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The increasing scarcity of resources and the escalating complexity of reality make the fairness ensuring in energy activities even more difficult. In this context, energy justice, as an emerging cross-field, tries to provide solutions based on practical problems. In the face of the surge of energy justice publications, it is necessary to review them in time, so that we can comprehend the significant achievements and the research directions worthy of further exploration. With the help of visualization tools, this paper conducts a comprehensive quantitative analysis of 1, 910 energy justice publications. Based on the results, we reach the following main conclusions: (1) The energy justice publications have only emerged rapidly in recent years ; (2) The research hotspots are closely related to the renewable energy transition ; (3) The distribution of prominent contributors in this field is relatively concentrated. The main contribution of this study is to comprehensively display the essential characteristics of the literature in this field, such as the evolutions of research themes and the performances of research contributors in different dimensions, so as to provide readers with an effective way to understand the knowledge structure in this field, and help related researchers rationally examine the existing results.

In recent years, double hierarchy linguistic expression models have developed rapidly in the field of decision making because their rich semantics are closer to people’s actual language environment. However, the existing double hierarchy linguistic expression models are difficult to deal with incomplete or missing information application situations. For example, online reviews provide some references for consumers to make decisions, but the information of many reviews is not necessarily complete. Therefore, we try to solve this problem and propose the concept of interval probabilistic double hierarchy linguistic term set (IP-DHLTS). At the same time, in order to ensure stability under different criteria weights, we choose to combine the EDAS method to obtain the average solution based on two measures. To sum up, we develop the interval probabilistic double hierarchy linguistic EDAS method and solve a real case with the natural language processing basic techniques about the hotel online reviews. Finally, the feasibility of the proposed method is verified by comparison with other methods.

The double hierarchy linguistic information is more close to people’s habits of expression and it can describe evaluation information more accurately, so it has been extensively utilized in multi-criteria decision-making (MCDM) problems in recent years. First of all, taking the advantage of the completeness of the double hierarchy linguistic information, this paper proposes the continuous interval-valued double hierarchy linguistic term set. It is vital that it not only can express more complex evaluation information but also can aggregate group opinions by continuous terms. At the same time, the gained and lost dominance score (GLDS) method is a outranking method that has emerged in recent years. It takes the perspective of individuals and groups more comprehensively, making the obtained ranking results more convincing and accurate. Therefore, we construct the GLDS method into the continuous interval-valued double hierarchy linguistic environment (named CIVDHL-GLDS method) based on the above considerations. Public transportation is an important part of urban transportation. A comprehensive and objective description of urban surface bus operation level is conductive to a more objective evaluation of urban traffic level. Afterwards, in order to justify its validity of our method, taking the performance evaluation of four subsidiaries of Chengdu Public Transport Group in Sichuan province as a case study. Finally, Some discussions and comparisons are provided to reveal our proposed method has some innovations and dominance.

In Internet venture capital (VC), it is very important to fully analyze and evaluate the influential factors. Because this activity usually involves amounts of experts, it makes sense to incorporate it into large-scale group decision-making (LSGDM). In this process, how to deal with the noncooperative behaviors and express the preference information are two important issues that need to be addressed. Given this, this paper is committed to evaluating the influential factors of Internet VC by managing noncooperative behaviors in LSGDM. Firstly, the preference information can be expressed by linguistic preference orderings (LPOs) which can be used to express unbalanced relationship between any two adjacent alternatives. Then, three kinds of noncooperative behaviors are taken into consideration, and we can identify the group who belongs to one of the three noncooperative behaviors, and then develop methods to manage them respectively. Furthermore, a consensus reaching model is established to manage these noncooperative behaviors. Moreover, we apply the proposed model to solve a practical LSGDM problem involving the evaluations of the influential factors in Internet VC. Finally, comparative analyses between the proposed model and some existing methods are made to show the validity and applicability of the proposed consensus reaching model.

