Linguistic Group Decision Research Articles

On consensus reaching process based on social network analysis in uncertain linguistic group decision making: Exploring limited trust propagation and preference modification attitudes

This paper explores a limited trust propagation-based consensus model considering individual attitude for preference modification in a social networked setting with uncertain preference information. To examine the construction of complete linkages, and the status of decision makers in group decision making, it is assumed that the group size and network density will affect the scale of mediators in the propagation process, then a definition of limited trust propagation is proposed and the propagation efficiency can be introduced. On this basis, we obtain missing trust relationships and individual centrality in network. In the process of consensus reaching, both the decision maker’s original preference and recommendation advice are considered for flexibly modeling the preference modification process: the individual attitude toward modification is determined by a newly introduced measure of comprehensive relative out-degree centrality, showing the degree of willingness to adjust assessments. When the willingness is too low to reach the preset consensus level, a multi-objective programming model is designed to improve the consensus as much as possible. Moreover, the proposed feedback mechanism narrows the individual acceptable modification range based on the previous adjustment rule, so as to simulate the personalized and targeted decision behavior. To guarantee obtaining a collective aggregated preference in a logical and precise manner, a two-stage optimization model composing of comprehensive relative in-degree centrality-based information aggregation and best consistency-based uncertainty elimination, is proposed. A numerical example and comparative analyses are performed to show the validity and feasibility of the proposed model.

Probabilistic Linguistic Group Decision-Making Method Based on Attribute Decision and Multiplicative Preference Relations

Probabilistic Linguistic Group Decision-Making Method Based on Attribute Decision and Multiplicative Preference Relations

Correction to: Generalized interval-valued picture fuzzy linguistic induced hybrid operator and TOPSIS method for linguistic group decision-making

A correction to this paper has been published: https://doi.org/10.1007/s00500-021-05720-6

Generalized interval-valued picture fuzzy linguistic induced hybrid operator and TOPSIS method for linguistic group decision-making

Generalized interval-valued picture fuzzy linguistic induced hybrid operator and TOPSIS method for linguistic group decision-making

Consistency and trust relationship-driven social network group decision-making method with probabilistic linguistic information

Unlike other linguistic modelings, probabilistic linguistic terms can clearly describe the importance of different linguistic terms. With respect to group decision-making (GDM) problems, it is convenient for experts to express their evaluation opinions with probabilistic linguistic preference relations (PLPRs), which can transform experts’ quantitative descriptions into qualitative probabilistic linguistic terms. The processes of consistency-adjustment and expert weights determination play a key role in GDM. Therefore, this paper aims at the design of a novel probabilistic linguistic GDM method with consistency-adjustment algorithm and trust relationship-driven expert weight determination model. First, we redefine the multiplicative consistency of PLPRs, which only involves changing the probabilities of linguistic terms. A new distance between PLPRs is presented to calculate the consistency index. Then, we propose a convergent consistency-adjustment algorithm to improve the consistency of a PLPR to an acceptable consistency level. Subsequently, a trust relationship-driven expert weight determination model is developed to derive the experts’ weights in a social network environment. Finally, a probabilistic linguistic GDM method is designed to determine the reliable ranking of alternatives. The advantages and applicability of the proposed method are illustrated by a case study concerning an evaluation of logistics service suppliers and associated comparative analyses.

Using Vector Random Linguistic Variables to Manage Consistency and Consensus in Linguistic Group Decision-Making for Public Project

With the development of political democratization, linguistic group decision-making for public project (LGDMPP) is playing more and more important role in the modern social activities. This paper introduces the fuzzy preference relation based on vector random linguistic variables (VRLVs-FPR) to improve the accuracy and flexibility of linguistic preference relation (LPR) in managing LGDMPP. First, an intact linguistic evaluation scale (ILES) is presented to directly describe the decision-maker’s personalized consciousness. Based on this, for depicting different kinds of hesitance in decision-makers’ expressions, we put forward the vector random linguistic variable (VRLV) and apply it into the pairwise comparisons of alternatives in order to get the VRLVs-FPR. Furthermore, a consistency improving method is given to manage the consistency of VRLVs-FPR and a consensus improving method is given to manage the consensus process of LGDMPP. Finally, a LGDMPP example of government’s investment project selection illustrates the use of new methods proposed in this paper, where the in-depth comparison and discussion verify the effectiveness of them.

