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Abstract The mixed metric dimension of a graph is an important parameter in characterizing its structural complexity, specifically in nanoscale networks where precision is paramount. In this article, we calculate the mixed metric dimension of hexagonal nano-network, a modal with significant applications in nanotechnology and material science. Through rigorous analysis, we set up that the mixed metric dimension of the hexagonal nano-network is exactly three, highlighting its minimal but enough resolving set that uniquely identifies all vertices. Furthermore, we check out the exchange property within this context, demonstrating the robust adaptability of the hexagonal network’s resolving sets. Our findings display that the alternate assets aren’t the handiest preserved but stronger in these nano-networks, allowing for flexible adjustments in resolving sets without compromising the network’s integrity. This examination offers critical insights into the fundamental properties of hexagonal nano-networks, offering a theoretical foundation for future research in nanomaterial design and optimization. The results underscore the potential of leveraging mixed metric dimensions and exchange properties to achieve efficient and scalable solutions in nano-network applications.

Meta-analysis is a statistical technique used to process an overall summary estimation, and the technique of meta-analysis is mostly used in medicine, social science, and psychology. In this manuscript, we aimed to combine the techniques of the Bonferroni mean (BM) operator based on circular Pythagorean fuzzy (CPF) sets, called the CPF Bonferroni mean (CPFBM) operator, and CPF weighted Bonferroni mean (CPFWBM) operator and described their special cases with the help of two parameters, "s" and "t", and some describable properties of them are also proposed. Further, we present the evaluation technique based on distance from average solution (EDAS) technique and the proposed operators. Moreover, we use some examples to show the flexibility and dominance of the proposed operators by comparing the proposed methods with some existing techniques.

Artificial neural networks (ANNs) are the collection of computational techniques or models encouraged by the shape and purpose of natural or organic neural networks. Furthermore, a cubic intuitionistic fuzzy (CIF) set is the modified or extended form of a Fuzzy set (FS). Our goal was to address or compute the model of Aczel-Alsina operational laws under the consideration of the CIF set as well as Aczel-Alsina t-norm (AATN) and Aczel-Alsina t-conorm (AATCN), where the model of Algebraic norms and Drastic norms were the special parts of the Aczel-Alsina norms. Further, using the above invented operational laws, we aimed to develop the model of Aczel-Alsina average/geometric aggregation operators, called CIF Aczel-Alsina weighted averaging (CIFAAWA), CIF Aczel-Alsina ordered weighted averaging (CIFAAOWA), CIF Aczel-Alsina hybrid averaging (CIFAAHA), CIF Aczel-Alsina weighted geometric (CIFAAWG), CIF Aczel-Alsina ordered weighted geometric (CIFAAOWG), and CIF Aczel-Alsina hybrid geometric (CIFAAHG) operators with some well-known and desirable properties. Moreover, a procedure decision-making technique was presented for finding the best type of artificial neural networks with the help of multi-attribute decision-making (MADM) problems based on CIF aggregation information. Finally, we determined a numerical example for showing the rationality and advantages of the developed method by comparing their ranking values with the ranking values of many prevailing tools.

Graph structures are an essential tool for solving combinatorial problems in computer science and computational intelligence. With an emphasis on signed graphs, picture-fuzzy graphs, and graphs with colored or labeled edges, this study explores the properties of picture-fuzzy graph topologies. Within these frameworks, it presents key ideas such as the lexicographic-max product, vertex degree, and total degree. The use of picture-fuzzy graphs' lexicographic-max product to tackle intricate problems like human trafficking is a key component of this study. The study illustrates how this strategy can improve decision-making processes in such crucial areas by utilizing the special qualities of picture-fuzzy graphs. The study is supported by informative numerical examples that show how useful these ideas are in real-world situations. In addition, the study offers a thorough algorithmic foundation for applying the lexicographic-max product in practical situations, especially those involving human trafficking. The goal of this framework is to provide a workable approach for applying picture-fuzzy graph structures to enhance decision-making and tackle important societal issues.

As a useful tool for managing ambiguous and inconsistent data, the Single Value Neutrosophic Set (SVNSs) is an extension of both Fuzzy Sets (FSs) and Intuitionistic Fuzzy Sets (IFSs). In the field of information theory, metrics like similarity, entropy, and distance are important. Although a number of entropy measures for SVNSs have been put forth and used in real-world situations, both academic research and real-world applications have pointed out certain drawbacks. Additionally, the Similarity Measures (SMs) is a useful instrument for determining how similar any two fuzzy values are to one another. The distance between the values allows the current SMs to evaluate the similarity. However, due to a few characteristics and intricate value operations, there are irrational and nonsensical cases. To deal with these preposterous cases, this paper proposed a parametric similarity measure in view of three parameters m1,m2,m3 in which decision makers can obtain the appropriate SMs by changing parameters with different decision styles. Furthermore, we analyze some existing SMs from a mathematical perspective and demonstrate the success of the proposed SMs using mathematical models. Ultimately, we apply the suggested SMs to resolve the Multi-Attribute Decision-Making (MADM) problems. We learn from the correlation and analysis that the suggested SM outperforms certain other SMs that are based on the SVNSs.

High-quality marine economic development (HMED) is regarded as a new development pattern of the marine economy in China. This paper aims to examine the dynamic changes and improvement strategies of HMED from the perspective of the green total factor productivity (GTFP) growth. First, the GTFP growth of the marine economy in China’s coastal regions for the period 2007–2020 is calculated using the bootstrapped Malmquist index. Second, the dynamic changes and spatial impacts of the GTFP growth are characterized using kernel density estimation (KDE). Moreover, a novel analytical framework to study the improvement strategies of the GTFP is developed. Within this framework, the fuzzy set qualitative comparative analysis (fsQCA) method is used to explore the paths to achieve HMED. The findings show that: (i) the GTFP growth for coastal regions shows significant fluctuations, suggesting that a stable pattern of marine economic development has yet to be established; (ii) the regional distribution of GTFP growth varies significantly, with provinces with fast GTFP growth gathering resources from neighboring provinces, resulting in a siphon effect; (iii) for coastal provinces that lack certain development conditions, the combined effect of other advantageous factors can be used to achieve HMED. Finally, this study presents policy recommendations for achieving HMED, which can provide insights into the design of China’s future marine economic policies. First published online 10 September 2024