Components procurement is a crucial process in supply chain management of the automobile industry. The problem is further complicated by imprecise information and discount policies provided by suppliers. This paper aims to develop a computational approach for assisting automobile components procurement with all-unit quantity discount policy and fuzzy factors, from potential suppliers offering different product portfolios. We propose a two-stage approach consisting of a DEA-TOPSIS (data envelopment analysis procedures followed with a technique for order preference by similarity to an ideal solution) approach for screening suppliers, and subsequentially a fuzzy mixed integer programming (FMIP) model with multiple objectives for optimizing order allocations. The DEA-TOPSIS approach integrates suppliers’ comparative performance and diversity performance into an overall index that improves the ranking of potential suppliers, while the FMIP model features a soft time-window in delivery punctuality and an all-unit quantity discount function in cost. By applying it in a case of automobile components procurement, we show that this two-stage approach effectively supports decision makers in yielding procurement plans for various components offered by many potential suppliers. This paper contributes to integrating multi-attribute decision analysis approach in the form of DEA crossevaluation with TOPSIS and FMIP model for supporting components procurement decisions. First published online 19 November 2020

Probabilistic linguistic term sets (PLTSs) can express the qualitative information of decision makers more accurately in the complicated linguistic setting. However, the existing comparison methods for PLTSs cannot compare some special PLTSs. To tackle this problem, a novel score function based on the concentration degree of an PLTS, called ScoreC-PLTS, is proposed. Additionally, the existing distance measures may distort the original information and lead to unreasonable results. Therefore, a novel probability splitting algorithm is proposed to preprocess PLTSs, based on which, a novel generalized hybrid distance is proposed for PLTSs. Moreover, a novel multiplicative analytic hierarchy process (MAHP) based on ScoreC-PLTS is proposed to determine the weight vector of attributes. Based on the generalized hybrid distance and MAHP, two novel TOPSIS-ScoreC-PLTS and VIKOR-ScoreC-PLTS methods are put forward to handle multi-attribute decision-making problems with PLTSs. Afterwards, an illustrative example concerning the selection of children English educational organization is solved using the proposed TOPSIS-ScoreC-PLTS and VIKOR-ScoreC-PLTS methods. In this example, four indicators are developed and the superiority of our studies is verified by comparing with the previous TOPSIS and VIKOR methods.

With the development of science and technology, the new road of scientific economic and financial development has played a decisive role in supporting the financial undertaking. To accelerate the economic development, it is very important to increase the guiding role of financial undertaking in the real economy. Therefore, it is necessary to promote the development of the real economy under the perspective of economic financialization based on some actions. To judge the implementation effect of these actions, this paper develops a multiple criteria decision-making (MCDM) method to evaluate them. First, the decision-making matrices are established with the probabilistic double hierarchy linguistic term set in which the probabilities are added to all double hierarchy linguistic terms. Additionally, a weight-determining method is developed to obtain the weight vector of criteria, and we develop a MCDM method named the probabilistic double hierarchy linguistic alternative queuing method (PDHL-AQM), where the decision-making result is intuitive by a directed graph or a 0–1 precedence relationship matrix. Furthermore, we apply the PDHL-AQM to solve a practical MCDM problem involving the real economy development evaluation under the perspective of economic financialization. Finally, some comparative analyses are made to show the advantages and reasonableness of the PDHL-AQM.

