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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.

AbstractWith 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.

AbstractMultiple 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.

AbstractNatural 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.

The hesitant fuzzy linguistic term set (HFLTS) turns out to be useful in representing people's hesitant qualitative information. The aim of this paper is to investigate new correlation measures between HFLTSs and apply them in decision-making process. Firstly, the concepts of mean and hesitancy degree of hesitant fuzzy linguistic elements are introduced. Based on them, we address the drawbacks of the existing correlation measures between HFLTSs. Then, a new correlation coefficient between HFLTSs is established. Additionally, the hesitancy degree of the hesitant fuzzy linguistic correlation coefficient is proposed, which is composed by the upper and lower bounds of the hesitant fuzzy linguistic correlation coefficient. To show the applicability of the proposed correlation measures, a correlation coefficient-based method is developed for multiple criteria decision making in the cases that the weights of criteria are either known or unknown. A practical example concerning the strategic management of Sichuan liquor brands in China is given to validate the proposed method. It is verified that the proposed correlation coefficients between HFLTSs is more convincing than the existing ones and the developed correlation coefficient-based hesitant fuzzy linguistic MCDM with the weights of criteria being either completely known or unknown is applicable. [ABSTRACT FROM AUTHOR]

AbstractFund 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.

AbstractThe 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.

Nested probabilistic-numerical linguistic term sets (NPNLTSs), which can be used to express two layers of evaluation information from qualitative and quantitative views, increase the flexibility of representing the nested uncertain information. In order to enhance and extend the applicability of the NPNLTSs, in this paper, we mainly investigate and develop some different types of distance and similarity measures for NPNLTSs. Firstly, a family of distance and similarity measures between two NPNLTSs with their properties and proofs are proposed. Then, we further establish a variety of weighted distance and similarity measures between two collections of NPNLTSs in discrete case, continuous case and ordered weighted case, respectively. Based on that, an approach based on the proposed measures is put forward to deal with multi-attribute decision-making problems. After that, a practical application concerning the evaluation of medical treatment is given to illustrate the usability and effectiveness of the proposed approach. Finally, some comparisons and analyses are provided from three angles including the impact of using various decision-making methods, various distance and similarity measures and the changed focal parameters.

• We define double hierarchy hesitant fuzzy linguistic preference relation (DHHFLPR). • A novel method is developed to calculate the consistency thresholds. • Two consistency repairing algorithms is proposed to improve the DHHFLPR. • A method is set up to deal with GDM problems with DHHFLPRs. • The proposed method is validated by a practical group decision making problem. Group decision making, refers to inviting a group of decision makers to evaluate, prioritize or select the optimal one among some available alternatives in the actual decision making process. Considering that the double hierarchy hesitant fuzzy linguistic term set can describe natural languages clearly, in this paper, we define the concept of double hierarchy hesitant fuzzy linguistic preference relation (DHHFLPR) and propose some additive consistency measures. To judge whether a DHHFLPR is of acceptable consistency or not, we introduce a consistency index, and develop some novel threshold values for judging whether a DHHFLPR is of acceptable consistency or not. Furthermore, we develop two consistency repairing algorithms based on the automatic improving method and the feedback improving method respectively, to improve the DHHFLPR with unacceptable consistency. Additionally, a method is set up to deal with group decision making problems with double hierarchy hesitant fuzzy linguistic preference information. Finally, the proposed method is validated by a case study that is used to evaluate the water resource situations of some important cities in Sichuan Province, and some comparative analyses are given to show the efficiency of the proposed method. [ABSTRACT FROM AUTHOR]

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.

Hesitant fuzzy linguistic term set (HFLTS) is a useful tool for describing people's subjective cognitions in the process of decision making. Multiple criteria decision making (MCDM) involves two important steps: (1) determining the criteria weights; (2) obtaining a suitable ranking of alternatives. In this paper, we propose some hesitant fuzzy linguistic entropy and cross-entropy measures, and then establish a model for determining the criteria weights, which considers both the individual effect of each hesitant fuzzy linguistic element (HFLE) and the interactive effect between any two HFLEs with respect to each criterion. Additionally, we give a hesitant fuzzy linguistic alternative queuing method (HFL-AQM) to deal with the MCDM problems. The directed graph and the precedence relationship matrix make the calculation processes and the final results much more intuitive. Finally, a case study concerning the tertiary hospital management is made to verify the weight-determining method and the HFL-AQM. [ABSTRACT FROM AUTHOR]