Abstract In 1960, Schweizer and Sklar introduced the novel Schweizer-Sklar t-norm and t-conorm which is used in the construction of aggregation operators. Schweizer-Sklar norms are more general than algebraic norms and Einstein norms. Additionally, computing the power operators based on the Schweizer-Sklar norms for complex Atanassov intuitionistic fuzzy (CA-IF) set is very awkward and complicated. In this manuscript, firstly, we propose the Schweizer-Sklar operational laws for CA-IF values, and secondly, we develop the CA-IF Schweizer-Sklar power averaging (CA-IFSSPA) operator, CA-IF Schweizer-Sklar power ordered averaging (CA-IFSSPOA) operator, CA-IF Schweizer-Sklar power geometric (CA-IFSSPG) operator, and CA-IF Schweizer-Sklar power ordered geometric (CA-IFSSPOG) operator. Some suitable and dominant properties for the above operators are also discussed. Furthermore, to simplify the above operators, we develop the procedure of decision-making technique, called multi-attribute decision-making (MADM) methods based on the proposed operators based on CA-IF values. Finally, we compare the proposed methods with some existing methods to describe the efficiency and capability of the discovered approaches by some examples.

Abstract A complex intuitionistic fuzzy (CIF) set contains the membership and non-membership in the shape of a complex number whose amplitude term and phase term are covered in the unit interval. Moreover, Hamacher interaction aggregation operators are the combination of two major operators, called Hamacher aggregation operators and interaction aggregation operators, and they are used to aggregate the collection of information into one value. In this manuscript, we present the concept of Hamacher interaction operational laws for CIF sets (CIFSs). Further, we develop the CIF Hamacher interaction weighted averaging (CIFHIWA) operator, CIF Hamacher interaction ordered weighted averaging (CIFHIOWA) operator, CIF Hamacher interaction weighted geometric (CIFHIWG) operator, and CIF Hamacher interaction ordered weighted geometric (CIFHIOWG) operator. For these operators, we also discuss some basic properties, such as idempotency, monotonicity, and boundedness. Additionally, we develop a MADM method based on the developed operators and apply it to solve the green supply chain management problems, which can implement environmentally friendly practices to minimize carbon emissions, resource consumption, and waste generation while promoting long-term sustainability. Finally, we verify the superiority and effectiveness of the proposed method based on a comparative analysis between the proposed techniques and existing methods.

Abstract Stock price prediction is a significant field of finance research for both academics and practitioners. Numerous studies have proved that the stock movement can be fully reflect various internal features of stock price including non-stationary behavior, high persistence in the conditional variance. The fusion of time-series prediction model such as Auto-Regressive Integrated Moving Average (ARIMA) and neural network is an availability but difficult approach for stock price prediction. Although the orientation has been studied through some methods in different research, there are still difficulties with the poor capture ability of time-series features and insufficient effectiveness of integrating temporal feature and frequency domain information. In this paper, we propose a Generative Adversarial Network (GAN) framework with the Convolution Neural Networks (CNN) as the discriminator and a hybrid model as the generator for forecasting the stock price. The hybrid model includes Attention-based Convolution Neural Networks (ACNN), Long Short-Term Memory (LSTM), and ARIMA model. Moreover, this proposed framework uses the Generative Adversarial patten and Attention Mechanism to achieve effective analysis and feature extraction for stock price movement. The extensive experiments in different history periods of dataset demonstrate an improvement in forecasting of stock price using our model as compared to the baseline models.

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

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

Abstract The complex q-rung orthopair fuzzy (CQ-ROF) set can describe the complex uncertain information. In this manuscript, we develop the Yager operational laws based on the CQ-ROF information and Yager t-norm and t-conorm. Furthermore, in aggregating the CQ-ROF values, the power, averaging, and geometric aggregation operators have played a very essential and critical role in the environment of fuzzy set. Inspired from the discussed operators, we propose the CQ-ROF power Yager averaging (CQ-ROFPYA), CQ-ROF power Yager ordered averaging (CQ-ROFPYOA), CQ-ROF power Yager geometric (CQ-ROFPYG), and CQ-ROF power Yager ordered geometric (CQ-ROFPYOG) operators. These operators are the modified version of the Power, Yager, averaging, geometric, and the combination of these all based on fuzzy set (FS), intuitionistic FS, Pythagorean FS, q-rung orthopair FS, complex FS, complex intuitionistic FS, and complex Pythagorean FS. Moreover, we also discuss the main properties of the proposed operators. Additionally, we develop a multi-attribute decision-making (MADM) method based on the developed operators. To show the supremacy and validity of the proposed method, the comparison between the proposed method and some existing methods is done by some examples, and results show that the proposed method is better than the others in terms of generality and effectiveness.

Abstract Service function chain (SFC) based on network function virtualization (NFV) technology can handle network traffic flexibly and efficiently. The virtual network function (VNF), as the core function unit of SFC, can experience software aging, which reduces the availability and reliability of SFC and even leads to service interruption, after it runs continuously for a long time. Software rejuvenation technique can effectively combat software aging. However, its effectiveness in improving the availability and reliability of SFC needs to be evaluated. Compared with existing models, this paper proposes a semi-Markov model to capture the behaviors of each VNF in a SFC from the occurrence of software aging to recovery by software rejuvenation technique under the condition that the failure times and recovery times follow general distribution, while considering trigger intervals of software rejuvenation technique. We then derive the calculation formulas of the steady-state availability, transient availability, and reliability, which are applied to evaluate the effectiveness of software rejuvenation technique. Finally, we conduct sensitivity analysis and numerical experiments to analyze the effects of system parameters, the number of VNFs and trigger interval of software rejuvenation technique on availability and reliability of SFC, and the effects of time-varying parameters on transient availability of SFC.