Risk evaluation is a primary but important task for technological innovation projects and this task is a multiple criteria group decision-making (MCGDM) process with probabilistic uncertainty and fuzzy uncertainty. Compromise programming decision-making methods with probabilistic linguistic term sets (PLTSs) are more appropriate for risk evaluation of technological innovation projects. This paper proposes a new approach named improved probabilistic linguistic-vise kriterijumska optimizacija kompromisno resenje (PL-VIKOR) method with probabilistic linguistic term sets for risk evaluation of technological innovation projects. Firstly, by fully considering both the relationship between each alternative and the positive ideal solution and the relationship between each alternative and negative ideal solution, the improved PL-VIKOR method for dealing with MCGDM problems is developed to make up the deficiency of the traditional PL-VIKOR method. Then, the improved PL-VIKOR method is applied to solve a practical MCGDM problem with probabilistic linguistic term sets involving the risk evaluation of technologically innovative projects for venture capital. Finally, we make some comparative analyses between the improved PL-VIKOR method and some existing methods to analyze the advantages and disadvantages of the proposed method. The results reflect that the improved PL-VIKOR method is more reasonable when calculating the distance measure between two PLTSs, and it can make the risk evaluation of technological innovation project MCGDM with PLTSs more objective.

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 structure...

Double hierarchy hesitant fuzzy linguistic term set (DHHFLTS) is a newly developed complex linguistic expression model, and has been well applied to multi-criteria decision-making (MCDM) problems. However, the determination of criteria weights and the innovation of decision-making methods are still two issues that worth exploring in this field. At present, conventional weight-determination methods sometimes have the disadvantages of complicated calculation and low consistency of the obtained results. On the other hand, the existing methods for linguistic information sometimes cannot consider the uncertainty of information caused by ignorance. Considering that the best-worst method (BWM) is a weight-determination method, which can not only greatly simplify the calculation process, but also improve the consistency degree of the results. Dempster-Shafer evidence theory (DSET) can better deal with information uncertainty caused by ignorance. Therefore, this paper extends the BWM and DSET to double hierarchy hesitant fuzzy linguistic environment to solve the above two problems respectively, and the DHHFL-BWM-DSET method is proposed. First, the weight of each criterion is derived based on the BWM-based weight-determination method. Then, inspired by DSET, we propose a DSET-based MCDM method which can not only obtain the decision results of a single decision maker, but also integrate the decision information of multiple decision makers to obtain more rational results. Therefore, decision makers can choose the method based on the specific situation. Finally, taking the selection of financial products as an example, it shows that the method proposed in this paper has some breakthroughs and advantages.

Natural language is more in line with the real thoughts of people than crisp numbers considering that qualitative language information is more consistent with the expression habits of experts. Double hierarchy hesitant fuzzy linguistic preference relation (DHHFLPR) can be used to express complex linguistic preference information accurately because the pairwise comparison methods are more accurate than non-pairwise methods. Consistency reflects the rationalization of a preference relation and can be used to judge whether a preference relation is self-contradictory or not. In this paper, an interval consistency index of DHHFLPR is developed, which is consisted by the consistency indices of all double hierarchy linguistic preference relations associated with the DHHFLPR. Additionally, an average consistency index of DHHFLPR is given by calculating the average value of the consistency indices of all double hierarchy linguistic preference relations. Moreover, we develop a consistency checking and repairing method for DHHFLPR. Finally, we apply the proposed method into a practical group decision-making problem that is to identify the most critical factors in developing lung cancer, and some comparative analyses involving the connections and differences among the proposed consistency indices are analysed.

Group decision making (GDM) can be defined as an environment where there exist a set of possible alternatives and a set of individuals (experts, judgements, etc.). Preference relation is one of the most widely used preference representation structures in GDM. Considering that the self-confidence degree is an important part to express preference information, and double hierarchy linguistic preference relation (DHLPR) is a cognitive complex linguistic information representation tool to express complex linguistic information, this paper presents a novel preference relation named as self-confident DHLPR. In addition, a weight-determining method is developed, which considers three kinds of information including the subjective weights and two kinds of objective weights. Furthermore, a consensus model is set up to manage the GDM problems with self-confident DHLPRs based on the priority ordering theory. The effectiveness of the proposed consensus model is illustrated by a case study concerning the selection of optimal hospitals in the field of Telemedicine. Finally, a simulation experiment is devised to testify the proposed consensus model and then some comparisons with other consensus reaching models are provided from three different angles including the number of iterations, the consensus success ratio and the distance between the original and adjusted preferences.

