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China is a developing country and with the speeding up of its industrialization, the environmental problems are becoming more serious, environmental pollution is a major environmental health problem in China. In order to have a more effective management and control of the significant growth issues of environment pollution, green supply chain incentives have started, which is kind of market incentive aiming to moderate the adverse effects of environmental pollution. Proper green chain supply selection and evaluation of companies is becoming very essential in sustainable green supply chain management. Generally speaking, decision-makers (DMs) prefer to provide a set of feasible and quantitative information for making performance evaluation, which motivates us to propose a framework using dual hesitant fuzzy linguistic term set (DHFLTS) and hesitant fuzzy linguistic term set (HFLTS) to select green suppliers. In this paper, group satisfaction and the regret theory are adopted for elicitation of preference information. The DHFLTS and HFLTS provide qualitative preferences of the DMs as well as reflect their hesitancy, inconsistency, and vagueness. Further, two new group satisfaction degrees are defined called the group satisfaction of hesitant fuzzy linguistic term set and dual hesitant fuzzy linguistic term set. Some properties of group satisfaction with DHFLST and HFL are also discussed. Unknown attribute weights are obtained to construct a novel Lagrange function optimization model to maximize the group satisfaction degree, which is an extension of general group satisfaction degree. A novel methodological approach based on two group satisfaction degrees framework and regret theory is developed to rank and select green chain suppliers focusing on specific selection objectives. The proposed model and method of this paper allow the DM to execute different fuzzy scenarios by changing importance weights attached to the triple-bottom-line areas. In the final part, the advantage of the proposed group satisfaction degree under DHFL and HFL background over the existing group satisfaction degree using examples have been presented with different computational combinations.

Because the natural disaster system is a very comprehensive and large system, the disaster reduction scheme must rely on risk analysis. Experts' knowledge and experiences play a critical role in disaster risk assessment. The hesitant fuzzy linguistic preference relation is an effective tool to express experts' preference information when comparing pairwise alternatives. Owing to the lack of knowledge or a heavy workload, information may be missed in the hesitant fuzzy linguistic preference relation. Thus, an incomplete hesitant fuzzy linguistic preference relation is constructed. In this paper, we firstly discuss some properties of the additive consistent hesitant fuzzy linguistic preference relation. Next, the incomplete hesitant fuzzy linguistic preference relation, the normalized hesitant fuzzy linguistic preference relation, and the acceptable hesitant fuzzy linguistic preference relation are defined. Afterwards, three procedures to estimate the missing information are proposed. The first one deals with the situation in which there are only n-1 known judgments involving all the alternatives; the second one is used to estimate the missing information of the hesitant fuzzy linguistic preference relation with more known judgments; while the third procedure is used to deal with ignorance situations in which there is at least one alternative with totally missing information. Furthermore, an algorithm for group decision making with incomplete hesitant fuzzy linguistic preference relations is given. Finally, we illustrate our model with a case study about flood disaster risk evaluation. A comparative analysis is presented to testify the advantage of our method., Competing Interests: The authors declare no conflict of interest.

Hesitant fuzzy linguistic term set provides an effective tool to represent uncertain decision information. However, the semantics corresponding to the linguistic terms in it cannot accurately reflect the decision-makers' subjective cognition. In general, different decision-makers' sensitivities towards the semantics are different. Such sensitivities can be represented by the cumulative prospect theory value function. Inspired by this, we propose a linguistic scale function to transform the semantics corresponding to linguistic terms into the linguistic preference values. Furthermore, we propose the hesitant fuzzy linguistic preference utility set, based on which, the decision-makers can flexibly express their distinct semantics and obtain the decision results that are consistent with their cognition. For calculations and comparisons over the hesitant fuzzy linguistic preference utility sets, we introduce some distance measures and comparison laws. Afterwards, to apply the hesitant fuzzy linguistic preference utility sets in emergency management, we develop a method to obtain objective weights of attributes and then propose a hesitant fuzzy linguistic preference utility-TOPSIS method to select the best fire rescue plan. Finally, the validity of the proposed method is verified by some comparisons of the method with other two representative methods including the hesitant fuzzy linguistic-TOPSIS method and the hesitant fuzzy linguistic-VIKOR method., Competing Interests: The authors declare no conflict of interest.

In this paper, we explore the ranking methods with hesitant fuzzy preference relations (HFPRs) in the group decision making environments. As basic elements of hesitant fuzzy sets, hesitant fuzzy elements (HFEs) usually have different numbers of possible values. In order to compute or compare HFEs, we have two principles to normalize them, i.e., the α -normalization and the β -normalization. Based on the α -normalization, we develop a new hesitant goal programming model to derive priorities from HFPRs. On the basis of the β -normalization, we develop the consistency measures of HFPRs, establish the consistency thresholds to measure whether or not an HFPR is of acceptable consistency, and then use the hesitant aggregation operators to aggregate preferences in HFPRs to obtain the ranking results.

Interval utility values, interval fuzzy preference relations, and interval multiplicative preference relations are three common uncertain-preference formats used by decision-makers to provide their preference information in the process of decision making under fuzziness. This paper is devoted in investigating multiple-attribute group-decision-making problems where the attribute values are not precisely known but the value ranges can be obtained, and the decision-makers provide their preference information over attributes by three different uncertain-preference formats i.e., 1) interval utility values; 2) interval fuzzy preference relations; and 3) interval multiplicative preference relations. We first utilize some functions to normalize the uncertain decision matrix and then transform it into an expected decision matrix. We establish a goal-programming model to integrate the expected decision matrix and all three different uncertain-preference formats from which the attribute weights and the overall attribute values of alternatives can be obtained. Then, we use the derived overall attribute values to get the ranking of the given alternatives and to select the best one(s). The model not only can reflect both the subjective considerations of all decision-makers and the objective information but also can avoid losing and distorting the given objective and subjective decision information in the process of information integration. Furthermore, we establish some models to solve the multiple-attribute group-decision-making problems with three different preference formats: 1) utility values; 2) fuzzy preference relations; and 3) multiplicative preference relations. Finally, we illustrate the applicability and effectiveness of the developed models with two practical examples.

