Medical images tend to exhibit blurred anatomical boundaries and similar intensity distributions across different organs or tissues, which reflects a high degree of self-similarity. Such characteristics hinder the effectiveness of current token reduction techniques applied to transformer-based medical image segmentation architectures, thereby limiting their applicability in point-of-care scenarios. To address this issue, we decouple self-similarity into intra-class and inter-class components and introduce a progressive token merging (PTM) method for medical Transformers. The key challenge is to (1) merge visually similar and semantically identical (i.e., intra-class) tokens to improve throughput, while (2) avoiding the merging of visually similar but semantically different (i.e., inter-class) tokens to maintain segmentation performance. Specifically, we perform token merging in two stages: visual token grouping (VTG) and semantic token matching (STM). At the initial layer, VTG merges tokens with similar appearance cues within a local window by average pooling, which suppresses noisy features and reduces the risk of incorrect inter-class merging. At the intermediate layer, STM leverages semantic cues in the tokens to construct a global bipartite graph and further reduces background or redundant tokens through bipartite matching. Through these two rounds of merging, PTM promotes a more balanced distribution of attention across semantic categories. Experimental results on two widely used medical image segmentation benchmarks demonstrate that the proposed method improves both segmentation quality and computational efficiency. The code and pretrained models will be publicly available at https://github.com/wuwen1994/PTM.

Multi-attribute group decision-making (MAGDM) refers to a series of decision-making problems that rank all possible alternatives based on decision makers’ cognition and evaluations over alternatives from multiple attributes. Hence, the precondition of MAGDM is felicitously describing decision makers’ fuzzy and uncertain cognitive information in complicated decision-making issues. The recently proposed linguistic q-rung orthopair fuzzy set (Lq-ROFS), which uses two linguistic terms to denote membership and non-membership degrees, has been proved to be an effective and promising tool to depict decision makers’ complex cognition in real MAGDM problems. Considering the drawbacks of existing Lq-ROFS-based decision-making methods, this paper focuses on MAGDM approaches where decision makers’ cognitive information is denoted by Lq-ROFSs. The main contribution of this paper is to propose a novel MAGDM method based on Lq-ROFSs. This paper introduces a new MAGDM method under Lq-ROFSs. In order to do this, this study first puts forward some new operational rules for linguistic q-rung orthopair fuzzy numbers (Lq-ROFNs) based on Archimedean copula. These new operational rules are more flexible than existing ones and some other operations can be derived by using different generators. Second, to effectively aggregate Lq-ROFNs, the extended power average operator is applied in linguistic q-rung orthopair fuzzy environment and based on the new operational rules, some novel aggregation operators are generated. Afterward, the developed aggregation operators are used in decision-making problems and a novel MAGDM method which concentrates on linguistic q-rung orthopair fuzzy decision environment is introduced. Specific steps of the new method are illustrated in detail and it is then applied in some illustrative examples to verify its effectiveness. Our proposed method is effective for handling MAGDM problems under Lq-ROFSs. Numerical examples have shown the effectiveness in handling realistic MAGDM problems. In addition, comparison with some existing methods illustrates the advantages and superiorities of our method. This paper introduces a new MAGDM method under Lq-ROFSs. This method is based on Archimedean copula, extended power average operator, and Lq-ROFSs, and is powerful and flexible to cope with MAGDM problems in reality.

The preference ranking organization method for enrichment evaluation (PROMETHEE) has been proved to be one of the most effective techniques to rank alternatives of multi-criteria decision-making (MCDM) problems. However, the existing PROMETHEE cannot accurately adjust the representation range of uncertain information. Besides, the weight determination in PROMETHEE heavily relies on the decision matrix of alternatives on the criteria. Moreover, the information aggregation in PROMETHEE models lacks consideration of the interrelationship among criteria. To address the aforementioned shortcomings, this paper introduces a novel MCDM method that integrates the best-worst method (BWM) and PROMETHEE to help the decision-maker (DM) select the optimum alternative under the probabilistic dual-hesitant Pythagorean fuzzy (PDHPF) environment. Firstly, we extend PROMETHEE method to PDHPF scenario, which not only helps the DM depict subjective evaluations, but also provides the DM with a laxer constraint to present decision information. Secondly, the PDHPF power weighted Hamy mean operator (PDHPFPWHM) is utilized to aggregate the preference information of PROMETHEE. Additionally, the BWM method is utilized and extended to the PDHPF environment for acquiring optimal weights of criteria. The high efficiency and consistency of BWM are well-suited for the complex PDHPF environment. Finally, the method is applied to a semiconductor supplier selection case to demonstrate the validity, superiority, and feasibility of the proposed approach.

