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The seamless integration of computerized methodologies into industrial engineering problem-solving is pivotal for optimizing efficiency. In the specific domain of multi-attribute group decision-making (MAGDM) with probabilistic linguistic term sets (PLTSs), these methodologies offer systematic approaches to consensus building, ensuring effective decision processes in intricate scenarios. Within the realm of PLTSs, the consensus-reaching process (CRP) for MAGDM is gaining prominence. This paper addresses this evolving area by proposing ordinal and cardinal CRPs within the framework of PLTSs, specifically incorporating the regret theory (RT) of three-way decisions (TWD). The paper introduces an initial distance formula under PLTSs, providing a complementary approach to assess similarity relations among decision-makers (DMs). To account for diverse semantics across DMs, personalized individual semantics (PIS) is integrated into the CRP, recognizing variations in DMs' alternatives and attributes. To enhance realism, the paper introduces the concepts of individual alternative sets and individual attribute sets. Additionally, the paper integrates ordinal and cardinal consensus, establishing a dynamic feedback adjustment mechanism grounded in the principles of RT and TWD. The method's reasonableness is validated through a real case study, and a comparative analysis with the existing methods underscores the superiority of the approach presented in this paper. • A new valid distance formula is proposed for probabilistic linguistic term sets. • Constructing a new utility maximization method to derive personalized individual semantics. • The individual attribute and alternative sets are proposed to construct group consensus. • A consensus methodology is designed to incorporate both ordinal and cardinal consensus. • Designing a feedback adjustment mechanism based on regret theory and three-way decision. [ABSTRACT FROM AUTHOR]

The metaverse, constructed through digital technology, serves as a virtual realm intertwining with reality. Within this context, the challenge of evaluating data from diverse sources arises, and the application of large-scale group decision-making (LSGDM) methods emerges as a viable solution. Handling incomplete information and reducing dimensionality for large-scale decision-makers (DMs) is crucial in addressing complex decision-making problems. Moreover, addressing missing data is a fundamental and pivotal concern in tackling real-world decision challenges, given the ubiquitous presence of information gaps that cannot be straightforwardly integrated into decision models. Besides, the intricacies of LSGDM amplify this challenge by introducing a wealth of DMs, thereby augmenting the complexity and diversity of decision-related information. This paper proposes an approach to supplement missing data by double-dimensions. This paper explores various facets of similarity relationships within the data to enhance data completeness. Additionally, this paper categorizes DMs into clusters based on their relevance and establishes a two-stage consensus-reaching process (CRP) that takes into account both group sizes and individual consensus contributions. These CRPs play a crucial role in enhancing the overall consistency and consensus within the decision group. Subsequently, this paper applies a robust decision-making method rooted in MULTIMOORA (Multi-Objective Optimization by Ratio Analysis plus the complete MULTIplicative form) to rank decision objects. Finally, this paper employs this proposed methodology in a practical case study that involves evaluating the operational status of a metaverse's urban construction metro system. Following these considerations, a comprehensive stability analysis of relevant parameters is conducted to guarantee the robustness and reliability of the decision-making process. • A similarity-based double-dimensional patching method for absent values is proposed. • A clustering-based dimensionality reduction for decision-makers is developed. • A two-stage consensus-reaching process based on weight adjustments is constructed. • A robust decision-making method based on MULTIMOORA and TODIM is explored. [ABSTRACT FROM AUTHOR]