Abstract Aczel–Alsina t-norm and t-conorm are important t-norm and t-conorm, and they are extended from algebraic t-norm and t-conorm. Obviously, Aczel–Alsina t-norm and t-conorm are more general than some existing t-norm and t-conorm. Furthermore, the power aggregation (PA) operator is also a very famous and valuable operator which can consider the power relation between any two input parameters. In addition, Interval-valued Atanassov-intuitionistic fuzzy set (IVA-IFS) can easily express uncertain information. In order to fully use their advantages, in this analysis, we extend the PA operators based on Aczel–Alsina t-norm and t-conorm to IVA-IFS and propose the interval-valued Atanassov-intuitionistic fuzzy Aczel–Alsina power averaging (IVA-IFAAPA), interval-valued Atanassov-intuitionistic fuzzy Aczel–Alsina power ordered averaging (IVA-IFAAPOA), interval-valued Atanassov-intuitionistic fuzzy Aczel–Alsina power geometric (IVA-IFAAPG) and interval-valued Atanassov-intuitionistic fuzzy Aczel–Alsina power ordered geometric (IVA-IFAAPOG) operators. Moreover, we discuss the properties of the presented operators such as idempotency, monotonicity, and boundedness. In addition, a multi-attribute decision-making (MADM) procedure is proposed to process the IVA-IF information. Finally, a practical example is used to show the effectiveness and superiority of the proposed method by comparing it with some existing operators.

Abstract The economic implications from the COVID-19 crisis are not like anything people have ever experienced. As predictions indicated, it is not until the year 2025 may the global economy recover to the ideal situation as it was in 2020. Regions lacked of developing category is among the mostly affected regions, because the category includes weakly and averagely potential power. For supporting the decision of economic system recovery scientifically and accurately under the stress of COVID-19, one feasible solution is to assess the regional economic restorability by taking into account a variety of indicators, such as development foundation, industrial structure, labor forces, financial support and government's ability. This is a typical multi-criteria decision-making (MCDM) problem with quantitative and qualitative criteria/indicator. To solve this problem, in this paper, an investigation is conducted to obtain 14 indicators affecting regional economic restorability, which form an indicator system. The interval type-2 fuzzy set (IT2FS) is an effective tool to express experts’ subjective preference values (PVs) in the process of decision-making. First, some formulas are developed to convert quantitative PVs to IT2FSs. Second, an improved interval type-2 fuzzy ORESTE (IT2F-ORESTE) method based on distance and likelihood are developed to assess the regional economic restorability. Third, a case study is given to illustrate the method. Then, robust ranking results are acquired by performing a sensitivity analysis. Finally, some comparative analyses with other methods are conducted to demonstrate that the developed IT2F-ORESTE method can supporting the decision of economic system recovery scientifically and accurately.

Abstract As a more massive feasible and prominent tool than the complex interval-valued Pythagorean fuzzy (CIVPF) set and complex interval-valued intuitionistic fuzzy (CIVIF) set, the complex interval-valued q-rung orthopair fuzzy (CIVQROF) set has been usually used to represent ambiguity and vagueness for real-life decision-making problems. In this paper, we firstly proposed some distance measures, Yager operational laws, and their comparison method. Further, we developed CIVQROF Yager weighted averaging (CIVQROFYWA), CIVQROF Yager ordered weighted averaging (CIVQROFYOWA), CIVQROF Yager weighted geometric (CIVQROFYWG), CIVQROF Yager ordered weighted geometric (CIVQROFYOWG) operators with CIVQROF information, and some certain well-known and feasible properties and outstanding results are explored in detail. Moreover, we proposed a new and valuable technique for handling multi-attribute decision-making problems with CIVQROF information. Lastly, a practical evaluation regarding the high blood pressure diseases of the patient is evaluated to illustrate the feasibility and worth of the proposed approaches.

Abstract The rapid expansion of renewable energy has attracted the attention of investors, which makes the evaluation of renewable energy projects a momentous issue. As the investment selection of renewable energy projects requires the joint discussion of experts from different professional backgrounds (such as energy, transportation, construction, economy, environment, etc.), it belongs to the category of large group decision-making (LGDM). Therefore, this paper is devoted to propose a novel LGDM method considering experts’ non-cooperative behavior for investment selection of renewable energy projects. First, considering that the complexity of renewable energy projects makes it difficult for experts to express their views in a single linguistic word, the hesitant fuzzy linguistic term set is used as the tool for expert evaluation in this paper. Second, since the assessment information provided by experts from different fields are often heterogeneous, a consensus-reaching process with a feedback mechanism is introduced which comprehensively considers three reliable sources: the experts’ trust relationship in the social trust network, the consensus contribution in the subgroup and the opinions’ similarity among experts. Further, to improve the efficiency and rationality of decision-making, an experts’ historical adjustment data-based non-cooperative behavior management method is proposed. Finally, the effectiveness and innovation of the proposed method are verified by a case of renewable energy power generation project investment selection in Qingdao, China and a series of comparative analysis.

The complexity of goods and services in the current world has caused individual companies that do not have the help and cooperation of other organizations to face many problems for their survival. In this paper, a system dynamics model was proposed by creating a cause-effect curve to increase supply chain (SC) performance with an emphasis on agility and flexibility (AAF) indicators. The proposed model aimed to reduce cost and delivery time and increase customer satisfaction by considering AAF indicators. To this end, the concepts used were first introduced. Afterward, the important goals were identified by reviewing the existing literatures and interviewing experts in the field of AAF indicators in the studied SC. In the next step, the model was constructed by determining the cause-and-effect (CAE) relationships between the variables. Finally, by developing and simulating different scenarios, the results showed that AAF alone and absolutely cannot enhance profitability. By implication, to increase profitability, AAF do not need to be enhanced to the highest level, but an optimal point must be found. Finally, an optimal level of AAF was estimated. by using this system and considering that this system supports the production line, the ability to respond to sudden demands is increased and as a result, the speed of covering these demands increases.

Abstract The development level evaluation of regional rural practical talents needs to comprehensively consider a variety of factors. The general development level of rural practical talents in different regions has little difference, but there are significant differences between different factors. This paper proposes a set of scientific indicators for evaluating rural practical talents, which can be used to understand the development status and level of rural practical talents in various regions and to further provide method support for the development level evaluation of rural practical talents in various regions of China. To avoid the overly subjective drawback of setting index weights in the Analytic Hierarchy Process (AHP), we set the indicator weights via the variation coefficient method and fuse the evaluation information based on an aggregation approach with a hybrid-indicator information power operator, which can lead to a more scientific and effective evaluation of the development level of rural practical talents. Finally, we apply the proposed approach to conducting the applied research on real cases, give relevant analysis and suggestions, and propose the training and introduction policies for the rural practical talents, to promote the development of rural revitalization and construction.