Decision-making processes are significantly influenced by internal social network interactions and external information inputs. While previous research has highlighted the role of social networks in opinion evolution, the dynamics of information dissemination and its interaction with these networks are less understood. To bridge this gap, we introduce the Social-Information-Opinion Dynamic Supernetwork (SIO-DS) model, which integrates critical factors such as the impact of external information and opinion propagation, alongside the influence of internal social network structures and individual willingness to adjust opinions. This model takes into account the varied levels of confidence and individualized dynamic influence among decision makers, recognizing both their asymmetry and diversity. It performs opinion dynamics using bounded confidence models and parameters that govern information dissemination. We found that scale-free networks, which feature influential leaders, are more effective at reaching consensus compared to small-world networks, which are hindered by limited inter-group connections. The speed of information dissemination is critical; moderate speeds help in maintaining a stable consensus by balancing social influence, while very fast or slow speeds risk exacerbating polarization based on how social influence is managed. The SIO-DS model has broad implications for enhancing decision-making in corporate management by optimizing network structures, in public policy by managing public opinion, and in crisis management by developing effective communication strategies. Ultimately, this model not only deepens our understanding of opinion dynamics but also provides practical tools for improving decision-making quality and efficiency in various contexts.

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

Online reviews are an important part of product information and have important effects on consumers’ purchasing decisions. Some sellers try to manipulate the market by inducing online reviews. In this study, a signal game model based on Bayesian conditional probability is constructed to analyze the preconditions, decision-making process, and effect on market demand and profit of this behavior. The results show that first, when consumer sensitivity to rebates reaches a certain threshold, low-quality sellers will adopt a conditional rebate strategy to induce consumers to give positive reviews. Second, the optimal rebate cost (β*) is obtained, where β* increases with the product price (p), but it is not necessarily monotonic in consumers’ sensitivity to rebates (ρ) or the proportion of high-quality products (α). Third, the conditional rebate strategy can only work in a market dominated by low-quality goods. Using the conditional rebate strategy in a market dominated by high-quality goods will not bring benefits to low-quality sellers but will harm their profits. This study proposes that some developing online markets have collusive behaviors owing to a lack of regulations and laws, as well as consumers’ concern for small interests. Ensuring the orderly development of online markets will require joint efforts by platform enterprises, government agencies, and consumers.

The presence of numerous uncertainties in hybrid decision information systems (HDISs) renders attribute reduction a formidable task.Currently available attribute reduction algorithms, including those based on Pawlak attribute importance, Skowron discernibility matrix, and information entropy, struggle to effectively manages multiple uncertainties simultaneously in HDISs like the precise measurement of disparities between nominal attribute values, and attributes with fuzzy boundaries and abnormal values.In order to address the aforementioned issues, this paper delves into the study of attribute reduction within HDISs.First of all, a novel metric based on the decision attribute is introduced to solve the problem of accurately measuring the differences between nominal attribute values.The newly introduced distance metric has been christened the supervised distance that can effectively quantify the differences between the nominal attribute values.Then, based on the newly developed metric, a novel fuzzy relationship is defined from the perspective of "feedback on parity of attribute values to attribute sets".This new fuzzy relationship serves as a valuable tool in addressing the challenges posed by abnormal attribute values.Furthermore, leveraging the newly introduced fuzzy relationship, the fuzzy conditional information entropy is defined as a solution to the challenges posed by fuzzy attributes.It effectively quantifies the uncertainty associated with fuzzy attribute values, thereby providing a robust framework for handling fuzzy information in hybrid information systems.Finally, an algorithm for attribute reduction utilizing the fuzzy conditional information entropy is presented.The experimental results on 12 datasets show that the average reduction rate of our algorithm reaches 84.04%, and the classification accuracy is improved by 3.91% compared to the original dataset, and by an average of 11.25% compared to the other 9 state-of-the-art reduction algorithms.The comprehensive analysis of these research results clearly indicates that our algorithm is highly effective in managing the intricate uncertainties inherent in hybrid data.