In hospital operation management, the medical supplier selection is a significant problem in which experts’ domain knowledge plays a critical role in selecting medical suppliers. The probabilistic linguistic preference relation (PLPR) whose elements are probabilistic linguistic term sets (PLTSs) is an effective tool to express experts’ preferences on alternatives based on pairwise comparisons. Due to the lack of knowledge of experts and the limit information of alternatives, some preference information may be missing and thus the incomplete PLPR (InPLPR) is constructed. In this study, a group decision-making (GDM) method with InPLPRs is proposed to deal with a practical medical supplier selection problem. To achieve this goal, we first propose a method to check whether an InPLPR is acceptable. Then, a procedure is developed to complete the acceptable InPLPR based on the property of additive consistency and a social strategy is proposed to complete the unacceptable InPLPR. Afterward, a GDM model based on InPLPRs is constructed in which the aggregation phase and exploitation phase are conducted by the probabilistic linguistic weighted averaging (PLWA) operator. Besides, an approach for calculating the weights of experts is proposed considering the characteristics of InPLPRs. Finally, we illustrate the proposed GDM model by a practical case about the medical supplier selection. A comparative analysis is presented to demonstrate the advantages of our method.

Automatic reasoning based on propositional logic is considered as an important tool in machine learning, and intuitionistic fuzzy sets have turned out to deal with vague and uncertain information effectively in real world. In this paper, a novel plausible reasoning based on intuitionistic fuzzy propositional logic is proposed. On the basis of it, the categories of intuitionistic fuzzy logic proposition (IFLP) formula are discussed both considering the true degree and the false degree at the same time. Some basic operational laws and inference rules of IFLPs on the basis of closely-reasoned scientific proofs are put out. Then, we develop two classification methods of IFLPs, i.e., truth table and figure of equivalence, respectively. After that, the reasoning theory of IFLPs is introduced and three reasoning methods are further established including direct proof method, additional premise proof method and reduction to absurdity method, respectively. Finally, a case study about strategy initiatives of HBIS GROUP on Supply-side Structural Reform is presented and some discussions are provided to validate the proposed methods. As a result, the proposed methods based on the plausible reasoning offer sound structure and can improve the efficiency of logic programming.

In real life, the assessment information is usually expressed by virtual linguistic terms, but the trust degrees of different assessment values to the same reference grade are usually ignored. In addition, the provided information is usually incomplete or uncertain, because the objective things’ characteristics are elusive and the decision maker's knowledge is limited. To solve such problems, in this paper, we first propose the virtual linguistic trust degree. Then, in view of the nonlinear changes of the decision maker's psychological states, we depict the virtual linguistic trust degree by a nonlinear function, and present some relevant aggregation operators. In order to avoid the loss of information, we propose a novel evidential reasoning approach that combines the virtual linguistic trust degree with basic unit-interval monotonic function. In this approach, the normalized basic probability mass can be obtained by the continuous basic unit-interval monotonic function, which satisfies the consensus axiom of original evidential reasoning. Meanwhile, we propose the normalized factor on the basis of the rule that the remaining unassigned probability mass is assigned into any subsets, and then present the whole framework of an extended evidential reasoning algorithm. Furthermore, a numerical example about the emergency response assessment of railway station is conducted to show the usage of the algorithm. Finally, the validity of this algorithm is demonstrated by the comparative analysis.

Tracking a maneuvering target is an important technology. Due to complex environment and diversity of sensors, errors need to be optimized with respect to various motion states during the tracking process. In this paper, we first propose how to unify the coordinate system and data preprocessing in case of tracking using multiple sensors. We then combine fuzzy sets with a novel trace optimization method based on extended Kalman filter (EKF) with nested probabilistic-numerical linguistic information (NPN-EKFTO). We present a case study of trace optimization of an unknown maneuvering target in Sichuan province in China. We solve the case by using both the proposed method and the traditional EKF and offer comparative analysis to validate the proposed approach.