The maximum expert consensus model (MECM) is a commonly used consensus model in group decision making (GDM). In traditional MECM, the consensus constraints are not fully considered and the adjustment cost of decision maker (DM) is certain. Moreover, directing the DM's opinion in a visual path is seldom considered in the consensus reaching process (CRP) of MECM. Inspired by these issues, this paper first proposed two MECMs with different types of consensus constraints. Then, this paper incorporated an adjustment path into MECM by using feedback coefficients that can prevent opinions from being overadjusted. Furthermore, the robust MECM (RMECM) is developed to address the uncertainty of unit adjustment cost under three uncertainty sets. Finally, the feasibility of the proposed models is verified by applying them to the allocation of special funds in the Chinese film industry, which is a large-scale group decision making (LSGDM) problem. The sensitivity analysis and comparative analysis are also conducted to show the efficiency of the proposed models. • Two MECMs with different constraints are proposed. • An explicit adjustment path is incorporated into the traditional MECM. • RMECMs are proposed to address the uncertainty in CRP under three uncertain scenarios. • The proposed models are applied to a specific LSGDM problem. [ABSTRACT FROM AUTHOR]

Density Peak Clustering (DPC) was proposed in the journal Science in 2014 and has been widely applied in many fields due to its simplicity and effectiveness. However, there are few studies on the effectiveness of DPC algorithm and its variants on non-clean data sets. Inspired by the idea that DPC algorithm combines density and distance when determining clustering center, this paper creatively designs a two-stage density clustering method with fuzzy connectivity (TS-DCM). It could be used to distinguish different cluster partitions and further identify noise points and sample points. In addition, this paper also introduces a new clustering index: fuzzy connectivity, which could not only adjust the selection of DPC cutoff distance, but also provide a reference for adaptive adjustment of TS-DCM parameter selection, greatly improving the operating efficiency of the clustering algorithm. At the same time, a self-adaptive two-stage density clustering method (STS-DCM) is proposed to adjust the selection of parameters according to the feedback of clustering results. Finally, compared with other traditional and popular clustering algorithms, it is verified that the proposed algorithm has significant advantages in speed and accuracy. Moreover, for non-clean data sets, the algorithm is robust and effective. • Propose fuzzy connectivity as an important index for density clustering; • A two-stage density clustering algorithm(TS-DCM) is proposed; • A novel STS-DCM algorithm to determine the parameter selection. [ABSTRACT FROM AUTHOR]

Three-way multi-attribute decision-making (3MADM) integrated with double hierarchy hesitant fuzzy linguistic term set (DHHFLTS) can not only effectively express the uncertainty of language, but also help reduce the risk of wrong decision-making. However, the existing compared methods for DHHFLTSs dismiss the variances in psychological reference points, resulting in mismatches in form and connotation for some linguistic terms. Furthermore, it is difficult or even impossible to obtain an accurate degree of difference using the existing DHHFLTS distance method for these linguistic terms. This directly affects the accuracy of obtaining conditional probabilities results in the three-way decision model. Therefore, this paper introduces the concept of the superior gradus for double hierarchy linguistic term set (DHLTS) and double hierarchy hesitant fuzzy linguistic element (DHHFLE), respectively. Then, some novel compared methods are defined that allow the identification of differences between linguistic variables. Subsequently, based on the superior gradus, a novel distance measurement is designed with a risk parameters. Through the adjustment of risk parameters, this method can respectively obtain optimistic and pessimistic results. Also, the relative loss functions designed for DHHFLTSs aim at getting more objective decision-making results. Finally, the paper proposes a novel 3MADM method under the double hierarchy hesitant fuzzy linguistic information system (DHHFLIS) and applies it to service assessment. To verify the effectiveness and rationality, the medical diagnosis data set is used, and the results are compared with other classic MAMD methods. • 3MADM with DHHFLTS reduces the risk of wrong decision-making. • Superior gradus is introduced to identify DHHFLTS's variances. • Novel distance measurement is designed with a risk parameters. • Relative loss functions for DHHFLTS enhance objective results. • Novel 3MADM method is applied in service assessment and compared with classic MAMD. [ABSTRACT FROM AUTHOR]