This paper advances the field of multi-attribute group decision making (MAGDM) by proposing a novel framework based on interval-valued q-rung dual hesitant fuzzy sets (IVq-RDHFSs). IVq-RDHFSs, which surpass most existing fuzzy sets, effectively represent complex fuzzy information by describing membership and non-membership degrees through interval value sets. However, prior MAGDM methods based on IVq-RDHFSs have been limited by the functions of operation rules and aggregation operators (AOs). This limitation is addressed through the construction of a new MAGDM framework, leveraging the robust Frank t-norm and t-conorm (FTT) operation and the extended power average (EPA) operator. The proposed framework features the interval-valued q-rung dual hesitant fuzzy Frank weighted extended power average (IVq-RDHFFWEPA) operator to obtain comprehensive evaluation values. The paper also introduces novel techniques for determining the weights of decision-makers and attributes. Practical applications of the proposed method are demonstrated through the assessment of desalination technology selection and rural green eco-tourism projects. Sensitivity and comparison analyses validate the superior functionality, accuracy, and flexibility of this method compared to many state-of-the-art methods. The contributions of this paper are two-fold: it develops efficient measurement techniques for IVq-RDHFSs, such as distance and weight calculation, and it introduces a comprehensive MAGDM method by integrating FTT and EPA under IVq-RDHFSs, which improves the efficiency of solving decision-making problems.

The ability of q-rung dual hesitant fuzzy sets (q-RDHFSs) in dealing with decision makers’ fuzzy evaluation information has received much attention. This main aim of this paper is to propose new aggregation operators of q-rung dual hesitant fuzzy elements and employ them in multi-attribute decision making (MADM). In order to do this, we first propose the power dual Maclaurin symmetric mean (PDMSM) operator by integrating the power geometric (PG) operator and the dual Maclaurin symmetric mean (DMSM). The PG operator can reduce or eliminate the negative influence of decision makers’ extreme evaluation values, making the final decision results more reasonable. The DMSM captures the interrelationship among multiple attributes. The PDMSM takes the advantages of both PG and DMSM and hence it is suitable and powerful to fuse decision information. Further, we extend the PDMSM operator to q-RDHFSs and propose q-rung dual hesitant fuzzy PDMSM operator and its weighted form. Properties of these operators are investigated. Afterwards, a new MADM method under q-RDHFSs is proposed on the basis on the new operators. Finally, the effectiveness of the new method is testified through numerical examples.

Beijing, Tianjin and Hebei are located in the Bohai Rim region of Northeast Asia, China. It is the region with the largest economic scale and strongest economic vitality in northern China. Due to historical development and administrative division, the economic strength of Beijing and Tianjin is strong, while the economic strength of Hebei Province is weak. The economic development of the Beijing-Tianjin-Hebei region is severely uneven. The “Beijing-Tianjin-Hebei Coordinated Development Strategy” is proposed and elevated to a national strategy in this context, aiming to explore the path of coordinated economic development in the Beijing-Tianjin-Hebei region, promote economic cooperation, balance economic differences, and enhance the overall economic strength of the Beijing Tianjin Hebei region through national leadership. The economic collaborative development evaluation in the Beijing-Tianjin-Hebei region is a classical multiple attribute decision making (MADM) problems. Recently, the TODIM and Evaluation based on Distance from Average Solution (EDAS) method has been used to cope with MADM issues. The hesitant triangular fuzzy sets (HTFSs) are used as a tool for characterizing uncertain information during the economic collaborative development evaluation in the Beijing-Tianjin-Hebei region. In this paper, the hesitant triangular fuzzy TODIM-EDAS (HTF-TODIM-EDAS) method is built to solve the MADM under HTFSs. In the end, a numerical case study for economic collaborative development evaluation in the Beijing-Tianjin-Hebei region is given to validate the proposed method. The main contributions of this paper are summarized: (1) the HTF-TODIM-EDAS method is proposed under HTFSs. (2) The MADM method is designed based on the information entropy and HTF-TODIM-EDAS method under HTFSs. (3) A numerical case study for economic collaborative development evaluation in the Beijing-Tianjin-Hebei region is given to validate the proposed method. (4) A comparison between proposed method and existing methods is carried out to check its effectiveness.