Considering the diversification of transaction information and complexity of matching environment, the original information with the language tendency plays an important role. Thus, under this circumstance, this paper gives a matching decision-making system under the probabilistic linguistic environment so as to improve the matching efficiency and quality. First, this paper demonstrates the multi-stage two-sided matching problem and illustrates the system frame. Then, for the multiple indicators, a probabilistic linguistic integrated cloud Bayesian network is constructed to present the dependency relationship, and determine the corresponding probability. It is known that the accuracy of agents' preference information acts on the stability of final matching results, which may involve the strong ranking, agents' psychological preferences and personal interests, etc. Thus, the improved ORESTE (organísation, rangement et Synthèse de données relarionnelles, in French) method is introduced to derive strong ranking and determine preference, indifference, and incomparability relation (PIR). Furthermore, this paper constructs the dynamic two-sided matching model considering the screening effect. Finally, a case study in second-hand house transaction is used to demonstrate the matching process. Simulation and comparison analysis validate its feasibility and effectiveness. [ABSTRACT FROM AUTHOR]

The strategy production in intuitionistic fuzzy multi-attribute decision-making is influenced by various factors. More realistic data representations are needed to portray ambiguity under increasingly complex decision-making contexts. Firstly, this study proposes a new approach for ranking independent trapezoidal intuitionistic fuzzy numbers based on the risk attitudes of decision-makers. The proposed ranking approach incorporates the decision-makers' risk preferences and considers all possible values in the feasible domain. After that, a novel similarity measure between two independent trapezoidal intuitionistic fuzzy numbers is presented based on the three-segment projection. The constructed similarity measure uses the image structure of the data to reflect the variation of vagueness and then also combines deviation to achieve optimization. Moreover, this study improves the VIKOR method under the independent trapezoidal intuitionistic fuzzy environment (V-ITIFE) to solve the multi-attribute decision-making problems. Finally, a numerical example is presented to illustrate the applicability and efficiency of the V-ITIFE method. [ABSTRACT FROM AUTHOR]

In some actual decision-making problems, experts may be hesitant to judge the performances of alternatives, which leads to experts providing decision matrices with incomplete information. However, most existing estimation methods for incomplete information in group decision-making (GDM) neglect the hesitant judgments of experts, possibly making the group decision outcomes unreasonable. Considering the hesitation degrees of experts in decision judgments, an approach is proposed based on the triangular intuitionistic fuzzy numbers (TIFNs) and TODIM (interactive and multiple criteria decision-making) method for GDM and consensus measure. First, TIFNs are applied to handle incomplete information due to the hesitant judgments of experts. Second, considering the risk attitudes of experts, a decision-making model is proposed to rank alternatives for GDM with incomplete information. Subsequently, based on measuring the concordance between solutions, a consensus model is presented to measure the group's and individual's consensus degrees. Finally, an illustrative example is presented to show the detailed implementation procedure of the proposed approach. The comparisons with some existing estimation methods verify the effectiveness of the proposed approach for handling incomplete information. The impacts and necessities of experts' hesitation degrees are discussed by a sensitivity analysis. [ABSTRACT FROM AUTHOR]

Pythagorean fuzzy sets, as a generalization of intuitionistic fuzzy sets, have a wide range of applications in many fields including image recognition, data mining, decision making, etc. However, there is little research on clustering algorithms of Pythagorean fuzzy sets. In this paper, a novel clustering idea under Pythagorean fuzzy environment is presented. Firstly, the concept of feature vector of Pythagorean fuzzy number (PFN) is presented by taking into account five parameters of PFN, and some new methods to compute the similarity measure of PFNs by applying the feature vector are proposed. Furthermore, a fuzzy similarity matrix by utilizing similarity measure of PFNs is established. Later, the fuzzy similarity matrix is transformed into a fuzzy equivalent matrix which is utilized to establish a novel Pythagorean fuzzy clustering algorithm. Based on the proposed clustering algorithm, a novel multiple attribute decision making (MADM) method under Pythagorean fuzzy environment is presented. To illustrate the effectiveness and feasibility of the proposed technique, an application example is offered. [ABSTRACT FROM AUTHOR]

The multiple global environments have triggered changes in the international environment, leading to a sharp decline of foreign direct investment (FDI) compared to pre-pandemic level. To evaluate the investment risk of FDI and make optimal investment decision becomes the most important issue for investors. This paper focuses on the evaluation of investment risk for FDI. First, an index system for risk evaluation of FDI is constructed. Then, we introduce the probabilistic linguistic entropy and cross entropy measures, based on which, a programming model is developed to identify the objective attribute weights. A composite weight derivation method, which takes both the objective attribute weights and the subjective attribute weights into account, is further introduced. In view of attributes' uncertainty and fuzziness and the conflicting characteristics of some attributes, the VIKOR (the Serbian name: VlseKriterijumska Optimizacija I Kompromisno Resenje, means multi-criteria optimization and compromise solution) method is used to evaluate the risk of FDI under the probabilistic linguistic environment. Furthermore, a case study is presented to illustrate the proposed method. The comparative analysis and some further discussions verify the validity of the proposed method for the FDI risk evaluation. [ABSTRACT FROM AUTHOR]