Improving Hospital Based Medical Procurement Decisions with Health Technology Assessment and Multi-Criteria Decision Analysis.

This research proposes a new medical procurement decision-making tool named Evaluation of Medical Technology Procurement (EMTP), which combines Mini-health Technology Assessment (Mini HTA) with the analytic hierarchy process (AHP), as well as the intuitionistic linguistic multi-criteria group decision model for multi-criteria decision analysis (MCDA). This tool was applied to a medical device procurement decision in a large provincial general hospital with more than 5000 beds in China as a case study. Specifically, the AHP evaluation framework is first established to determine the evaluation dimensions and criteria. This goal is achieved by applying the AdHopHTA Mini-HTA template and gathering data from questionnaires completed by experts from 33 major public hospitals in Anhui Province, China. The professionals within the application hospital were invited to evaluate the alternative products in a pairwise comparison and obtain a ranking of their advantages and disadvantages. This goal is achieved using the intuitionistic linguistic fuzzy model to deal with the subjectivity and uncertainty that may be present in the professional evaluation by experts in different fields. At the same time, the Keeney-Raiffa MCDA (KRM) method was used to demonstrate the accuracy of the application results. The results show that our tool can achieve the same effect as the verification method while being more efficient, easier to use, and requiring fewer participants. The advantages and disadvantages of several evaluation methods combined with multi-criteria methods are discussed, including verification methods, pointing out the advantages and limitations of this research tool as well as the prospects for the future.

A novel process to determine consensus thresholds and its application in probabilistic linguistic group decision-making

When solving group decision-making (GDM) problems, the proper values of consensus thresholds are vital for consensus checking and improving. Decision makers are usually not confident to select a proper threshold. In the linguistic setting, this paper presents a new process to support the determination of consensus thresholds. A new concept, namely random consensus index, is presented to serve as a reference object so that the risk preference of a decision maker could be induced by comparing the quality of the information in hands with the averaging quality of randomly generated information. In this sense, admissible consensus thresholds could be determined automatically, and decision makers are not necessary to focus on the detail of consensus measures. Furthermore, the process is applied to the GDM problems with probabilistic linguistic preference relations, and a new GDM approach is presented. Different from the existing contributions, the consensus is measured by the probability of a set of preference relations being with acceptable consensus, and then the consensus is improved by revising the involved probability distributions. All the involved parameters are intuitive and interpretable. A case study, regarding the departure audit in China, demonstrates that the proposed GDM approach is effective even if the original preferences of experts are with low consistency and consensus.

Integrating Continual Personalized Individual Semantics Learning in Consensus Reaching in Linguistic Group Decision Making

In computing with words, it has been stressed that words mean different things for different people, which entails that decision makers (DMs) have personalized individual semantics (PISs) attached to linguistic expressions in linguistic group decision making (GDM). In particular, the PISs of DMs are not fixed, and they will be changing during the consensus building process, which indicates the necessary of continual PIS learning. Therefore, in this article, we propose a continual PIS-learning-based consensus approach in linguistic GDM. Specifically, a continual PIS learning model with the consistency-driven methodology is proposed to update the PISs taking into account all the linguistic preference data given by DMs during the consensus process. Then, the consensus measurement and feedback recommendation based on PIS are developed to detect the consensus process. Finally, numerical examples and simulation analysis are presented to illustrate and justify the use of the continual PIS-learning-based consensus approach.

A consensus model for hesitant fuzzy linguistic group decision-making in the framework of Dempster–Shafer evidence theory

In group decision-making (GDM), a consensus building process (CRP) is necessary to improve the level of consensus within the group. This paper develops a new CRP model for GDM problems with hesitant fuzzy linguistic term sets (HFLTSs), which also considers the reliability of experts. Firstly, we present the calculation of expert reliability by measuring the hesitancy degree and similarity degree, simultaneously. Next, we propose an approach to generate group opinions based on the reliability of experts within the framework of the Dempster–Shafer evidence theory (DSET). In this way, the original individual opinions can be retained well and the discourse power of experts with higher reliability but lower weights can be strengthened. Further, the reliability is introduced to build a new feedback mechanism that provides experts with explicit advice during the consensus reaching process. Subsequently, a new CRP algorithm for hesitant fuzzy linguistic GDM (HFLGDM) problems is proposed to help the group achieve consensus. A practical case study is utilized to illustrate the application of the proposed algorithm. Finally, we conduct a comparison experiment to verify the advantages of the proposed CRP algorithm.