This paper aims to propose a novel multi‐attribute group decision‐making (MAGDM) method based on linguistic Pythagorean fuzzy copula extended power average operator. Existing researches under linguistic Pythagorean fuzzy environment lack of the ability to handle with extreme values and the flexible operational rules. To fill these two gaps, this paper first provides the definition of Archimedean copula and co‐copula operational rules under linguistic Pythagorean fuzzy environment, which can reflect the connection among arguments and provide more choices for experts to express their preferences. Then, we gather the extended power average (EPA) operator to present some new aggregation operators, which can reduce the negative influence of extreme evaluation values. To show the application of the proposed method to MAGDM problems, we apply it to handle a case of takeout O2O platform assessment problem. The numerical case and comparative analysis with other existing methods illustrate that our proposed method is more scientific and flexible.

This paper aims at proposing a novel multiattribute group decision-making (MAGDM) method in complex decision-making environments. To this end, we first introduce a tool, called q-rung interval-valued probabilistic dual hesitant fuzzy sets (q-RIVPDHFSs), for decision makers to express their evaluation information over a set of finite alternatives in MAGDM procedures. The q-RIVPDHFS consists of some possible membership and nonmembership degrees, along with their interval-valued probabilistic information. Due to this structure, q-RIVPDHFSs are more powerful and flexible than the traditional q-rung probabilistic q-rung dual hesitant fuzzy sets, in which probabilistic information of membership and nonmembership degree is denoted by crisp numbers. Second, some other related concepts of q-RIVPDHFSs, such as operational laws, comparison method, distance measure, and aggregation operators, are introduced. Third, based on these novel concepts, two MAGDM methods (Algorithms 1 and 2) are put forward. Last but not least, a practical decision-making example is provided to show the effectiveness of our proposed MAGDM method. We also compare our Algorithms 1 and 2 with some existing decision-making methods to explain why our methods are more powerful and useful.

This study aims to introduce a novel Non-Linear Diophantine Fuzzy Multi-Criterion Decision-Making Model for COVID-19 diagnosis and control. The study is organized into three sections to encourage individuals and to develop an appropriate strategy for emergency decision-making circumstances. First, we propose a generalizations of Pythagorean fuzzy sets, q-rung orthopair fuzzy sets, and linear Diophantine fuzzy set, called Non-linear Diophantine fuzzy set (Non-LDFS) and discussed their important properties. Moreover, mathematical criteria for Non-LDFSs are established based on certain operating laws. In the second part of the study, we propose a set of Non-LDF averaging and geometric aggregation operators for aggregating expert judgments based on TOPSIS techniques. In final part, the newly defined Non-LDF Topsis Method is used to solve a medical diagnosis challenge for the COVID-19 virus, and the findings are reported. Using a set of five separate criteria, our newly implemented multi-criteria decision-making (MCDM) technique can assess and select the best alternative solution for dealing with the COVID-19 pandemic.) A comparative analysis is also performed for the novel Non-LDF Topsis, and the prospects of the designed research are addressed.