Abstract The complexity and significance of decision-making in selecting suppliers highlight the need for a systematic and transparent approach. The more organizations rely on suppliers, the more harmful the direct and indirect consequences of poor decision-making are. This study attempted to identify factors affecting supplier selection and develop a system dynamics model for supplier selection by taking into account social corporate responsibility (CSR) practices. This model aims to increase CSR practices when selecting suppliers and thus help supply chain members gain competitive power and satisfy customer demands optimally. The system dynamics model for supplier selection was developed by considering profitability, productivity, social transparency, and customer satisfaction. To this end, first, the indicators affecting supplier selection were identified. Then, a cause–effect model was extracted by surveying subject-matter experts. Finally, the system dynamics model was developed. The final output of the third stage was a dynamic model of a supplier selection system that considers CSR practices. The results showed that profitability increases only by implementing the policy of reducing the average distance between suppliers and increasing the number of suppliers. This issue causes lower costs, reduced delivery time due to reduced average distance between suppliers, and increased suppliers, resulting in increased customer satisfaction and increased demand.

In this paper, the quantitative analysis is implemented on the relationship between strategy deviation of listed firms and institutional investors’ recognition. For research methodology, financial complex networks and clustering techniques are employed to measure the de-gree of recognition by creating links to the common stockholding behaviour of institutional investors. Besides, quarterly panel data from 2006 to 2020 are constructed for an innovative study of the degree of recognition of institutional investors’ strategy deviation of listed firms under different innovation fields, firm properties, and market style heterogeneity and asymmetry. The stability test is conducted by the transformation of the measures and methods, thereby effectively avoiding the “cluster fallacy”. We validate the mechanism by which the differences in strategic choices and propensities of listed firms affect capital market recognition, and enrich the microscopic research perspective and methodology on related issues. First published online 26 October 2021

Globalization initiated the challenges in Supply Chain (SC) such as management and control. In this situation, Blockchain as a digital distributed ledger can guarantee clarity, tractability, and safety. Many case studies proved that we can use Blockchain Technology (BT) to solve global supply chain problems especially in smart contracts with their potential applications. BT is in its early period and it is hard to find supply chains that have successfully implemented this technology to track their sustainable actions. Therefore, it is worth studying about the role of customers, members, domestic, national, and international challenges that could resist implementing Blockchain and may affect SC sustainability. Accordingly, four categories of barriers to the use of BT are introduced which are inter-organizational, intra-organizational, technical, and external barriers. Then with Bayesian Best Worst Method, we ranked the BT barriers and the sub-barriers. The study illustrates the interconnection of these barriers and the priority of each element. The lack of business models and the best practices in implementing Blockchain technology is a challenge and it is important that practitioners acknowledge these barriers in the first steps. First published online 04 May 2021

Considering the frequent occurrence of hazy weather, single image dehazing has become an important research task. Physical model-based and deep learning-based methods are two competitive methods in single image dehazing, but achieving fidelity and effectively removing haze at the same time in real hazy scenes is still a challenging problem. In this work, we propose a mixed iterative model to restore high-quality clear images by integrating a physical model-based approach and a learning-based approach, which can combine the advantages of the physical model-based method in maintaining natural attributes and the advantages of the learning-based method in completely removing haze. For a hazy image, first, according to the haze density, it is divided into separate regions to calculate the local atmospheric light. Then, we utilize the dark channel prior and DehazeNet to jointly estimate the transmission, which can estimate an accurate recovered image that is more in line with the real scene. Finally, a numerical iterative strategy is employed to further optimize the atmospheric light and transmission. The experiments on both synthetic and natural hazy image datasets indicate that the proposed method can restore natural and clean images and has superior performance than other state-of-the-art algorithms in peak signal-to-noise ratio, structural similarity, information entropy, color natural index, and color histogram. And in the four indicators of the quantitative results of the synthetic hazy test set, we achieve the highest score in three of them and the second highest result in another. In the comparison of the two quantitative indicators of natural hazy images, our average objective results are both the highest.

House purchasing has become an important asset al.ocation choice for most families in China. House price fluctuation is also one of the important factors that leads to systematic risks in the financial market, which might cause economic crises and then reduce consumption. Since China formally established the dual-pillar management framework of macroprudential policy in 2019, it has played a crucial role in maintaining the stability of house prices. This article employs the mediating effect model to comb the internal mechanism of the interaction between macroprudential policies, housing prices, and household consumption and test by the panel data of 30 provinces and cities in China from 2004 to 2019. Experience implies that macroprudential policy can not only stabilize consumption demand directly and effectively, but also affect consumption indirectly through the cross of the real estate market and the credit market. Further research has also found that macroprudential policies may fail between regions with higher GDP and high-income groups. This finding will contribute to research on the relationship between macroprudential policies and real economics. In addition, it would be helpful in making policies to increase consumption.

In this paper, we apply an RV coefficient network to investigate the topological structure of China’s new energy stock market via daily prices of 60 component stocks of CSI (China Stock Index) New Energy Index spanning the period January 4, 2012 to March 29, 2019. Compared with the Pearson correlation coefficient, RV coefficient can better reflect the similarity between stocks from the perspective of multi-dimensional data. The empirical result indicates that (1) the scale-free characteristics of China’s new energy stock market are not significant; (2) the new energy storage is the leading sub-sector of the new energy sector and the new energy interactive equipment plays a connecting role between renewable energy production and new energy storage; (3) the most influential stock in the network is Group DMEGC Magnetics Co., Ltd., Xiamen Tungsten Co., Ltd. and GEM Co., Ltd. play an important role in the network connection. These findings are of great significance to understand the interaction between Chinese new energy stocks and the pricing mechanism of stocks. The authority should pay more attention to the new energy storage industry. Investor’s portfolios can be optimized according to the influence assessment of stocks and sub-sectors. First published online 26 May 2020