A linguistic distribution behavioral multi-criteria group decision making model integrating extended generalized TODIM and quantum decision theory

In most existing multi-criteria group decision making (MCGDM) problems, the decision makers (DMs) are usually regarded as independent and DMs’ psychological behaviors are rarely considered. However, in many cases, the opinions of DMs are likely to influence each other and the DMs often hold subjective bounded rationality in the decision making process. To address this issue, a linguistic distribution behavioral MCGDM model integrating extended generalized TODIM (an acronym in Portuguese of interactive and multi-criteria decision making) method and quantum decision theory is developed. First, linguistic distribution assessments considering the sample size information are used to gather the group linguistic evaluations, which can integrally depict the quantitative distribution and qualitative vagueness. Second, an extended generalized linguistic distribution TODIM method is presented to reflect the DMs’ bounded rational behaviors. It is used to calculate the dominance of each alternative. Third, a quantum possibilistic aggregation framework is constructed to explore the interference effects among DMs’ opinions. In this process, DMs’ opinions are viewed as synchronously occurred wave functions that interfere with each other and influence the aggregated result. Finally, a case study is examined to recommend the optimal automobile for customers based on distributed online reviews in newcar.xcar.com and autohome.com. Three separate scenarios with conjunctive, neural, and disjunctive modes are considered respectively. The sensitivity analysis is given to show the effect of risk factors and interference factors. The parameters show to be dominant in the final best automobile recommendation. The comparisons with some existing methods confirm the validity and stability of the proposed MCGDM method.

A Revised Picture Fuzzy Linguistic Aggregation Operator and Its Application to Group Decision-Making

The complexity of decision environments poses challenges for individuals engaged in decision-making proceedings. Picture fuzzy linguistic sets (PFLSs) are an effective tool for depicting the inherent subjective nature of human cognition. Aiming for the promotion of a general theory on PFLSs, we conduct a critical research to identify some limitations of a recent publication in Cognitive Computation [2018, 10(2), 242–259]. This published article is a meaningful and interesting study that initiates the PFLS as well as introduces the corresponding operations and the Archimedean picture fuzzy linguistic weighted arithmetic averaging operator. Unfortunately, we have carefully analyzed these operations and found that they may not be appropriate to all situations within picture fuzzy linguistic environment, which would result in the violation of human cognition. To eliminate this limitation, we explore and suggest novel operational laws and an aggregation operator for PFLSs from a modified version, so as to support further study on picture fuzzy linguistic group decision-making. Furthermore, a comparative and illustrative example is presented to validate the advantages of our modified operations. Towardly , the research outcome will be of significant benefit to promoting the development of picture fuzzy linguistic decision-making theory. Accordingly, our contribution to improving the current research on PFLSs makes their application in solving realistic problems feasible and practical.

Identifying and prioritizing factors affecting in-cabin passenger comfort on high-speed rail in China: A fuzzy-based linguistic approach

Factors affecting customer comfort are crucial for the success of many services such as public transportation, health facilities, and so on. Therefore, the identification and prioritization of such factors is an important demand from stakeholders. This research aims to identify and prioritize the factors that affect in-cabin passenger comfort on high-speed rail (HSR) based on empirical evidence collected from China. For the identification process, the quality-management tool known as quality function deployment (QFD) to capture the voice of the customer is used to discover the most important demands as the driving influencing factors of in-cabin passenger comfort, by utilizing passengers’ feedback regarding their experiences with HSR posted in social media. Such factors will be prioritized by a fuzzy linguistic group decision-making approach based on the adoption of generalized comparative linguistic expressions obtained from a questionnaire investigation on randomly selected HSR passengers, and accomplishing a decision-solving procedure that includes consistency-checking and consensus-reaching processes to achieve an effective, reliable, and agreed prioritization of the factors. The research outputs will suggest the factors of greatest concern among all HSR passenger demands. This study gives HSR operators and designers not only insights and tools for managing HSR passenger demands but also advice for refining the design and service quality of HSR in China.