Fuzzy decision-making is increasingly becoming a pivotal approach to solving complex and intricate issues in tourism and hospitality management. The primary objective of this study is to unveil the developmental status, key themes and research trends within fuzzy decision-making in tourism and hospitality management (FDMTH) using Bibliometrix, CorText Manager and VOSviewer tools. As such, we conduct a comprehensive bibliometric and content-wise analysis of selected 341 publications concerning FDMTH. For one thing, we use valuable bibliometric indicators to conduct a general feature peek and performance analysis of the audited corpus. The research findings reveal a sustained scholarly interest in FDMTH. As a critical player, Pappas, Nikolaos leads the volume of publications. The Journal of Intelligent & Fuzzy Systems stands out as the preferred outlet for FDMTH research. For another, the contingency matrix and bump graph modules are employed to detect the knowledge flow and intellectual connections in FDMTH. The results of network mapping tentatively identify geographic and thematic biases in FDMTH. More importantly, bibliographic coupling analysis reveals four specific themes, namely multi-criteria decision-making and evaluation, factors identification, fuzzy programming and forecasting, and fuzzy intelligence. Our pioneer work will contribute to the present understanding of the complexity and interdisciplinarity of FDMTH. [ABSTRACT FROM AUTHOR]

Healthcare management (HCM) has attracted significant attention from scholars and practitioners, and decision-making (DM) is always perceived as a crucial managerial function. This paper attempts to explore the trend and structure of DM research in the field of HCM (DM-HCM) by conducting a bibliometric analysis of publications from 1998 to 2021. A total of 581 documents covering all the available evidence are retrieved from the Web of Science (WoS) core collection. First, a descriptive performance analysis is performed based on widely accepted bibliometric indicators, followed by identifying primary contributors in the research community. Then, a science mapping analysis is implemented to discover the structural connections among different research constituents using three visualization tools, namely, VoS viewer, CiteSpace, and Bibliometrix. The citation-related and co-authorship networks are analyzed to explore the intellectual structure of the bibliometric corpus. Moreover, the keyword co-occurrence, timeline view, and evolution analysis enrich the understanding of thematic clusters and identify the DM-HCM research focus. Finally, the main findings are summarized, and possible research directions are proposed. [ABSTRACT FROM AUTHOR]

In recent years, more and more attention is paid to the OWA operator in the academy. Growth curve analysis, which is often used in ecosystem studies, also indicates that this growth trend will continue. However, prior literature has not made a big picture to help researchers make clear of the development of this field by identifying the evolution path. The classic main path analysis is an excellent method combining quantitative analysis and qualitative analysis. We conducted the classic main path analysis and its variants on a citation network with 1474 papers to probe the development trajectories and research topics of OWA. We obtained several findings by constructing local and global main path, and multiple main paths. The path results indicate that weight generation and operator generalization run through the overall OWA domain, show that the multiple criteria decision making process assumed in the related research begins to be dynamic and multi-period, and reveal that some theories such as social network theory are introduced into the OWA operator and the applications are also greatly expanded. [ABSTRACT FROM AUTHOR]

The majority of real-life decision-making problems often require the analysis and evaluation of multiple factors. The nested probabilistic linguistic term set is a good tool for describing multidimensional uncertain information because it contains a collection of inner-layer and outer-layer terms and expresses both ordinal and nominal terminologies. In order to avoid losing information in the process of converting linguistic terms into numerical values, this paper proposes a series of new equivalent transformation functions for nested probabilistic linguistic term sets and defines the corresponding comparison rules. The criteria importance through inter-criteria correlation (CRITIC) method is conducted to calculate the objective weights of attributes. Using equivalent transformation functions and the weighting approach with the nested probabilistic linguistic information, this paper combines the weighted MULTIMOORA method with dominance-directed graph to solve the doctor–patient shared decision-making problem. In addition, the results of comparative analysis show that the proposed method is reasonable and effective, and it is applicable to other decision-making scenarios. [ABSTRACT FROM AUTHOR]

Varied extensions of preference relations have been developed to cope with uncertain scenes. However, the introduced uncertainty, which might decrease the reliability of a final decision, has not been paid sufficient attention. In this study, a new concept, referred to as complex preference relation (CPR), is proposed to formalize most of the existing types of preference relations under uncertainty. Two distinct uncertainty measures are proposed to restrict the uncertainty degree of a CPR. The preference-oriented measure, which looks into the uncertainty of each piece of preference, gives limits to a CPR by its maximum variance. The rank-oriented measure, which focuses on the resultant ranks, restricts uncertainty by the probability of rank reversal. Stochastic uncertainty degrees are defined as a reference to enable the determination of uncertainty thresholds by risk appetites directly. A series of simulation experiments are conducted to demonstrate the features and connections of the two measures. [ABSTRACT FROM AUTHOR]

Compared with the general fuzzy decision making, the calculation process under the probabilistic hesitant fuzzy environment involves two new issues that need further consideration, namely quantitative element probability and qualitative element preference. The contributions of this study are to address them in the same modeling framework. For the quantitative element probability, also element occurrence probability, we propose an optimization method by developing the probabilistic hesitant fuzzy envelopment rate and introducing six behavior strategies. This method deals with two complex scenarios, namely, the occurrence probabilities are completely unknown or partially missing. For the qualitative element preference given by decision makers, we design a fusion technique and propose the probabilistic hesitant fuzzy element preference fusion (PHFEF) model based on the above optimization method. Thus, the PHFEF model is used to address the above issues in the same modeling framework. To apply the above models, we further provide a step-by-step decision-making process to reasonably use the PHFEF model in the probabilistic hesitant fuzzy environment. Finally, an illustrative example is used to show the feasibility and further comparisons are given to present the rationality of the proposed methods. [ABSTRACT FROM AUTHOR]