The sustainable medical supplier selection (SMSS) is an important issue facing the medical industry in the context of sustainable development, which can be regarded as a typical multi-attribute group decision making (MAGDM) problem. In the MAGDM process, linguistic term set (LTS) is particularly natural and convenient for decision makers (DMs) to express evaluation information. Especially, probabilistic linguistic term set (PLTS) is a very critical and effective tool, which can reflect the importance of different linguistic terms. Due to the different preferences and experience of different DMs, they may use multi-granularity probabilistic linguistic term sets (MGPLTSs) to represent different linguistic information. In this article, in order to study the comparison method of MGPLTSs, a new possibility degree formula is firstly proposed and its properties is proved. Then, in order to build a weight model, a possibility degree-based Best-Worst method (BWM) and a probability degree based-maximizing deviation method are established to calculate the subjective weights and objective weights of attributes, respectively. Where after, a MAGDM method is proposed by combining the ELimination Et Choix Traduisant la REalite (ELECTRE) method with Evaluation based on Distance from Average Solution (EDAS) method in the multi-granularity probabilistic linguistic information environment. Finally, the created MAGDM method is applied to the SMSS, and its effectiveness and advantages compared with other existing methods are verified. First published online 17 January 2022

The present work introduces a quantitative structure-property relationship (QSPR)-based stochastic gradient boosting (SGB) decision tree framework for simulating and capturing of the thermal decomposition kinetics of biomass considering effective parameters of the ultimate analysis (such as carbon, hydrogen, oxygen, nitrogen, and sulfur content) and process heating rate. Through a total of 149 pyrolysis kinetics, this study developed an artificial model and subjected it to training and testing phases. The proposed model was validated using error analysis, sensitivity, regression, and outlier detection. The coefficient of determination (R2) and mean relative error (%MRE) were calculated to be 0.993 and 4.354%, respectively, suggesting good performance in the estimation of the pyrolysis kinetic parameters. Also, the sensitivity results indicated the process heating rate to have the strongest effect on the model output with a relevancy factor of 0.43. Eventually, the proposed model showed superior performance compared to earlier frameworks.

In this study, the neutrosophic cubic graphs are further developed. We discussed and explored the open and the closed neighborhood for any vertex in neutrosophic cubic graphs, regular and totally regular neutrosophic cubic graphs, complete neutrosophic cubic graphs, balanced and strictly balanced neutrosophic cubic graphs, irregular and totally irregular neutrosophic cubic graphs, complement of a neutrosophic cubic graph, neighborly irregular and neighborly totally irregular neutrosophic cubic graphs, and highly irregular neutrosophic cubic graphs. It has been demonstrated that the proposed neutrosophic cubic graphs are associated with specific conditions. The comparison study of the proposed graphs with the existing cubic graphs has been carried out. Eventually, decision-making approaches for handling daily life problems such as effects of different factors on the neighboring countries of Pakistan and selection of a house based on the notions of proposed graphs are presented.

Purpose – Accurately judging the quality of marine economic development is the premise of grasping the level and status of marine economic development. In order to scientifically evaluate the development quality of regional marine economy, the purpose of this paper is to select the marine area of Qingdao as the research object, and construct a marine economic development quality evaluation index system with 16 indicators. Design/methodology/approach – The raw data is normalized by the range conversion method, and the weight of the index is determined by the information entropy model. Further, the grey relational analysis (GRA) method is used to evaluate the quality of marine economic development of Qingdao from 2012 to 2017. Findings – The results show that the marine economic development capacity of Qingdao is with the generally increasing trend, the total marine economy is with on the rising trend, the marine storage and transportation capacity, and marine ecological environment are first decreased, and then increased. The utilization of marine resources is generally decreasing, and the comprehensive management of oceans varies with the changes of environment and economy. Therefore, in view of the development capacity of marine economy, the coordinated development of economy and environment should be carried out. Originality/value – This paper uses the GRA to evaluate the quality of marine economic development and provides a reference for the development of marine economy in Qingdao.

T-spherical fuzzy set (T-SPFS) is a generalization of several fuzzy concepts such as fuzzy set (FS), intuitionistic FS, picture FS, Pythagorean FS, and q-rung orthopair FS. T-SPFS is a more powerful mathematical tool to handle uncertain, inconsistent, and vague information than the above-defined sets. In this paper, some limitations in the operational laws for SPF numbers (SPFNs) are discussed and some novel operational laws for SPFNs are proposed. Furthermore, two new aggregation operators for aggregating SPF information are proposed and are applied to multiple-attribute group decision-making (MAGDM). To take the advantages of Muirhead mean (MM) operator and power average operator, the SPF power MM (SPFPMM) operator, weighted SPFPMM operator, SPF power dual MM (SPFPDMM) operator, weighted SPFPDMM operator are introduced and their anticipated properties are discussed. The main advantage of these developed aggregation operators is that they take the relationship among fused data and the interrelationship among aggregated values, thereby getting more information in the process of MAGDM. Moreover, a novel approach to MAGDM based on the developed aggregation operators is established. Finally, a numerical example is given to show the effectiveness of the developed approach and comparison with the existing approaches is also given.

How to select an appropriate and effective health-care waste treatment technology (HCW-TT) is an especially important task in the management of health-care waste (HCW), which can be regarded as a typical multi-attribute group decision making (MAGDM) problem. In the selection of HCW-TT, the expression of evaluation information given by decision makers (DMs) under uncertain decision-making environment and the reflection of interrelationships among multi-attributes are two critical issues. In response, a new MAGDM technique is presented for the selection of HCW-TT based on the intuitionistic uncertain linguistic Hamy mean with linguistic scale functions (LSFs). First, considering the lack of closeness and flexibility of existing operations, some new operations of intuitionistic uncertain linguistic variables (IULVs) are redefined by combining with LSFs. New expected value and accuracy function are also presented to compare IULVs. Then, based on the new operations of IULVs, the intuitionistic uncertain linguistic Hamy mean and its weighted version (IULWHAM) are proposed to aggregate IULVs. The proposed operators can simultaneously model the interrelationship among multi-inputs and handle the semantic translation requirements of different DMs. Meanwhile, several attractive properties and special cases of these two operators are studied and analyzed. Subsequently, a MAGDM method (IUL-MAGDM) is presented based on the proposed IULWHAM. Finally, a numerical example is given to demonstrate the proposed IUL-MAGDM method, and results indicate that the proposed IUL-MAGDM can effectively and flexibly handle the selection of HCW management by comparing with other IUL-MAGDM methods.