Increased demand for knowledge, evolving consumer attitudes, and the convenient online transaction opportunities provided by Internet technology have led to the rapid rise and growth of online knowledge payment. At present, studies on the online knowledge payment industry mainly focus on exploring the influencing factors of users' willingness to pay for online knowledge payment products (OKPPs), and there are fewer studies on the evaluation and rating methods of OKPPs. To address this problem, this paper proposes an improved group decision-making method based on consensus adjustment and prospect theory to realize the evaluation of OKPPs from the perspective of consumer experience value. The method uses interval-valued intuitionistic fuzzy numbers to process evaluation information, selects leading users (LUs) as decision makers, and identifies four evaluation criteria based on consumer experience value, which are functional value, self-fulfillment value, hedonic value, and emotional value. The proposed group decision-making method in this paper takes into account the consensus problem of LUs' opinions, proposes a consensus adjustment method, and uses prospect theory to incorporate the psychological factors of LUs into the group decision-making process. Finally, the effectiveness and advantages of the method proposed in this paper are verified using an example and a comparison with existing methods. This research will provide methodological reference for knowledge payment platforms (KPPs) to select high quality OKPPs, and will also urge knowledge producers (KPs) to create OKPPs that can bring higher experience value to knowledge consumers (KCs). At the same time, this research makes possible the co-creation of knowledge between KPs and KCs, and enriches and develops the relevant research on the online knowledge payment industry. • A novel group decision-making method based on prospect theory is proposed to evaluate online knowledge payment products. • Our consensus method avoids the omission of critical information and knowledge used for evaluation. • Our consensus adjustment method is superior to other alternative methods. [ABSTRACT FROM AUTHOR]

In multiple attribute group decision-making (MAGDM), a consensus exists that the psychological factors of decision makers (DMs) generally influence their choice of optimal alternatives. To quantify well the influence of DMs' risk attitudes on the group decision-making process, this paper develops a new approach to MAGDM by introducing DMs' utility functions into the aggregation process. First, the ordered weighted utility distance (OWUD) operator is constructed by introducing DMs' utility functions into the distance operator. As a novel operator, the OWUD operator not only satisfies both the basic features of distance measures and the desirable properties of aggregation operators, but also has some unique characteristics. Then, the linear risk tolerance (LRT) utility function is further used in the OWUD operator as the basic utility function, and a specific form of the OWUD operator, which is named as the ordered weighted-linear risk tolerance utility distance (OW-LRTUD) operator, is proposed. The OW-LRTUD operator can quantify well the influence of DMs' risk attitudes on the group decision-making process. It also has an analytically tractable form and includes many well-known distance measures and aggregation operators, and thus can be applied to many different kinds of decision-making problems. Subsequently, to determine the weights of the OW-LRTUD operator, an extension of the maximum Bayesian entropy method is proposed by incorporating the prior known weight information and different risk attitudes of all individual DMs. An approach to MAGDM based on the OW-LRTUD operator and the proposed weight determination method is developed. An application for determining the optimal alternative in the investment selection is provided to show the feasibility, effectiveness and robustness of our approach in practice, and the corresponding sensitive analysis illustrates the influence of DMs' risk attitudes on the group decision-making process. • This paper develops a class of distance operators, named as the ordered weighted utility distance operators, which can quantify the influence of DM's risk attitudes or the satisfaction degrees on the group decision-making process. • New weighting models for both attributes and DMs are provided respectively by combining the prior known weight information and subjective considerations of all individual DMs. • It is shown that the Arrow-Pratt measure of absolute/relative risk aversions of DMs significantly impact the optimal option of alternatives by numerical experiments and sensitivity analysis. [ABSTRACT FROM AUTHOR]