It is very common to use linguistic information to solve decision-making problems in real life, and the double hierarchy hesitant fuzzy linguistic term set (DHHFLTS) has been widely used because of its powerful ability of expressing complex linguistic information. There is no doubt that the comparison method of double hierarchy hesitant fuzzy linguistic elements (DHHFLEs) not only occupies an important theoretical and practical position, but also is the basis for further study of DHHFLTSs. However, the existing comparison methods of DHHFLEs still have some limitations. Therefore, this paper proposes a new DHHFLE comparison method, which is an improvement and perfection of the existing DHHFLE comparison methods. In addition, considering that the current research on distance and similarity measures of DHHFLEs is mostly based on the algebraic point of view, this paper proposes a cosine similarity measure of DHHFLEs, which fills the gap in the study of distance and similarity measures from the geometric point of view. Then, the cosine similarity-based DHHFL-ELECTRE II method is proposed to solve the multi-attribute decision-making (MADM) problem in the double hierarchy hesitant fuzzy linguistic environment. Finally, this method is used to solve a MADM problem in the performance evaluation of financial logistics enterprises. The results show that the proposed method has certain applicability and feasibility. [ABSTRACT FROM AUTHOR]

Big data starts booming in 2013 and has multiple applications in all walks of life. In such an environment, big data for information technology (BDI) and decision making (BDD) have formed some hot topics in common. This paper reviews the body of BDI and BDD research studies from 1994 to 2020, using bibliometrics analysis. The aim of this paper is to explore the current status, the correlation between BDI and BDD, the future trends and challenges. From time and space dimensions, CiteSpace and VOS viewer are used to obtain the annual trends of documents, the distribution of countries and sources, the citations and the h-index of BDI and BDD. The top three productive countries are the USA, China and the UK. From the perspective of h-index, the USA and the UK are at the forefront of the world. The value of big data is realized through information acquisition, storage, analysis, expression transmission and service sharing technologies, and the decision-making techniques exist throughout the process of big data analysis. "Business" and "Information science library science" are the latest hotspots of BDI. The appliances in the organization, supply chain management, education, and the environment are recent themes of BDD. Big data technology processing capabilities and network security issues are the main challenges in the future. This study contributes to the body of knowledge on BDI and BDD, and hops to help in understanding the evolution of them in relevant fields. [ABSTRACT FROM AUTHOR]

In real world, a typical decision-making problem in the medical field can be seen as an uncertain hesitant fuzzy multiattribute decision-making problem when existing experiences of decision-makers are insufficient. A three-way decision model is an effective tool to deal with uncertain decision-making problems, which can realize the classification of objects. However, different psychological behaviors of decision-makers are likely to affect decision-making results in actual decision-making processes. In order to address this challenge, we first propose a regret-theory-based three-way decision model in hesitant fuzzy environments, which mainly combines regret theory with hesitant fuzzy sets to calculate the perceived utility value of objects. Second, since one of the core ingredients for regret theory is the regret–rejoice function, we put forward a new regret–rejoice function that preserves the original indecisive uncertainty in hesitant fuzzy environments. In addition, according to the inherent relationship of the used data, this article provides a three-way classification method based on the preference ranking organization method for enrichment evaluations I method. Finally, the practicability, rationality, and superiority of the proposed method are shown via the case analysis and comparative analysis in the medical field. [ABSTRACT FROM AUTHOR]

Group opinion often has an important influence on the development and decision-making of major events. However, there are existing two problems with group opinion: (1) As opinions evolve, group opinion may diverge sharply, which is not conducive to obtaining final decision opinion. (2) The evolution of opinions can also cause serious systemic biases in group, which can lead to a final decision that is far from the truth. Hence, this paper deeply investigates two important strategies of consensus boost and opinion guidance in opinion management. Meantime, considering the urgency of some decision-making problems, such as major public crisis events, opinion management process is also subject to time constraint. In this paper, we firstly formalize the minimum adjustment cost consensus boost and opinion guidance with time constraint as Markov decision process because of the intersection and evolution rule of opinions described by opinion dynamics holds Markov property. In this case, the minimum adjustment cost can improve the efficiency of opinion management. We further propose consensus boost algorithm and opinion guidance algorithm based on deep reinforcement learning, which availably mirrors human learning by exploring and receiving feedback from opinion dynamics. Then, by combining the above-mentioned algorithms, we design a new opinion management framework with deep reinforcement learning (OMFDRL). Finally, through comparison experiments, we verify the advantages of our proposed OMFDRL, which can provide managers with more flexible usage conditions. [ABSTRACT FROM AUTHOR]

Financing group decision-making (FGDM), which is an important stage of project financing, has unique characteristics: large investments and long payback horizons. Its evaluation results are likely to be distorted if we ignore the uncertain information and inconsistent assessment during the decision-making process. In this study, we propose a double interaction-based FGDM framework under uncertain information and inconsistent assessment. We modify the weight setting of evidence reasoning and aggregation method of probabilistic linguistic term sets to process the above two issues. The proposed framework is applied in a detailed case study analysis to display its effectiveness and stability. We expect the double interaction-based group decision-making framework under uncertain information and inconsistent assessment to be a useful tool to understand FGDM processes. [ABSTRACT FROM AUTHOR]