A Probabilistic Linguistic Group Decision-Making Method From a Reliability Perspective Based on Evidential Reasoning

A probabilistic linguistic multiattribute group decision-making (PLMAGDM) problem is studied from a reliability perspective based on an evidential reasoning approach and linguistic granulation optimization. As decision-making reliability, indicating the validity and accuracy, greatly depends on the reliabilities of both group similarity and the degree of familiarity, it is helpful to study a decision-making problem from the perspective of information reliability. To this end, a PLMAGDM method which considers reliability is put forward in this paper. First, two sets of information (i.e., probabilistic linguistic terms on alternative grades, and linguistic terms on familiarity) are given by experts as measures of expert reliability and attribute reliability. A granulation optimization model is then constructed to generate the utility of grades while maximizing group similarity, and a model that redistributes the probabilities of grades is established for the situation of incomplete information. We further provide another granulation optimization model to generate the degree of familiarity. Additionally, using the evidential reasoning rule, the aggregated weights of experts are obtained employing an optimization method that is used to retrieve attribute information. Lastly, through the method comparison in two cases as well as the sensitivity analysis, the validity and applicability of the method are verified.

Linguistic group decision making: Axiomatic distance and minimum cost consensus

The axiomatic distance-based method is a powerful tool to aggregate individual preferences, and the extant axiomatic distance-based aggregation methods are with regard to individual numerical preferences. However, in some real-world decision problems with qualitative aspects, it is more convenient and natural for individuals to express their preferences through linguistic terms rather than through numerical values. Therefore, in this paper, we propose axiomatic distance in the linguistic context based on ordered linguistic term sets to aggregate individual linguistic preferences. Specifically, we provide some natural axioms on the distance measure among linguistic preferences. We then prove that there exists a unique distance function that satisfies all the proposed axioms. Based on the axiomatic distance function, we aggregate individual linguistic preferences into the group linguistic preference, which minimizes the total distance among individual linguistic preferences. Furthermore, we present a novel consensus measure based on the unique axiomatic distance and develop a minimum cost consensus model to obtain the optimal adjusted linguistic preference, which serves as a reference for the moderator to persuade individuals to modify their linguistic preferences.

A consensus reaching process with quantum subjective adjustment in linguistic group decision making

The consensus reaching process (CRP) is essential to obtain a final solution in group decision making (GDM). This paper focuses on constructing a consensus mechanism where decision makers (DMs) use linguistic term sets (LTSs) to express their preferences. LTSs can describe real decision making well. Adjusting opinions can improve the consensus level, we assume that the adjusted opinion combines an initial preference and a referenced preference. The subjective behavior characteristics expressed by DMs would affect the CRP. To simulate human behavior, quantum probability theory is applied to aggregate referenced opinions, reflecting the interference effect caused by subjective beliefs flowing toward decision classification paths. The paths are composed of the clusters with the highest consensus and consistency degrees. Moreover, the combination is generated based on the subjective willingness defined by the consensus position of the recognized DM in the group. An optimization model is set to control individual consistency after implementing modifications. Finally, a numerical example illustrates the principle of the constructed model.

Managing individual evaluator’s personalized semantic environment of linguistic term with improved vector expression in multi-granularity linguistic group decision making

Group linguistic assessment with the vector symbolic of linguistic evaluation information has been recently proposed for qualitative group decision making. Due to various individualized characteristics and knowledge levels, evaluators in group assessment often provide linguistic terms based on different individual linguistic evaluation scales to express their preferences on alternatives. In some situations, decision maker needs to distinguish different meanings of the same linguistic term in different individual evaluators’ understandings. To further develop the resolution and the operational performance of the vector expression of linguistic term in multi-granularity linguistic group decision making (MGLGDM), in this study, we present the concept of improved vector expression of linguistic term. First, we present a method of rewriting the numerical symbolic of linguistic term into the improved vector expression based on the individual linguistic evaluation scale. Based on this, we introduce an approach to compare individual linguistic evaluation scales in MGLGDM. Then, an algorithm with improved vector expression is proposed for ranking alternatives in MGLGDM. Finally, a case illustration and some comparative studies have shown that the new proposed algorithm with improved vector expression of linguistic term is accurate and efficient in distinguishing and computing linguistic evaluation information in MGLGDM.