Fund performance has been a hot topic in the financial research area, fair and correct evaluation of fund performance is of great significance for fund investors and companies. However, most of the relevant publications do not have any retrospective analysis of this topic in terms of knowledge domain to show its development trends and research concerns. To address this issue, two effective bibliometric tools namely Citespace II (The 5.3.R4 Edition) and SciMat are used to analyze the knowledge domain of this field in this paper. We have analyzed 979 articles related to fund performance from Web of Science between 1966 and 2019 (July), the analysis content includes the current status, collaboration network, co-citation network, and emerging trends of fund performance research, then we have derived the following desired conclusions: (1) In the last twenty years, there was a significant increase in the publication and citation numbers of fund performance research; especially, the relative research has become interdisciplinary and internationalized. (2) “Mutual Fund Performance”, “Fund Return”, “Investment Performance”, and “Portfolio Selection” are the hottest topics in the fund performance research. (3) “Small Fund” and “Investor Reaction” are the two emerging trends in the fund performance research. To sum up, there are two main contributions in this paper: First, we provide a full bibliometric analysis about the fund performance research. Second, we make the further development of fund performance research easier and more clearly to show the directions to learn and study for beginners.

Big data have been in use since the 1990s, which usually include some complex data sets whose sizes are beyond the ability of commonly used software to handle within a reasonable period of time. In recent years, big data analytics by providing personalized medicine and regulation analysis, providing clinical risk intervention and forecast analysis, reducing waste and nursing patients with external and internal variability, standardization of medical terminology and patient registration, and fragmentation of the solution, help to improve health care. This paper provides an overview of the contents of big data healthcare. We summarize some kinds of medical big data, including the electronic health records, the medical image data, the healthcare system big data, the health Internet of Things and healthcare informatics, the remote medical monitoring big data, the biomedical big data, and other sources of big data. Furthermore, we discuss some methods for handling different kinds of medical big data. Additionally, we analyze the privacy of medical big data and summarize some methods and technologies to protect privacy. Aiming at some special cases, we list some other analyses and methods for them. Most importantly, we discuss the potential challenges and future research directions related to big data healthcare.

Quality function deployment (QFD) is an effective method that helps companies analyze customer requirements (CRs). These CRs are then turned into product or service characteristics, which are translated to other attributes. With the QFD method, companies could design or improve the quality of products or services close to CRs. To increase the effectiveness of QFD, we propose an improved method based on Pythagorean fuzzy sets (PFSs). We apply an extended method to obtain the group consensus evaluation matrix. We then use a combined weight determining method to integrate former weights to objective weights derived from the evaluation matrix. To determine the exact score of each PFS in the evaluation matrix, we develop an improved score function. Lastly, we apply the proposed method to a case study on assembly robot design evaluation.

Hesitant fuzzy linguistic term sets have been an active field of research in recent times. Notwithstanding its usefulness to capture the human way of reasoning using linguistic expressions involving different levels of precision, in some situations they do not depict enough details. In this paper, we present a new kind of linguistic term sets, called free double hierarchy linguistic term sets, and their corresponding free double hierarchy hesitant fuzzy linguistic elements, in order to describe the complexity of linguistic expressions used by the decision makers in a more accurate and precise way. Furthermore, an order and a distance between free double hierarchy hesitant fuzzy linguistic elements are introduced to present an approach based on the TOPSIS method to rank alternatives with free double hierarchy hesitant fuzzy linguistic information by taking into consideration the opinions of a group of decision makers. A case study based on tourism management in Barcelona is also provided to illustrate the usefulness of the presented approach.