In real decision-making problems, decision makers (DMs) usually select the most potential project from several ones. However, they unconsciously show different confidence levels in decision-making process because they come from various backgrounds and have different experiences, etc., which affects the decision results. Moreover, the probabilistic linguistic term set, which not only includes the linguistic expressions used by DMs in their daily life but also contains the probability for each linguistic term, can well portray the real perceptions of DMs for the projects. Furthermore, large-scale consensus has gradually been a popular way to effectively solve complex decision-making problems. To sum up, in this paper, we are dedicated to constructing a large-scale consensus model considering the confidence levels of DMs under probabilistic linguistic circumstance. Firstly, the endo-confidence is defined and measured by DM's probabilistic linguistic information. Then, the DMs are clustered according to the similarities of both evaluation information and the endo-confidence levels. Both evaluation of the non-consensus cluster and evaluation integrated by the clusters with higher endo-confidence level than this non-consensus cluster are used as the reference to adjust its evaluation information. Then, a case study and the comparative analysis are carried out. Finally, some conclusions and future work are given. [ABSTRACT FROM AUTHOR]

The increasing complexity of social activities requires an expanding number of people to be involved in decision-making, so that the large-scale multi-attribute group decision-making problems have gained widespread attention. After overviewing the researches of large-scale multi-attribute group decision-making methods, we have found that: The existing methods only consider consensus based on evaluation information of alternatives, while ignoring the consensus on importance of attributes. Thus, in order to tackle the issues and describe the hesitancy of decision makers in the decision-making process, this paper proposes a novel dual consensus method in large-scale multi-attribute group decision making under hesitant fuzzy linguistic environment. In the consensus reaching process, the method considers not only the consensus on the evaluation information of alternatives, but also the consensus on the importance of attributes, where both consensus reaching processes are implemented by the particle swarm optimization algorithm. The subjective weights of attributes are derived from the consensus reaching process of preference matrices, and the objective weights of attributes are obtained from the consensus reaching process of decision matrices, so as to acquire the comprehensive weights. After that, the overall ranking of alternatives can be obtained by TODIM. Finally, the proposed method is applied to a case study of medical imaging equipment purchasing decision-making, and the comprehensive analysis is provided to clarify advantages of the proposed method. • Propose a novel dual consensus method which considers alternatives and attributes. • The decision-making process is realized by particle swarm optimization algorithm. • Attribute weights contain both subjective and objective information. • Apply the proposed method to medical imaging equipment purchasing decision-making. • Clarify the advantages of the proposed method through comprehensive analyses. [ABSTRACT FROM AUTHOR]

In this paper, a fresh multi-attribute decision-making (MADM) method is proposed for group-oriented decision analysis. For group-oriented multi-attribute decision-making (GOMADM) problems, this paper proposes local advantage–disadvantage degrees and advantage–disadvantage degrees from the perspective of a strict attribute containing relation between group members and other group members, and studies the related properties. Based on the above two degrees, a new GOMADM method is designed, and this method is locally optimized according to the related properties. Finally, an example is used to analyze the rationality of the GOMADM method, and their ranking results are comparatively analyzed and discussed. [ABSTRACT FROM AUTHOR]

Due to the complex application scenarios and different user requirements, it is usually difficult to evaluate communication technologies objectively and comprehensively. Compared with the traditional quantitative methods, multi-attribute group decision-making (MAGDM) methods based on qualitative analysis can reflect the evaluation opinions of experts more comprehensively. To address the above difficult by utilizing the advantage of the MAGDM based on qualitative analysis, this paper proposes a new linguistic expression model called uncertain linguistic term with weakened hedge (ULTWH), which expresses decision information better and closer to the original terms of experts, and then the model is applied to solve MAGDM problems. An ULTWH is consisted of a linguistic term interval where the real value of a linguistic variable is most likely to appear, and a weakened hedge which is used to express the degree of uncertainty. In the paper, the order relations, operation rules and the aggregation operators for ULTWHs are formulated and presented. Then, a new multi-granular group decision making (GDM) method based on ULTWHs is developed. After that, the developed method is used to solve a specific problem of communication technology evaluation. Finally, a comparative analysis of several multi-granular GDM methods is made. Through comparison, it is shown that the proposed method has a wider range of applications and better interpretability. [ABSTRACT FROM AUTHOR]

Considering the conditions that: 1) same linguistic term means different things for different people; 2) flexible semantics cannot be represented by original linguistic term; and 3) some semantics given by decision makers are possible to be changed during the consistency improving process, we bring some flexibility and personality into hesitant fuzzy linguistic preference matrix structures by allowing the linguistic preference matrices to be granular rather than numeric, providing a new characterization of linguistic preference matrices. Inspired by the thought of granular computing, this article proposes a new hesitant fuzzy linguistic method to deal with issues when a lot of decision makers provide hesitant and uncertain preference information in the decision-making process. First, we design a multiplicative consistency index and calculate its thresholds corresponding to different dimensions of preference matrix by the Monte Carlo experiment. Then, we construct a hesitant fuzzy linguistic model with granularity level, so as to recharacterize original assessment information and improve the consistency of preference matrices as far as possible. Considering the features of some large-scale group decision-making situation, where the decision makers have little opportunity to take part in multiple consensus reaching processes, hesitant fuzzy linguistic fuzzy $C$ -means clustering algorithm is developed to integrate the assessment information given by decision makers. Finally, the final decision-making results are derived. An illustrative example of assessing psychological situation of some COVID-19 infected persons clarifies the reasonability of the proposed method. Finally, we complete some comparative studies and simulation experiments to demonstrate the method’s validity and advantages. [ABSTRACT FROM AUTHOR]