Fuzzy theory defined by Zadeh has been developed through both analytical and computational categories of diverse sciences in light of time. The goal of applying fuzzy theory is to incorporate uncertainties with conventional deterministic calculations to enhance the reliability of results. Since fuzzy theory has been developed and carried out by so many researchers, various types of generalizations, including Z-numbers, type-2 fuzzy sets, intuitionistic sets, and hesitant sets, have been revealed to estimate real-world variables more accurately. Toward these goals, utility-numbers or H-numbers theory is proposed with an ordered set of (n, M (n), N(n)), to assign satisfaction degrees to corresponding uncertain numbers. The first component, n, is a constraint on the values, which a stochastic real-structured variable, X, may take. The following components, M (n), N(n), represent the maximum and minimum utilities assigned to the first component, respectively. This paper first substantiates immediate H-numbers as (n, M (n)), and the mathematical operations over them; then, these H-numbers are elaborated to (n, M (n), N(n)) in which both the minimum and maximum utility values are considered. Meanwhile, the main contribution of the proposed model leads to obtain satisfaction value for each fuzzy number component and helps practitioners to concentrate on total satisfaction that is aggregated by each alternative. The proposed model is validated by comparison tables and reasonable values over conventional fuzzy sets.

The Hamy Mean (HM) operator is a useful aggregation tool characterized by considering the correlation between multiple integral parameters. The linguistic intuitionistic fuzzy numbers (LIFNs) use linguistic variables (LVs) to represent membership degree (MD) and non-membership degree (NMD), which can flexibly and accurately represent the ambiguity in the actual decision problem. Based on the operational laws of LIFNs, we extend the HM operator to the LIFNs, and put forward the HM operator for LIFNs (LIFHM) and the weighted HM operator for LIFNs (WLIFHM). In addition, we discuss the properties of LIFHM and WLIFHM operators and some special cases, then we propose a multiple-attribute group decision making (MAGDM) method based on the WLIFHM operator. Lastly, a practical example is given to illustrate the effectiveness of the proposed operators by comparing it with different methods.

The main purpose of this paper is the allocation of orders to suppliers in an agile and flexible manner suitable to the automobile industry. In this paper, parts supplied by a single source were eliminated from the set of parts. Using mathematical modeling and through the interval-valued fuzzy-rough numbers best worst method (IVFRN-BWM), we try to achieve the results that can meet the proposed model's needs and provide the ideal results by introducing new modes. This paper addressed some new aspects of the subject and achieved robust results by considering five objective functions. These five functions are as follows: minimization of production line disruptions due to the performance of suppliers, minimization of the complaints of production line about supplied parts, minimization of defective parts received from suppliers (PPM), maximization of on-time delivery services, and minimization of overall costs of supplied parts. Reviewing the literature, the originality of this study are as follows: 1) identifying the structure of a supply chain (SC) in general and particularly in an automobile industry SC; 2) investigating the modeling techniques of the existing SC models for coordinating all the members of a product SC; 3) building a hybrid model of IVFRN-BWM and a robust goal programming agile and flexible supply chain in an uncertain situation; and 4) identifying the suitable scenarios/cases for testing the proposed models to validate the models. This paper can help decision makers and managers to opt for the best suppliers and also allocate the right numbers of parts to those supplier(s) based on a real situation of each firm.

The q-Rung orthopair fuzzy set (q-ROFS) is an effective and powerful tool for expressing fuzzy information. It can cover more complex and more hesitant fuzzy evaluation information. The aggregation operators are an effective tool to deal with decision problems, but when faced with these new types of fuzzy set whose operational rules are defective, they often causes a lot of information distortion. Therefore, based on the advantages of q-ROFSs, this paper presents a new extended fuzzy group TOPSIS method which doesn't need aggregation technology. This method can effectively reduce the distortion of decision information and improve the accuracy of evaluation results. In addition, this method involves an expert weight model, which can deal with the group decision problems with unknown weight of experts by using the importance of experts and the rationality of evaluation results. By using this weight model, the proposed method can effectively eliminate the unreasonable impact of the extreme evaluation value on the evaluation results, further solve the decision-making situation in which experts' opinions are divergent and experts are manipulated. In order to verify the effectiveness and superiority of the proposed method, this paper applies it to some practical examples and makes a detailed comparison with other existing methods.

As an expansion of 2-tuple linguistic intuitionistic fuzzy set, the newly developed 2-tuple linguistic neutrosophic set (2-TLNS) is more satisfactory to define decision maker’s assessment information in decision-making problems. 2-TLN aggregation operators are of great significance in multiple attribute group decision making (MAGDM) problems with a 2-tuple linguistic environment. Therefore, in this paper, our main contribution is to develop novel 2-TLN power Heronian aggregation (2-TLNPHM) operators. First, we develop new operational laws established on Dombi T-norm (DTN) and Dombi T-conorm (DTCN). Second, Taking full advantages of the power average (PA) operator and Heronian mean (HM) operator, we develop some new novel power Heronian mean operator and discuss its related properties and special cases. The main advantages of developed aggregation operators are that they not only remove the effect of awkward data which may be too high or too low but also have a good capacity to model the extensive correlation between attributes, making them more worthy for successfully solving more and more complicated MAGDM problems. Thus, we develop a new algorithm to handle MAGDM based on developed aggregation operators. Finally, we apply the proposed method and algorithm to risk assessment for the construction of engineering projects to show the efficiency of the developed method and algorithm. The dominant novelties of this contribution are triplex. First, new operational laws are proposed for 2-TLNNs. Second, novel 2-TLNPHM operators are developed. Third, a new approach for 2-tuple linguistic neutrosophic MAGDM is developed.

In this paper, we pointed out that the transfer function for computing the fuzzy preference degree for the construction of upward/downward fuzzy relations are not additive consistent. Appropriate counterexample is given. Further their modified versions are presented. Similarly, we construct upward consistency matrices of experts which satisfy the upward additive consistency and the upward order consistency simultaneously. After that, by introducing some new fuzzy upward $\beta $ -coverings, fuzzy upward $\beta $ -neighborhoods and fuzzy upward complement $\beta $ -neighborhoods are proposed and related properties are studied. Furthermore, we propose multi-granulation optimistic/pessimistic fuzzy upward rough set based on fuzzy upward $\beta $ -covering and investigate some of their properties. Finally we developed a new technique to multiple attribute decision making problem based on multi-granulation optimistic/pessimistic fuzzy upward rough set. The decision making procedure and the methodology as well as the algorithm of the proposed technique are given. The detailed comparison of the present work with other methods to multiple attribute decision making problem illustrate the advantages of the this work and limitations of other studies.