Uncertainty inference, which is used to infer the reasons corresponding to the results, has permeated through various fields, such as medicine, risk assessments, and marine management. Tackling ambiguity under fuzzy environment by using the Bayes and Dempster–Shafer theories has recently received special attention. In actual cases and experiments, we can estimate probabilities of occurrence and non-occurrence of events, which are expressed by intuitionistic fuzzy numbers (IFNs) or interval-valued intuitionistic fuzzy numbers (IVIFNs). To accomplish the multi-source uncertain inference in a fuzzy environment, this paper proposes the standard forms of Bayes formula under the intuitionistic fuzzy environment and the interval-valued intuitionistic fuzzy environment to solve grey models and decision-making problems with incomplete information. Firstly, we give some basic properties of IFN-probability and define its conditional probability based on the basic probability assignment of Dempster–Shafer theory. Subsequently, we also propose the independence of events, multiplication rule for the conditional probability of IFNs, and the law of total probability and the Bayes formula of IFNs. Due to the complexity and uncertainty of objective things, the indeterminacy degrees are often difficult to be expressed with crisp numbers. To address the challenge, interval values are used to describe the indeterminacy degrees instead of crisp numbers. Secondly, we give some basic properties of IVIFN-probability and define its conditional probability based on the IFN-probability theory. Afterward, we further propose the independence of events, multiplication rule for the conditional probability of IVIFNs, and the law of total probability and the Bayes formula of IVIFNs. From the angle of modeling and complexity, our approaches are more convenient and feasible than the interval probability method. Meanwhile, the practical applications show the feasibility of the proposed methods.

Fuzzy preference relation (FPR) is commonly used in solving multi-criteria decision making problems because of its efficiency in representing people’s perceptions. However, the FPR suffers from an intrinsic limitation of consistency in decision making. In this regard, many researchers proposed the consistent fuzzy preference relation (CFPR) as a decision-making approach. Nevertheless, most CFPR methods involve a traditional aggregation process which does not identify the interrelationship between the criteria of decision problems. In addition, the information provided by individual experts is indeed related to that provided by other experts. Therefore, the interrelationship of information on criteria should be dealt with. Based on this motivation, we propose a modified approach of CFPR with Geometric Bonferroni Mean (GBM) operator. The proposed method introduces the GBM as an operator to aggregate information. The proposed method is applied to a case study of assessing the quality of life among the population in Setiu Wetlands. It is shown that the best option derived by the proposed method is consistent with that obtained from the other methods, despite the difference in aggregation operators.

Fuzzy linguistic approach is considered as an effective solution to accommodate uncertainties in qualitative decision making. In the face of increasingly complicated environment, we usually face the fact that multi-attribute group decision making contains nested information, and the whole process needs to be evaluated twice so that the experts can make full use of decision information to get more accurate result, and we call this kind of problem as two-stage multi-attribute group decision making (TSMAGDM). However, the existing linguistic approaches cannot represent such nested evaluation information to deal with the above situation. In this paper, a novel linguistic expression tool called nested probabilistic-numerical linguistic term set (NPNLTS) which considers both quantitative and qualitative information, is proposed to handle TSMAGDM. Based on which, some basic operational laws and aggregation operators are put forward. Then, an aggregation method and an extended TOPSIS method are developed respectively in TSMAGDM with NPNLTSs. Finally, an application case about strategy initiatives of HBIS GROUP on Supply-side Structural Reform is presented, and some analyses and comparisons are provided to validate the proposed methods.

Hesitant fuzzy linguistic term set (HFLTS), as a flexible tool to represent people’s uncertain cognition, has attracted lots of scholars’ research interests, and a series of methodologies have been proposed to deal with a variety of decision-making problems. In this paper, we develop a hesitant fuzzy linguistic possibility degree-based linear assignment (HFL-PDLA) method to tackle the multiple criteria decision-making (MCDM) problems under hesitant fuzzy linguistic environment. Firstly, we define the possibility degree of hesitant fuzzy linguistic element (HFLE). Additionally, some relevant concepts related to the HFL-PDLA method are proposed, such as the relative difference matrix, the rank contribution matrix, the optimal permutation matrix, etc. Furthermore, the algorithm of the HFL-PDLA method is given to deal with hesitant fuzzy linguistic MCDM problems. Moreover, we apply the HFL-PDLA method to deal with a practical case which is to select the optimal treatment technology for disposing the outspent or old medical apparatuses and instruments in West China Hospital (WCH). Finally, we show the advantages of the HFL-PDLA method by making some comparative analyses with the TOPSIS method, the VIKOR method the PROMETHEE method and the LINMAP method.