Background Medical alliance plays an important role in promoting resource sharing, optimizing the allocation of medical resources, establishing a hierarchical diagnosis and treatment system featuring primary diagnosis at the grassroots level, a two-way referral system, separated treatment for acute and chronic diseases, and dynamic cooperation. Thus, comprehensive performance evaluation for medical alliance is a necessary research that involves a multi-attribute group decision-making problem. Objective The aim of this paper is to develop a new multi-attribute group decision-making evaluation framework and new weight method to better efficaciously resolve the issues of evaluation for the medical alliance. Methods Firstly, Archimedean copula and co-copula operational rules, called Archimedean co-copula, and the form of q -rung orthopair fuzzy Hamy mean aggregation operator based on Archimedean co-copula operational rules are also developed. Secondly, an extended q -rung orthopair fuzzy extended best-worst method satisfying multiplicative consistency is developed to originate the weight information of the attributes. The new weight method can integrate the membership and non-membership of assessment information, improve constancy for group decision making and get an extremely reliable weight consequence. Finally, a novel multi-attribute group decision-making framework is presented based on the proposed q -rung orthopair fuzzy Archimedean copula and co-copula Hamy mean aggregation operator and q -rung orthopair fuzzy Euclidean best-worst method. Furthermore, the new multi-attribute group decision-making method is applied to comprehensive performance evaluation for medical alliance in Shanghai, and the effectiveness of the new method is also demonstrated. Results The results show that the proposed multi-attribute group decision-making method with Archimedean copulas-based Hamy operators and extended best-worst in this paper outperforms some existing methods and provides support for policymakers seeking the use of patient- and community-centered health evaluations to improve health services. Conclusion The proposed method is a theoretical guidance method and a good reference for the evaluation of medical alliances of other regions in China.

This paper studies a novel tool for describing fuzzy information, called linguistic Fermatean fuzzy sets (LFFSs), in the process of multi-attribute decision-making (MADM). Compared to linguistic intuitionistic fuzzy sets and linguistic Pythagorean fuzzy sets, our LFFSs are more flexible and can depict more complicated decision-making information then the former two. In this study, we first introduce the notion of LFFSs. Afterwards, some other related concepts, such as operational rules, ranking methods as well as distance measure are interpreted. When considering aggregation operators for linguistic Fermatean fuzzy information, we generalize the classical power average (PA) operator into LFFSs and introduce the linguistic Fermatean fuzzy power average operator and its weighted form. Subsequently, a new MADM method based on LFFSs and their aggregation operator is developed. At last, an illustrative example is provided to show how our proposed method can be applied in solving realistic MADM problems.

This paper aims to propose a new multi-attribute decision making (MADM) method in complicated and fuzzy decision-making environment. To express both decision makers (DMs') quantitative and qualitative evaluation information comprehensively and consider their high hesitancy in giving their assessment values in MADM process, we combine q-rung dual hesitant fuzzy sets (q-RDHFSs) with uncertain linguistic variables and develop a new tool, called the q-rung dual hesitant uncertain linguistic sets (q-RDHULSs). First, the definition, operations and comparison method of q-RDHULSs are proposed. Second, given the interrelationship among multiple q-rung dual hesitant uncertain linguistic variables (q-RDHULVs) we introduce some aggregation operators (AOs) to fuse q-rung dual hesitant uncertain linguistic (q-RDHUL) information based on the Muirhead mean, i.e. the q-RDHUL Muirhead mean operator, the q-RDHUL weighted Muirhead mean operator, the q-RDHUL dual Muirhead mean operator, and the q-RDHUL weighted dual Muirhead mean operator. To cope with MADM problems with q-RDHUL information, we propose a new method based on the proposed AOs. Afterwards, we apply the proposed method to an enterprise informatization level evaluation problem to verify its effectiveness. In addition, we also explain why our proposed method is more powerful and flexible than others.

The interval-valued q-rung dual hesitant fuzzy sets (IVq-RDHFSs) has been proposed for effectively representing complex fuzzy information. IVq-RDHFSs can describe the membership degree and non-membership degree respectively through interval value set, and can flexibly adjust the space of information expression, which makes them surpass most existing fuzzy sets. Nevertheless, the main shortage of the existing multi-attribute group decision making (MAGDM) methods based on IVq-RDHFSs is that the functions of operation rules and aggregation operators (AOs) are very limited. Therefore, this paper investigates a new MAGDM under IVq-RDHFSs, established on the powerful Frank t-norm and t-conorm (FTT) operation and extended power average (EPA) operator. With the help of FTT, the basic operation of IVq-RDHFSs is redefined, then the interval-valued q-rung dual hesitant fuzzy Frank extended power average operator and the interval-valued q-rung dual hesitant fuzzy Frank weighted extended power average (IVq-RDHFFWEPA) operator are developed by combining FTT and EPA. Likewise, the desirable properties and special cases of the new AOs are explored. Afterwards, a novel MAGDM framework is constructed on the foundation of IVq-RDHFFWEPA operator. Compared with most existing approach, the proposed MAGDM in this paper possesses prominent ability in controlling the effect of extreme evaluation as well as modeling the risk attitude of decision-makers, so it is more appropriate for practical application. Finally, diverse experiments are devised to analyze the use and advantages of our method.