Attitude quantifier based possibility distribution generation method for hesitant fuzzy linguistic group decision making

The possibility distribution-based approach is one of the powerful tools available to manage hesitant fuzzy linguistic term set (HFLTS) information. However, existing possibility distribution studies have not considered the experts’ satisfied preference for HFLTSs in the process of generating the possibility distribution. This paper aims at filling this research gap. To achieve this goal, a novel possibility distribution generation method based on the concept of linguistic quantifier is proposed. This is accomplished by defining a new attitude linguistic quantifier, which is supported with theoretical results to analyze the relationship between the proposed attitude linguistic quantifier with the original linguistic quantifier, attitude indices and the expected linguistic term. The new possibility distribution generation method is proved to be (1) more general than the two main existing approaches, which are particular cases for specific linguistic quantifiers; and (2) useful to implement the concept of soft majority in the resolution process of the decision making situation. Additionally, a new two stages feedback mechanism of attitude adjustment and assessment adjustment is devised to guarantee the convergence of the consensus reaching process. Finally, a framework of group decision making with HFLTSs information is presented and an illustrative example is conducted to verify the proposed method.

Generalized Shapley Choquet Integral Operator Based Method for Interactive Interval-Valued Hesitant Fuzzy Uncertain Linguistic Multi-Criteria Group Decision Making

This paper develops a new method based on generalized hybrid Shapley Choquet integral for interval-valued hesitant fuzzy uncertain linguistic multi-criteria group decision making (MCGDM), where interactive characteristics of criteria is taken into account. First, a score function and a new accuracy function are defined to rank the interval-valued hesitant fuzzy uncertain linguistic elements (IVHFULEs). Based on the Shapley Choquet integral, some generalized Shapley Choquet operator for IVHFULEs are proposed including an interval-valued hesitant fuzzy uncertain linguistic generalized Shapley Choquet (IVHFULGSC) operator and an interval-valued hesitant fuzzy uncertain linguistic generalized hybrid Shapley Choquet (IVHFULGHSC) operator and some attractive properties for these two operators are investigated in detail. Then a Shapley Choquet integral-based Minkowski distance between interval-valued hesitant fuzzy uncertain linguistic sets (IVHFULSs) is defined. Subsequently, based on the maximization deviation method, a linear programming model is built to determine the individual fuzzy measure on criteria set for each decision maker (DM). By utilizing the individual closeness coefficients matrices, a new multi-objective fractional programming model which maximizes the collective relative closeness degrees of all alternatives is constructed to obtain the fuzzy measure on DMs set. The individual decision matrices are aggregated into the collective one by using the IVHFULGHSC operator. To obtain the collective Shapely fuzzy measure on criteria set, a linear programming model is established by maximizing the deviation of the evaluations of different alternatives on each criterion. Then, the collective closeness coefficients of alternatives are calculated to rank the alternatives. Thus, a new method based on generalized hybrid Shapley Choquet integral operator is brought forward for MCGDM with IVHFULEs. Finally, an example of investment on shared bikes is provided to illustrate the applicability of the proposed method and a validity test is conducted to demonstrate the effectiveness of the proposed method.

An Entropy-Based Method for Probabilistic Linguistic Group Decision Making and its Application of Selecting Car Sharing Platforms

As the tourism and mobile internet develop, car sharing is becoming more and more popular. How to select an appropriate car sharing platform is an important issue to tourists. The car sharing platform selection can be regarded as a kind of multi-attribute group decision making (MAGDM) problems. The probabilistic linguistic term set (PLTS) is a powerful tool to express tourists’ evaluations in the car sharing platform selection. This paper develops a probabilistic linguistic group decision making method for selecting a suitable car sharing platform. First, two aggregation operators of PLTSs are proposed. Subsequently, a fuzzy entropy and a hesitancy entropy of a PLTS are developed to measure the fuzziness and hesitancy of a PLTS, respectively. Combining the fuzzy entropy and hesitancy entropy, a total entropy of a PLTS is generated. Furthermore, a cross entropy between PLTSs is proposed as well. Using the total entropy and cross entropy, DMs’ weights and attribute weights are determined, respectively. By defining preference functions with PLTSs, an improved PL-PROMETHEE approach is developed to rank alternatives. Thereby, a novel method is proposed for solving MAGDM with PLTSs. A car sharing platform selection is examined at length to show the application and superiority of the proposed method.