Probabilistic preference decision-making (PPDM) is a branch of uncertain decision-making, which identifies decision-makers' preferences with probability to deal with uncertain decision-making problems more comprehensively. In order to understand the status and development process of publications related to PPDM, this paper conducts a bibliometric study. Based on the Web of Science (WoS) core collection, a total of 487 publications are obtained. Firstly, this paper makes a general analysis of the basic characteristics of PPDM, including the type of articles, the number of annual publications and the research directions. Secondly, according to the information of the country/region/institution/author/journal regarding the publications, the publication structure is analyzed, the most productive items are explored, and the partnership of each item is detected with the VOSviewer. The paper then examines the citation structure of PPDM publications, uses the VOSviewer to visualize the citation network and discusses the most influential items. Finally, VOSviewer and Bibliometrix are used to analyze the keywords and study the work focus and current hot topics of PPDM. The keywords are divided into three stages in chronological order to analyze the development trend and theme evolution of the research topics. Based on a series of analyses, we further discuss the characteristics of PPDM publications, give some reasonable suggestions and draw some main conclusions. This research thoroughly analyzes and summarizes the essential features, research status and development trend of PPDM publications, which is helpful for the interested researchers to carry out further scientific research. [ABSTRACT FROM AUTHOR]

For practical multiple attribute decision making problems, it is common to involve heterogeneous attribute information and a rational choice may be distorted by the judgments of decision-makers due to their limited personal cognition. In this regard, this article puts forward an integrated model to solve multiple attribute decision-making problems considering the interaction among heterogeneous attributes based on the regret theory. First, a target-based utility function that is in line with people's perceptions is developed. Based on this function, the specific utilities of different forms of performance scores, including crisp numbers, interval numbers, and hesitant fuzzy sets, are given. Then, the regret theory is used to identify the partial perceived utilities of alternatives on each attribute, which include the utility, regret, and rejoicing values of decision-makers. In addition, to address both positive and negative interactions among attributes, the Choquet integral is employed to derive the global utilities of alternatives. An application to determine the optimal provider of waste classification service in multiattribute reverse auction is given, and the corresponding comparative and sensitive analyses verify the applicability and effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

Faced with any decision-making problems with fuzzy multicriteria information, decision-makers generally set a minimum requirement on each criterion for satisfying their own preferences, thereby forming a fuzzy set on the criterion universe, which is called the criterion fuzzy set. From the perspective of realistic decision, the final decision of all alternatives should be determined according to this criterion fuzzy set. In view of this, this article proposes the criterion-oriented three-way ranking and clustering strategies, which can solve the qualitative clustering and ranking problems of all alternatives from the perspective of criterion fuzzy sets. First, we define a criterion fuzzy set as a criterion-oriented fuzzy concept and propose a criterion-oriented relative risk loss model and discuss related properties accordingly. Meanwhile, we use the generalized fuzzy rough lower (upper) approximation to estimate the absolute (relative) conditional probability between the binary fuzzy class of the alternative and the criterion-oriented fuzzy concept. Then, a criterion-oriented absolute (relative) three-way clustering strategy is proposed, which can perform qualitative analysis on all alternatives. Furthermore, based on the three-way semantics and global cost function, we recommend a criterion-oriented absolute (relative) three-way ranking strategy, which can rank all alternatives. Finally, through numerical example, comparative analysis and sensitivity analysis, we test the feasibility and effectiveness of the proposed criterion-oriented three-way ranking and clustering strategies. [ABSTRACT FROM AUTHOR]

By comparing attributes of objects in an information system, the advantage matrix on the object set is established in this paper. The contributions can be identified as follows: (1) The advantage degree is proposed by the accumulation of the advantage matrix. (2) Based on the advantage matrix, the advantage (disadvantage) neighborhood approximation operator and the advantage (disadvantage) correlation approximation operator are defined and studied. Based on these two new operators, the neighborhood degree and the correlation degree are presented. The relationships between them are also investigated to demonstrate the value of the proposed method. (3) Finally, based on the above three degrees, new algorithms are designed, in which the effectiveness and robustness of the algorithms are analyzed by practical examples. [ABSTRACT FROM AUTHOR]

Nowadays, the decision environment is becoming more and more complicated due to the development of society and science, and people receiving different types of information every day and gradually form their unique cognitions and knowledge backgrounds. In this situation, people tend to provide their preferences or evaluations through multiple information expression formats, such as the probabilistic hesitant fuzzy sets, the probabilistic linguistic term sets and the probabilistic interval preference ordering sets. In this paper, we deeply investigate the relationships among these three probabilistic-based expressions and introduce two transformation functions for them in order to make the information formats unified. Besides, for the probabilistic hesitant fuzzy sets, three novel distance measures are proposed, i.e., the minimal distance, the central distance, and the improved distance, which are useful tools to measure the difference between the probabilistic hesitant fuzzy elements. In order to fuse the different formats of information and get valuable results from it, the K-medoids algorithm for the probabilistic-based expressions is developed. The algorithm is applied to classify the merchants on the website of Dianping.com, so that the results can be provided to customers to help them make decisions. [ABSTRACT FROM AUTHOR]

This article proposes two decision-making models in an incomplete fuzzy hesitant linguistic environment and applies them to address the site selection problems for hydropower stations. For better depicting a decision maker's judgments under uncertainty, based on the concept of incomplete hesitant fuzzy linguistic preference relation, this article first defines its consistency measures from the perspective of additive consistency and multiplicative consistency, respectively. By introducing decision maker's satisfaction degree to measure the differences between the incomplete hesitant fuzzy linguistic preference relation and its corresponding weight vector, two decision-making models, which aim to achieve the maximum satisfaction degree, are established for determining the optimal weight vector. This article further designs experiments to make decision support by evaluating the proposed models from the correlation and time complexity point of view and providing sensitivity analysis. A case study concerning the site selection for a hydropower station at Yalong River is given to illustrate the decision-making process and the effectiveness of the proposed models. [ABSTRACT FROM AUTHOR]