The hesitant fuzzy linguistic term set (HFLTS) has been studied from different research directions. To describe the complicated linguistic information more accurately and reasonably, the double hierarchy linguistic term set (double hierarchy LTS) and double hierarchy hesitant fuzzy linguistic term set (double hierarchy HFLTS) were defined. Considering that the distance and similarity measures are the basis of decision making with double hierarchy hesitant fuzzy linguistic information, this paper proposes some distance and similarity measures of double hierarchy hesitant fuzzy linguistic elements (DHFLEs) and double hierarchy HFLTSs from different angles. We develop a decision-making method to deal with multiple criteria decision making (MCDM) problems on the basis of these distance and similarity measures. Finally, we apply this method to deal with a practical MCDM problem about Sichuan liquor brand assessment.

Multiple experts decision-making (MEDM) can be regarded as a situation where a group of experts are invited to provide their opinions by evaluating the given alternatives, and then select the optimal alternative(s). As a useful linguistic expression model, linguistic preference orderings (LPOs) were established in which the order of alternatives and the relationships between two adjacent alternatives are fused well. Considering that prospect theory has the superiority in depicting risk attitudes (risk seeking for losses and risk aversion for gains) during the uncertain decision-making process, this paper develops a consensus model based on prospect theory to deal with MEDM problems with LPOs. Firstly, each LPO provided by expert is transformed into the responding DHLPR with complete consistency. Then, the reference point of expert is determined and the prospect preference matrix is established. Moreover, we can obtain the overall prospect consensus degree for a MEDM problem by calculating the similarity degree between individual and collective prospect preference matrix. Furthermore, a consensus improvement method is developed to complete the consensus reaching process. Finally, we apply the proposed method to deal with a practical MEDM problem involving the construction project investment, and make some comparative analyses with existing methods., National Natural Science Foundation of China (NSFC) 71771155, China Postdoctoral Science Foundation 2020M680151, Sichuan Postdoctoral Science special Foundation, Sichuan University Postdoctoral Interdisciplinary Innovation Startup Foundation, Fundamental Research Funds for the Central Universities YJ202015, European Union (EU) TIN2016-75850-R, Sichuan Province System Science and Enterprise Development Research Center Xq20B03

In decision-making processes, preference relations are popular and powerful techniques for expert preference modeling (Urena et al. in Inf Sci 302:14–32, 2015). Consistency measures of preference relations are the vital basis of group decision-making (GDM) and have been studied extensively, which show that the supplied preferences satisfy some transitive properties (Wu and Xu in Omega 65(3):28–40, 2016). Consistency measures mainly consist of two parts: (1) judging whether each preference relation is of acceptable consistency; (2) improving the preference relation with unacceptable consistency. Based on double hierarchy hesitant fuzzy linguistic preference information, Gou et al. (Inf Sci 489:93–112 2019), Gou et al. (Int J Strateg Prop Manag 42(1):1–23, 2020) discussed the additive consistency measures and multiplicative consistency measures for DHHFLPRs, respectively. In this chapter, we will deeply discuss these two consistency measures for DHHFLPRs.

In decision-making processes, measure methods, such as distance and similarity measures, correlation measure, entropy and cross entropy measure, etc., play an important role in many research fields including decision-making (Liao et al. 2015b; Xu and Wang 2011; Xu and Xia 2011), pattern recognition (Arevalillo-Herraez et al. 2013; Li et al. 1993), intelligent computing (Chen et al. 2010), recommended system (Liao et al. 2014), distance learning techniques (Gao et al. 2017), electricity markets (Gao et al. 2018), and ontological sparse vector learning (Gao et al. 2015), etc.