Blockchain is a decentralized distributed ledger technology. The public chain represented by Bitcoin and Ethereum only realizes the limited anonymity of user identity, and the transaction amount is open to the whole network, resulting in user privacy leakage. Based on the existing anonymous technology, the concealment of the sender, receiver, amount of the transaction, and does not disclose any information, which makes the supervision difficult. Therefore, the design of blockchain scheme with privacy protection and supervision functions is of great significance. In this paper, a blockchain transaction model with both privacy and supervision function is proposed. It uses probability encryption to realize the hiding of the true identity of the blockchain transaction, and uses the commitment scheme and zero-knowledge proof technology to realize the privacy protection and guarantee legitimacy verification of the transaction. With the use of encryption technology, the regulators can supervise blockchain transactions without storing the users' information, which greatly reduces the pressure on storage, computing and key management. In addition, it does not rely on specific consensus mechanism and can be used as an independent module. The security performance analysis shows that the proposed scheme has great practicability and has potential application in many fields.

As a modification of the q-rung orthopair fuzzy sets (QROFSs), complex QROFSs (CQROFSs) can describe the inaccurate information by complex-valued truth grades with an additional term, named as phase term. Cosine similarity measures (CSMs) and distance measures (DMs) are important tools to verify the grades of discrimination between the two sets. In this manuscript, we develop some CSMs and DMs for CQROFSs. Firstly, the CSMs and Euclidean DMs (EDMs) for CQROFSs and their properties are investigated. Because the CSMs do not keep the axiom of similarity measure (SM), we investigate a technique to develop other SMs based on CQROFSs, and they meet the axiom of the SMs. Moreover, we propose a cosine DM (CDM) based on CQROFSs by considering the interrelationship among the SMs and DMs, then we propose an extended TOPSIS method to solve the multi-attribute decision-making problems. Finally, we provide some sensible examples to demonstrate the practicality and efficiency of the suggested procedure, at the same time, the graphical representations of the developed measures are also utilized in this manuscript.

In this article, we introduce a new notion of generalized convex fuzzy mapping known as strongly generalized preinvex fuzzy mapping on the invex set. Firstly, we have investigated some properties of strongly generalized preinvex fuzzy mapping. In particular, we establish the equivalence among the strongly generalized preinvex fuzzy mapping, strongly generalized invex fuzzy mapping, and strongly generalized monotonicity. We also prove that the optimality conditions for the sum of G-differentiable preinvex fuzzy mappings and non-G-differentiable strongly generalized preinvex fuzzy mappings can be characterized by strongly generalized fuzzy mixed variational-like inequalities, which can be viewed as a novel and innovative application. Several special cases are discussed. Results obtained in this paper can be viewed as improvement and refinement of previously known results.

The quality of teaching can be improved by teaching performance evaluation from multiple experts, which is a multiple attribute group decision-making (MAGDM) problem. In this paper, a group decision-making method under proportional hesitant fuzzy linguistic environment is proposed to evaluate teaching performance. Firstly, proportional hesitant fuzzy linguistic term set (PHFLTS) is applied to express the decision makers' (DMs) preferences for teaching performance index. Secondly, the PHFLPrCA operator is developed and its properties are discussed. Then based on the PHFLPrCA operator, a MAGDM method is formulated. Thirdly, the method is applied in teaching performance evaluation of Chinese-foreign cooperative education project. Finally, this method is proved more scientific, objective and accurate by compared with other two methods.

Complex T-spherical fuzzy 2-tuple linguistic set (CTSF2-TLS), which is a combination of complex fuzzy set (CFS), T-spherical fuzzy set (TSFS), and 2-tulpe linguistic variable set (2-TLVS), is a proficient technique to express uncertain and awkward information in real decision-making. CTSF2-TLS contains 2-tuple linguistic variable, truth, abstinence, and falsity grades, which gives an extensive freedom for decision-makers to express the uncertain information compared to other existing notions. In this article, we firstly propose a new concept of CTSF2-TLS by using the CFS, TSFS, and 2-TLVS, and the operational laws and comparison methods for CTSF2-TLSs are established, then the complex T-spherical fuzzy 2-tuple linguistic Muirhead mean (CTSF2-TLMM) operator and the complex T-spherical fuzzy 2-tuple linguistic dual Muirhead mean (CTSF2-TLDMM) operator are explored, and some special cases and the desirable properties of the explored operators are also studied. Moreover, we establish a method to solve the multi-attribute decision-making (MADM) problems, in which the evaluation information is described by CTSF2-TLSs. Finally, we use some numerical examples to explain the advantages of the explored method by comparing with other existing methods.

Multi-attribute decision-making (MADM) has been receiving great attention in recent years due to two major issues which are basically to describe attribute values and secondly to aggregate the described information to generate a ranking of alternatives. For the first case it entails the hesitant fuzzy elements (HFEs) as a more flexible and general tool in comparison to fuzzy set theory and for the second one, we allow the aggregation operator (AO) as an effective tool. Having said that there is not yet reported an AO which can provide desirable generality and flexibility in aggregating attribute values under hesitant fuzzy (HF) environment, although many AOs have been developed earlier to attempt to meet above such eventualities. So, the primary objective of this paper is to develop some general as well as flexible AOs that can be exploited to solve MADM problems with the HF information. From this perspective, at the very beginning, we develop some operations between HFEs by uniting the features of Dombi and Archimedean operations. Next, we bring up some HF weighted AOs based on Dombi and Archimedean operations. We discuss in detail some intriguing properties of the proposed AOs. Secondly, we emphasize establishing a procedure of MADM endowed by the proposed operators under the HF environment. Finally, we present a practical example concerning human resource selection to gloss the decision steps of the proposed method and at the same time, we explore the feasibility of the new method.

q-rung picture fuzzy sets can handle complex fuzzy and impression information by changing a parameter q based on the different hesitation degree, and Yager operator is a useful aggregation technology that can control the uncertainty of valuating data from some experts and thus get intensive information in the process of decision-making. Thus, in this paper, we develop specific types of operators, namely, q-rung picture fuzzy Yager weighted average, q-rung picture fuzzy Yager ordered weighted average, q-rung picture fuzzy Yager hybrid weighted average, q-rung picture fuzzy Yager weighted geometric, q-rung picture fuzzy Yager ordered weighted geometric and q-rung picture fuzzy Yager hybrid weighted geometric operators. We propose q-rung picture fuzzy Yager aggregation operators to handle multiple attribute decision-making problems in a modernize way. Moreover, we discuss the effect of parameter on the decision-making results. To demonstrate the superiority and advantage of our proposed method, a comparison with existing methods is presented.