Developing low-carbon tourism can not only improve the ecological environment, but also promote the development of economy in China. To select a desirable low-carbon tourism destination, we need to consider multiple conflicting and incommensurate criteria, simultaneously. However, traditional decision-making methods such as analytical hierarchy process and Delphi fail to model the complex cognition of decision makers. In this regard, this article proposes a novel multi-criteria decision making method called the thermodynamic feature-based method to aid decision makers to select the optional low-carbon tourism destination. The q-rung orthopair fuzzy set (q-ROFS), as a recently proposed information representation model, is used to express the imprecise information of decision makers. We first introduce new distance measures of q-ROFSs and investigate their desirable properties in detail. Afterwards, a thermodynamic feature-based method is developed from the aspects of energy, exergy and entropy of alternatives integrating both quantitative and qualitative decision information. Finally, a case study concerning the selection of low-carbon tourism destination is given to illustrate the applicability and superiority of the proposed method. [ABSTRACT FROM AUTHOR]

The past decade has witnessed the rapid growth in the hesitant fuzzy domain. To provide an in-depth discussion, based on the retrieved 1080 papers from the Web of Science (WoS), this paper first investigates what topics are the research interested in and how they have changed over the past decade in the hesitant fuzzy area. Main path analysis is adopted further to identify the most influential connections between papers and analyze the knowledge diffusion trajectories in the past decade, including the local and global main paths and the key-route main path. The results show that there are five hot topics which are decision-making, information measure, aggregation operator, extensions of HFS and preference relation. Among them, decision-making and extensions of HFS are two topics that are beginning more and more prevalent. The result of main path analysis consolidates the findings, showing that the application of hesitant fuzzy theory in the decision-making field has been and remains the most popular, and the object of the research has shifted to different types of HFSs being hesitant fuzzy linguistic term set (HFLTS) the most remarkable one. This paper not only provides a framework to investigate the research in a certain field, but also provides an in-depth summary of the field to provide theoretical guidance for researchers and practitioners. [ABSTRACT FROM AUTHOR]

In the decision-making process, retaining the original data information has become a most crucial step. Dual hesitant fuzzy sets (DHFS), which can reflect the original membership degree and non-membership degree information given by the DMs, is a kind of new tool for the DMs to provide the original information as much as possible. In this paper, we focus on the decision- making problem by a projection model (Algorithm I) whose attribute values are given in the forms of dual hesitant fuzzy elements (DHFEs). In order to reflect the information of the data more accurately, we first divide the dual hesitant fuzzy decision matrix into membership degree matrix and non-membership degree matrix. Then we gain the virtual positive ideal solution from the membership degree matrix and the negative positive ideal solution from the non-membership degree matrix. And then the projection values from every solution to the virtual positive ideal solution and the negative positive ideal solution are calculated. In combination with the two projection values, the relative consistent degree is further calculated to rank all the alternatives. At the same time, in order to guarantee the rationality of the decision-making result, a variation coefficient method is developed to determine the weights of the attributes under dual hesitant fuzzy environment objectively. Finally, the existing algorithms (Algorithm II and Algorithm III, Algorithm IV, Algorithm V) are compared with our algorithm (Algorithm I). The comparison result shows that Algorithm I is a valuable tool for decision making. [ABSTRACT FROM AUTHOR]

Aiming at three issues in large-scale group decision-making (LSGDM): risk attitudes, dynamically changing roles, and dynamically adjust evaluation information of decision makers (DMs), this paper constructs an LSGDM model by considering risk attitudes and dynamically changing roles. Firstly, we introduce the concept of risk attitudes and the method of identification and creatively combine it with Decision Making Trial and Evaluation Laboratory to divide DMs into four categories including core DMs, driven DMs, independent DMs, and followers. Considering the dynamically changing roles of DMs, an adjustment method for evaluation information is proposed. Then a double recognition mechanism is developed to determine whether the consensus has been reached. Moreover, we construct a method to determine the weights of DMs. Based on the above research, an LSGDM model based on probabilistic double hierarchy linguistic term set is constructed and applied to a practical problem of the selection of emergency medical distribution schemes. Finally, a sensitivity analysis is performed to examine the impact of different adjustment coefficients on the results, and the validity of our method is further illustrated by comparative analysis. [ABSTRACT FROM AUTHOR]

Probabilistic linguistic term sets (PLTSs) provide a flexible manner to model complex linguistic expressions in qualitative decision making. Some fundamental aspects of PLTSs, such as order relations and basic operations, are not built in a solid way. The lack of required properties makes their applications be not sufficiently reliable. In this study, a PLTS is mapped to a stochastic variable. A partial order of PLTSs is defined based on the idea of stochastic order. The concept of total order is then provided by refining the partial order. Moreover, aggregation functions of PLTSs are proposed by defining an aggregation function in a set of linguistic terms. Operations and aggregation operators of PLTSs are further carried out based on the aggregation functions. The above theoretical developments own some merits such as the partial order is reasonable because the ranking results coincide with rational decision-makers who consider increasing utility functions, the operations preserve desirable properties that are satisfied by the linguistic aggregation functions, and the operations and aggregation operators of PLTSs could be specified according to practical applications based on the proposed theoretical frame work. [ABSTRACT FROM AUTHOR]

The data are not always real numbers due to the complexity and uncertainty of the real-world decision environment. This requires us to use probability-based expressions to describe the complex decision-making data in reality. In order to understand the probability-based decision-making information more comprehensively, this paper reviews and summarizes the current development of probability-based decision-making information. First, the number and the distribution of publications related to the probability-based decision-making information are analyzed. Then, based on presenting literature related to different concepts, all the existing different concepts are reviewed and discussed. Considering different forms of decision-making information, this paper summarizes decision-making methods from two aspects: the decision-making methods based on decision matrix and the decision-making methods based on preference information. We also summarize the existing literature from the perspective of application. In addition, based on current developments and the discussions above, some challenges concerning probability-based expressions are listed, which can be regarded as future research directions. [ABSTRACT FROM AUTHOR]

