this paper, the generalized Heronian mean operator and geometric Heronian mean operator under the q-rung orthopair fuzzy sets is studied. First, the q-rung orthopair fuzzy generalized Heronian mean (q-ROFGHM) operator, q-rung orthopair fuzzy geometric Heronian mean (q-ROFGHM) operator, q-rung orthopair fuzzy generalized weighted Heronian mean (q-ROFGWHM) operator, and q-rung orthopair fuzzy weighted geometric Heronian mean (q-ROFWGHM) operator are proposed, and some of their desirable properties are investigated in detail. Furthermore, we extend these operators to q-rung orthopair 2-tuple linguistic sets (q-RO2TLSs). Then, an approach to multiple attribute decision making based on q-ROFGWHM (q-ROFWGHM) operator is proposed. Finally, a practical example for enterprise resource planning system selection is given to verify the developed approach and to demonstrate its practicality and effectiveness.

In this paper, we utilize power aggregation operators to develop some Pythagorean fuzzy power aggregation operators: Pythagorean fuzzy power average operator, Pythagorean fuzzy power geometric operator, Pythagorean fuzzy power weighted average operator, Pythagorean fuzzy power weighted geometric operator, Pythagorean fuzzy power ordered weighted average operator, Pythagorean fuzzy power ordered weighted geometric operator, Pythagorean fuzzy power hybrid average operator, and Pythagorean fuzzy power hybrid geometric operator. The prominent characteristic of these proposed operators are studied. Then, we have utilized these operators to develop some approaches to solve the Pythagorean fuzzy multiple attribute decision-making problems. Finally, a practical example is given to verify the developed approach and to demonstrate its practicality and effectiveness.

The Maclaurin symmetric mean (MSM) operator is a classical mean type aggregation operator used in modern information fusion theory, which is suitable to aggregate numerical values. The prominent characteristic of the MSM operator is that it can capture the interrelationship among the multiinput arguments. In this paper, we extend MSM to Pythagorean fuzzy environment to propose the Pythagorean fuzzy Maclaurin symmetric mean and Pythagorean fuzzy weighted Maclaurin symmetric mean operators. Then, some desirable properties and special cases of these operators are discussed in detail. Finally, a numerical example is provided to illustrate the feasibility of the proposed methods and deliver a comparative analysis.

Hamacher product is a t-norm and Hamacher sum is a t-conorm. They are good alternatives to algebraic product and algebraic sum, respectively. Nevertheless, it seems that most of the existing hesitant fuzzy aggregation operators are based on the algebraic operations. In this paper, we utilize Hamacher operations to develop some Pythagorean hesitant fuzzy aggregation operators: Pythagorean hesitant fuzzy Hamacher weighted average (PHFHWA) operator, Pythagorean hesitant fuzzy Hamacher weighted geometric (PHFHWG) operator, Pythagorean hesitant fuzzy Hamacher ordered weighted average (PHFHOWA) operator, Pythagorean hesitant fuzzy Hamacher ordered weighted geometric (PHFHOWG) operator, Pythagorean hesitant fuzzy Hamacher induced ordered weighted average (PHFHIOWA) operator, Pythagorean hesitant fuzzy Hamacher induced ordered weighted geometric (PHFHIOWG) operator, Pythagorean hesitant fuzzy Hamacher induced correlated aggregation operators, Pythagorean hesitant fuzzy Hamacher prioritized aggregation operators, and Pythagorean hesitant fuzzy Hamacher power aggregation operators. The special cases of these proposed operators are studied. Then, we have utilized these operators to develop some approaches to solve the Pythagorean hesitant fuzzy multiple attribute decision making problems. Finally, a practical example for green supplier selections in green supply chain management is given to verify the developed approach and to demonstrate its practicality and effectiveness.

In this paper, we presented 10 similarity measures between Pythagorean fuzzy sets (PFSs) based on the cosine function by considering the degree of membership, degree of nonmembership and degree of hesitation in PFSs. Then, we applied these similarity measures and weighted similarity measures between PFSs to pattern recognition and medical diagnosis. Finally, two illustrative examples are given to demonstrate the efficiency of the similarity measures for pattern recognition and medical diagnosis.

In this paper, we propose an uncertain linguistic hybrid geometric mean (ULHGM) operator, which is based on the uncertain linguistic weighted geometric mean (ULWGM) operator and the uncertain linguistic ordered weighted geometric (ULOWG) operator proposed by Xu [Z. S. Xu, "An approach based on the uncertain LOWG and induced uncertain LOWG operators to group decision making with uncertain multiplicative linguistic preference relations", Decision Support Systems41 (2006) 488–499] and study some desirable properties of the ULHGM operator. We have proved both ULWGM and ULOWG operators are the special case of the ULHGM operator. The ULHGM operator generalizes both the ULWGM and ULOWG operators, and reflects the importance degrees of both the given arguments and their ordered positions. Based on the ULWGM and ULHGM operators, we propose a practical method for multiple attribute group decision making with uncertain linguistic preference relations. Finally, an illustrative example demonstrates the practicality and effectiveness of the proposed method.