Decision makers (DMs) are often hesitant about the evaluations for subjective or objective reasons, and established preference relations always have various limitations on the way that DMs express themselves. Aiming at investigating the consensus reaching process where DMs needs more decision freedom, this study proposes a novel decision support model for AHP with q-rung dual hesitant fuzzy preference relations (q-RDHFPRs). To do this, we give the definition of q-RDHFPRs and explore the corresponding operational rules. On account of this, we propose a family of algorithms to check and improve consistency and consensus of q-RDHFPRs, which can automatically obtain scientific and effective consensus results. Moreover, a priority method for q-RDHFPRs is proposed to rank the alternatives. The procedure of the q-RDHF-AHP is given in detail, and the example of risk evaluation of Hospital-acquired infections is employed to demonstrate our results. Comparative analyses show that the proposed q-RDHF-AHP method is more powerful for coping with the hesitant and uncertain situations and greatly expands the information description scope of the method.

Abstract In recent years, the development of electric vehicles has received extensive attention. However, how to choose a suitable charging pile manufacturer for electric vehicles is a matter of concern. The selection of charging pile manufacturers involves many factors, and it is hard for decision makers (DMs) to provide accurate assessments due to the uncertainty of subjective or objective factors. As a combination of q-rung orthopair fuzzy set (q-ROFS) and dual hesitant fuzzy set (DHFS), q-rung dual hesitant fuzzy set (q-RDHFS) provides more possibilities for information expression and gives DMs greater decision-making freedom. Because of the advantages of q-RDHFS in expressing uncertain information, we propose a novel decision method to capture DMs’ hesitant information with q-rung dual hesitant fuzzy elements (q-RDHFEs) to obtain the optimal scheme. Firstly, Frank t-norm and t-conorm (FTT) is well known for its flexibility in coping with compatibility compared to traditional algebraic operation. Considering the advantages of FTT, we extend FTT to q-RDHFS and provide the definition of Frank operational rules of q-RDHFS. Subsequently, according to generalized power average (GPA) and generalized power geometric (GPG) operators, some corresponding operators based on the novel operational laws are proposed. Then, with the proposed operators, a novel multi-attribute decision-making (MADM) method under q-RDHFS environment is introduced and applied to the selection of charging pile manufacturers. Finally, compared with the existing methods, the method proposed in this paper can better handle extreme evaluation information and is more flexible in operation.

The interval-valued q-rung dual hesitant linguistic (IVq-RDHL) sets are widely used to express the evaluation information of decision makers (DMs) in the process of multi-attribute decision-making (MADM). However, the existing MADM method based on IVq-RDHL sets has obvious shortcomings, i.e., the operational rules of IVq-RDHL values have some weaknesses and the existing IVq-RDHL aggregation operators are incapable of dealing with some special decision-making situations. In this paper, by analyzing these drawbacks, we then propose the operations for IVq-RDHL values based on a linguistic scale function. After it, we present novel aggregation operators for IVq-RDHL values based on the power Hamy mean and introduce the IVq-RDHL power Hamy mean operator and IVq-RDHL power weighted Hamy mean operator. Properties of these new aggregation operators are also studied. Based on these foundations, we further put forward a MADM method, which is more reasonable and rational than the existing one. Our proposed method not only provides a series of more reasonable operational laws but also offers a more powerful manner to fuse attribute values. Finally, we apply the new MADM method to solve the practical problem of patient admission evaluation. The performance and advantages of our method are illustrated in the comparative analysis with other methods.