Generally, when making decisions, decision makers always have their subjective opinions regarding attributes, alternatives or even themselves based on their experience and knowledge. Although some methods, such as weighted aggregation, preference analysis, and fuzzy decision-making, can be used to describe and fuse these opinions, these methods involve two limitations, specifically, inaccurate numerical presentation and stepwise aggregation method. To address these issues, in this paper, we define multiple order relations expressed as several inequalities to describe these subjective opinions, and then propose hesitant fuzzy global fusion models to simultaneously fuse the multiple order relations and make a decision. To this end, we first introduce the hesitant fuzzy envelopment rate and develop partial fusion models for single order relations; subsequently, multiple order relations and global fusion model are proposed. Moreover, to ensure computability, we further derive the linear forms of these models and summarize the improvement schedules for the nonoptimal alternatives. According to these calculations and results, a hesitant fuzzy decision analysis including subjective opinion fusion, evaluation presentation, decision-making calculation, alternative ranking and selection, and nonoptimal improvement, can be performed. Finally, an illustrative example based on a real background is considered to show the effectiveness of the models and decision analysis processes. [ABSTRACT FROM AUTHOR]

With the emergence of outsourcing logistics and the rapid development of the e-commerce business, Third Party Logistics (TPL) plays an indispensable role in modern business. In the TPL provider selection process, uncertain information brings more challenges to decision makers. This paper uses probabilistic linguistic term sets (PLTSs) to describe uncertain decision making information. Firstly, we propose an improved Decision Making Trial and Evaluation Laboratory method, which allows a certain relationship between decision criteria and calculates criteria weights in multi-criteria decision making (MCDM) problems. Then, in order to make full use of uncertain TPL provider information and maximize the values of data, the probabilistic linguistic complex proportional assessment method is proposed and applied to solve the MCDM problems under probabilistic linguistic environment, which needs much less computation than other MCDM methods. Finally, an application example of TPL provider selection is presented to demonstrate the proposed method. A comparative analysis is further conducted to validate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

Probabilistic hesitant fuzzy sets (PHFSs) add the probability value corresponding to each degree of membership on the basis of hesitant fuzzy sets, so as to express the initial decision information given by experts more accurately and comprehensively. In this article, we mainly study how to integrate large-scare probabilistic hesitant fuzzy information more efficiently. We first discuss some basic operation laws of probabilistic hesitant fuzzy numbers, based on which the concepts of continuous PHFSs and continuous probabilistic hesitant fuzzy functions (c-PHFFs) are defined. They are the main objects of our research. We further explore definite integrals of the c-PHFFs and their related properties. They have direct and powerful applications in continuous probabilistic hesitant fuzzy environments, and lay the foundation for subsequent theoretical analysis. Based on the weight density function, we finally get the weighted-integral operator of continuous probabilistic hesitant fuzzy information. Then, some important properties of this integration operator are studied, including normalization, monotonicity, boundedness, etc. We are also devoted to revealing the inner connection between the continuous probabilistic hesitant fuzzy weighted-integral operator and the probabilistic hesitant fuzzy weighted averaging operator, the latter is usually used when dealing with discrete information. At last, we state why it is necessary to introduce a novel aggregation method based on continuous probabilistic hesitant fuzzy definite integrals, and in turn provide an application of the proposed method to prove its validity and rationality. [ABSTRACT FROM AUTHOR]

With the number of patients with chronic diseases increasing, a hierarchical diagnosis and treatment system is a feature of long-term treatment. During the treatment, if patients with chronic diseases are relieved, they can be referred to community hospitals for rehabilitation treatment, and to promote the rational allocation of hospital medical resources. Therefore, hospitals need referral standards to encourage patients to refer down. Existing ranking research which is mainly based on referral criteria,has not considered the low reliability due to different opinions within each group when making referral standard. In view of this, we propose a probabilistic linguistic-multiple criteria decision-making (PL-MCDM) method based on the decision-making reliability of multi-group for patients with chronic diseases requiring downward referral. First, the decision information of different groups on referral criteria is expressed as probabilistic linguistic preferences, and then the reliability levels of groups are measured when setting standards respectively. After that, the decision information and referral standards are re-adjusted for the least reliable group to improve the whole reliability. Secondly, the patients requiring downward referral are ranked by the similarity measure based on statistics of probability preference to acquire the formal referral standards. Finally, compared with the methods without reliability improvement, the real case of coronary heart disease in First Hospital of Qinhuangdao is used to verify the effectiveness of the proposed method, which illustrates its superiority. [ABSTRACT FROM AUTHOR]

Double hierarchy hesitant fuzzy linguistic term set (DHHFLTS) can be used to express complex linguistic information by combining two hierarchy linguistic term sets with 2-tuple linguistic structures. In decision-making processes, experts' assessment information may often be represented by some possible double hierarchy hesitant fuzzy linguistic elements (DHHFLEs) or some DHHFLEs with probability information, and we cannot ignore these probabilities when they are directly provided or aggregated by the experts' assessments. As we are aware that representing probability information is a new improvement and challenge for DHHFLTSs, this paper defines a novel and more general concept named probabilistic double hierarchy linguistic term set (PDHLTS). Then, to propose some more reasonable operations and a distance measure of PDHLTSs, we develop an adjustment method to ensure that two PDHLTSs have same probability distribution. Additionally, this paper develops an extended probabilistic double hierarchy linguistic VIKOR method by improving the traditional VIKOR method. Moreover, the advantages and practicality of the proposed method are demonstrated by applying it to solve a practical multiple criteria decision-making problem involving smart healthcare. Finally, we make some comparative analyses, as well as discussing possible directions for future studies. [ABSTRACT FROM AUTHOR]