Complex q-rung orthopair fuzzy set (CQROFS), as a modified notion of complex fuzzy set (CFS), is an important tool to cope with awkward and complicated information. CQROFS contains two functions which are called truth grade and falsity grade by the form of complex numbers belonging to unit disc in a complex plane. The condition of CQROFS is that the sum of q-powers of the real part (Also for imaginary part) of the truth grade and real part (Also for imaginary part) of the falsity grade is limited to the unit interval. Bonferroni mean (BM) operator is an important and meaningful concept to examine the interrelationships between the different attributes. Keeping the advantages of the CQROFS and BM operator, in this manuscript, the complex q-rung orthopair fuzzy BM (CQROFBM) operator, complex q-rung orthopair fuzzy weighted BM (CQROFWBM) operator, complex q-rung orthopair fuzzy geometric BM (CQROFGBM) operator, and complex q-rung orthopair fuzzy weighted geometric BM (CQROFWGBM) operator are proposed, and some properties are discussed, further, based on the CQROFWGBM operator, a multi-attribute group decision-making (MAGDM) method is developed, and the ranking results are examined by score function. Finally, we give some numerical examples to verify the rationality of the established method, and show its advantages by comparative analysis with some existing methods.

Purpose – Intuitionistic linguistic fuzzy information (ILFI), characterized by linguistic terms and intuitionistic fuzzy sets (IFSs), can easily express the fuzzy information in the process of muticriteria decision making (MCDM) and muticriteria group decision making (MCGDM) problems. The purpose of this paper is to provide an overview of aggregation operators (AOs) and applications of ILFI. Design/methodology/approach – First, some meaningful AOs for ILFI are summarized, and some extended MCDM approaches for intuitionistic uncertain linguistic variables (IULVs), such as extended TOPSIS, extended TODIM, extended VIKOR, are discussed. Then, the authors summarize and analyze the applications about the AOs of IULVs. Findings – IULVs, characterized by linguistic terms and IFSs, can more detailed and comprehensively express the criteria values in the process of MCDM and MCGDM. Therefore, lots of researchers pay more and more attention to the MCDM or MCGDM methods with IULVs. Originality/value – The authors summarize and analyze the applications about the AOs of IULVs Finally, the authors point out some possible directions for future research.

Considering the limitations of the applications of a Dempster-Shafer evidence theory (DSET) in multiple attributes decision-making (MADM) and the defects of the existing MADM methods with intuitionistic linguistic numbers (ILNs), in this paper, we propose a new MADM approach. First, we provide a method to translate the evaluation values denoted by ILNs into the mass functions (MFs) under the framework of DSET. Second, we calculate the subjective weights of attributes based on the AHP method. Then, we propose a new definition of fuzzy entropy (FE) for ILNs and the objective weights of attributes are calculated by the defined FE. Moreover, we develop a linear objective programming model to obtain the comprehensive weights of attributes based on the obtained subjective and objective weights of attributes. Third, we introduce some procedures to modify the MFs of alternatives on each attribute. On these bases, a new DSET-based MADM approach with ILNs is presented. Furthermore, an application example of hotel selection is used to illustrate the presented approach. At last, some comparative analyses with other MADM methods are conducted to show the feasibility and superiority of the proposed approach.

In actual decision making, there are many multiple criteria decision making (MCDM) problems with prioritization and interaction among the criteria. In this paper, we proposed a novel method to handle the intuitionistic fuzzy MCDM problems with weakly ordered prioritization and interaction among the criteria. First, we presented some novel Einstein operations of intuitionistic fuzzy sets (IFSs), which could capture the relationship between non-membership and membership functions of various IFSs. Then, we proposed a novel operator called prioritized interactive Choquet (PIC) operator based on fuzzy measure, generalized prioritized measure, and Choquet integral. Meanwhile, three fundamental features of this operator were discussed. Besides, we combined the PIC operator and Einstein operations to IFSs, and proposed the intuitionistic fuzzy prioritized interactive Einstein Choquet (IFPIEC) operator, which could consider the prioritization and interaction among the criteria. Additionally, we utilized O’Hagan’s maximum entropy to obtain the quantity of each priority level in the generalized prioritized measure. Finally, the detailed decision making steps for the intuitionistic fuzzy MCDM problems with weakly ordered prioritization and interaction were developed, and two practical cases were given to check the created approach and to illustrate its validity and superiority.

As a powerful extension to hesitant fuzzy sets (HFSs), dual hesitant fuzzy sets (DHFSs) have been closely watched by many scholars. The DHFSs can reflect the disagreement and hesitancy of decision-makers (DMs) flexibly and conveniently. However, all the evaluation values under the same membership degree are endowed with similar importance. And DHFSs are not able to express DMs' preference degrees on different variables. To overcome this drawback, in this paper, we propose the concept of interval-valued probabilistic dual hesitant fuzzy sets (IVPDHFSs) by providing each element with an interval-valued probability value, which can describe DMs' preferences, hesitancy and disapproval simultaneously. Then we define the basic operation laws, score function and deviation function for interval-valued probabilistic dual hesitant fuzzy elements (IVPDHFEs). Besides, the ordered distance and similarity measures are proposed to calculate the deviation of any two IVPDHFSs and to derive the weight vector for DMs objectively, respectively. To aggregate decision-making information, we present interval-valued probabilistic dual hesitant fuzzy ordered weighted averaging (IVPDHFOWA) operator. Moreover, the water-filling theory is first introduced into IVPDHFSs environment and utilized to obtain unified criteria weights mathematically. Furthermore, a three-phased multi-criteria group decision-making (MCGDM) framework is constructed to address IVPDHFSs information. Finally, a case study concerning Arctic risk evaluation is provided to verify the effectiveness and superiority of the proposed three-phased framework.