Interval-valued intuitionistic fuzzy set, generalized by Atanassov and Gargov, can be used to characterize the uncertain information more sufficiently and accurately when we face the fact that the values of the membership function and the non-membership function in an intuitionistic fuzzy set are difficult to be expressed as exact real numbers in many real-world decision-making problems. In this paper, we provide an overview of interval-valued intuitionistic fuzzy information aggregation techniques, and their applications in various fields such as decision-making, entropy measure, supplier selection and some practical decision-making problems. Meanwhile, we also review some important methods for decision-making with interval-valued intuitionistic fuzzy information, including the QUALIFLEX-based method, the TOPSIS method, the extended VIKOR method, the module partition schemes evaluation (MPSE) approach, the outranking choice method, the inclusion-based LINMAP method and the risk attitudinal ranking method, the evidential reasoning methodology, etc. Finally, we point out some possible directions for future research.

In the process of decision making, people sometimes may feel more comfortable to express their preferences by linguistic terms instead of the quantitative form. However, as the basic premise of operations, the existing operational laws of linguistic terms and the extended linguistic term sets are very unreasonable. In order to overcome this issue, in this paper, we redefine some more logical operational laws for linguistic terms, hesitant fuzzy linguistic elements (HFLEs) and probabilistic linguistic term sets (PLTSs) based on two equivalent transformation functions. These novel operational laws can not only avoid the operation values exceeding the bounds of LTSs, but also keep the operation results more reasonable in decision making with linguistic information. Furthermore, the operational laws can keep the probability information complete when computing with PLTSs. Additionally, lots of properties of the operational laws are discussed, and some three-dimensional figures are drawn to show the regions of different operational laws of linguistic terms more vividly. [ABSTRACT FROM AUTHOR]

Multiple criteria decision making (MCDM), concerning the selection of the most optimal alternative(s), is an essential activity in various fields of management science. In many practical MCDM problems, it is common that there are different types of fuzzy evaluation information as well as ranking information on candidate alternatives with respect to different criteria. In this paper, we propose an alternative queuing method (AQM) to deal with this kind of hybrid fuzzy MCDM problems. Firstly, we develop an algorithm of the AQM to solve the hybrid fuzzy MCDM problems in which the criteria weights are completely known. Secondly, we propose a satisfaction degree based method to derive the criteria weights for the hybrid fuzzy MCDM problems in which the weight information is partly known, and then use the developed algorithm to further solve this kind of problems. Thirdly, we propose a least square method to derive the criteria weights for the hybrid fuzzy MCDM problems in which the weight information is completely unknown. Finally, we apply the AQM to select the optimal treatment technology for disposing the outspent or old medical apparatuses and instruments in West China Hospital. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

This paper aspires to explore and construct a more objective and automated large-scale group decision-making (LSGDM) model. The concept of vacillation degree based on probabilistic double hierarchy linguistic term set is proposed to describe the characteristics of decision makers (DMs). The criteria weights are obtained by entropy measure, and then a clustering method is constructed. Moreover, the autonomous learning probability is presented to characterize the extent to which DMs accept the opinions of others. The complex connections between DMs can be more clearly described by visualizing the autonomous learning. Considering the deficiencies of the existing feedback adjustment mechanism on the setting of the suggested adjustment range, the autonomous learning and opinions-updating process for internal and external subgroups are designed. Then consensus judgment method is also proposed from subgroups and group. Based on the above work, an opinions-updating model for LSGDM driven by autonomous learning is constructed. The validity of the model is verified by a case study of emergency medical service agency selection. Finally, three simulation models and comparative analysis are established to test the opinions-updating model. [ABSTRACT FROM AUTHOR]

• A novel definition of concentration degree for probabilistic linguistic term sets. • A novel score function for probabilistic linguistic term sets. • Two decision-making methods are proposed for probabilistic linguistic term sets. • The effectiveness and robustness of decision-making methods are tested. 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. [ABSTRACT FROM AUTHOR]