Recently, Artificial Intelligence (AI) has become more and more popular and important in real life and consists of many research fields such as language recognition, image recognition, natural language processing and expert systems.

In GDM processes, after ensuring that all DHHFLPRs are of acceptable consistencies, we cannot overlook another important step: the consensus reaching process, which is an essential process in GDM for enabling sufficient communications among all experts and obtaining an accepted decision result. Therefore, in this chapter, we will first focus on developing methods to manage the consensus reaching process and ensure that all experts reach consensus.

With the rapid development of society and continual progress of science and technology, large-scale group decision-making (LSGDM) problems are very commonly encountered in real-life situations. Considering that the information required for decision-making and people’s cognition processes is becoming more and more complex, double hierarchy linguistic preference relation (DHLPR) can be used to express complex linguistic information reasonably and intuitively. Sometimes experts in LSGDM unwillingly modify their preferences or even modify them on purpose in a contrary way to the other experts. Thus, differing opinions or minority preferences are often referred to as obstacles to decision-making. This article develops a consensus model to manage minority opinions and noncooperative behaviors in LSGDM with DHLPRs. In addition, to establish the consensus model, some basic tools, such as the clustering method, weights-determining method, and adjustment coefficients-determining method, are developed. Finally, a practical LSGDM problem is set up to prove that the proposed consensus model is feasible and effective, and some comparative analyses are made to highlight the advantages of these methods and models, as well as to analyze current deficiencies.

In multiple attribute group decision making (MAGDM) processes, decision makers often use hesitant fuzzy linguistic term sets (HFLTSs) to express their opinions. However, it is incapable of representing the importance degrees or weights of different linguistic terms. The probabilistic linguistic term set (PLTS) gives each linguistic term a probability to denote their importance degree, and thus is more suitable for group decision making problems where the distribution information is available. In this paper, the PLTSs are utilized to express the experts’ assessments on each alternative with respect to each attribute in the MAGDM problem. Additionally, we establish two optimization models to derive the attribute weights. Then we propose a projection model to calculate the alternatives’ projections on both the positive and negative ideal solutions. A practical decision making problem about crossover development is given to validate the effectiveness of the projection method with PLTS information. Finally, we make some comparisons between the projection method and other existing methods, meanwhile, the advantages and limitations of the projection model are summarized.

Large-scale group decision making (LSGDM) or complex group decision making (GDM) problems are very commonly encountered in actual life, especially in the era of data. At present, double hierarchy hesitant fuzzy linguistic term set is a reasonable linguistic expression when describing some complex linguistic preference information. In this paper, we develop a consensus reaching process for LSGDM with double hierarchy hesitant fuzzy linguistic preference relations. To ensure the implementation of consensus reaching process, we also propose the similarity degree-based clustering method, the double hierarchy information entropy-based weights-determining method and the consensus measures. Finally, we apply our model to deal with a practical problem that is to evaluate Sichuan water resource management and make some comparisons with the existing approaches.

Service improvement is of great importance for hotels to gain advantages. Several studies determined the prioritization of service improvement by identifying the relationship between service performance and customer satisfaction but ignored the impact of consumer expectations and managers' subjective opinions. This paper provides an online reviews-driven method for hoteliers to determine the prioritization of improvements in hotel services. Firstly, the improved penalty–reward contrast analysis that quantifies the sentiment tendencies and intensities in online reviews is used to identify types of service attributes. Secondly, based on the categorization of attribute types, three types of consumer expectations that affect consumer satisfaction are mined. Thirdly, the improved three-way decision model is used to determine the priority of allocation resources combining with managers’ subjective opinions. Finally, the proposed method is applied to the case study of Four Seasons Hotel service improvement, and the advantages of this method are illustrated by comparative analysis.