In Multi-Criteria Group Decision-Making (MCGDM), linguistic evaluation is widely used due to its flexibility. In particular, Personalized Individual Semantics (PIS), namely decision-makers hold heterogeneous understandings of the same word, has been extensively studied to elicit numeric meaning to the linguistic scale. However, few studies consider the need to tailor linguistics to the different indicators used, as well as the semantic difference in the same level linguistic that experts use when situations change. The traditional PIS models overlook the psychological aspect of the decision makers. To solve these problems, this paper proposes a method that considers semantic differences arising from the decision-makers and the indicators and incorporates the experts' psychological behavior. We apply this method to assess the alternatives for a smart refrigerator product service system. The results suggest that a large semantic difference, when evaluating the linguistic indicators, can influence the final outcome. We validate the flexibility and the effectiveness of the method by comparing against the base case of no semantic difference, using the Euclidean and Manhattan distance measures. • We proposed a method to obtain more accurate numeric meanings of the linguistic terms. • The method can tailor linguistics to the different indicators. • The method considers semantic differences arising from the decision-makers and the indicators. • The method incorporates the psychological behavior of the decision-makers. • The method uses more information, including alternative-preference matrix, criteria-preference matrix and decision matrix. [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]

This paper synthesizes and analyses relevant data at multiple levels (i.e., multi-scale information systems (MSIS)) by fusing social network (SN) and three-way decision (TWD). It enables us to effectively address the complexity and uncertainty intrinsic to rich decision making environments. In addition, in group decision making (GDM) it is likely, often desirable, that agents view problems from different perspectives. Therefore, they need to reach consensus through negotiated discussions and changes in opinions. Such discussions will stop when either the group reaches a satisfactory consensus, or its members' willingness to adjust reaches a maximum value. Within this context, the goal of this article is to investigate the consensus reaching process (CRP) of decision makers in an MSIS setting, and to establish a least-cost consensus method by fusing SN and TWD perspectives, referred to as the CRP-SN-MSIS method. First, optimal scale combinations in MSISs are filtered based on the spirit of TWD. In this way, we obtain multiple decision makers from a GDM viewpoint. Then, a measure method of their trust relations is designed to establish a social network among decision makers. Subsequently, the detailed process of the CRP-SN-MSIS method is presented and applied to a case study targeting a real dataset. Finally, the applicability and superiority of the designed method is fully validated through both qualitative and quantitative arguments. • A social network-based least-cost consensus method is established. • A scale combination selection method is developed from three-way decision perspectives. • A measure of the trust relationship of decision makers is constructed. • Decision makers' willingness to modify is measured in the consensus feedback process. [ABSTRACT FROM AUTHOR]

The strategic management of reverse logistics (RL) is essential for enterprises to enhance their operational efficiency, customer satisfaction, and sustainability performance in today's competitive marketplace. Many manufacturing firms have to cooperate with professional RL providers to overcome resource constraints and technological limitations, ultimately driving business success. Thus, it is critical for every enterprise to select the most suitable third-party RL provider (3PRLP). This paper provides a novel group decision making (GDM) method with incomplete triangular fuzzy multiplicative preference relations (TFMPRs) to cope with the selection of the most optimal 3PRLP. Firstly, a definition of acceptable incomplete TFMPRs is given. Then, the sufficient and necessary condition of an acceptable incomplete TFMPR is proposed. By analyzing the properties of consistent TFMPRs, a graph-based algorithm is designed to estimate the unknown elements in incomplete TFMPRs. Based on the proposed acceptable consistency definition of TFMPRs, an optimization model is set up to improve the consistency degree of inconsistent TFMPRs. The optimal normalized triangular fuzzy multiplicative weight vector (Tri-MWV) is obtained by computing two analytic expressions and solving a linear programming model. To measure the closeness degree of two TFMPRs, the concept of logarithmic correlation coefficient (LCC) between two TFMPRs is proposed. Combining the incomplete preference information in incomplete TFMPRs with the LCC s of any two TFMPRs, an algorithm of computing experts' weights is displayed. Subsequently, a novel method of GDM with incomplete TFMPRs is presented. Lastly, a practical example of evaluating 3PRLPs is conducted to illustrate the effectiveness of the proposed GDM method with incomplete TFMPRs. • A novel group decision making with incomplete triangular fuzzy multiplicative preference relations for the selection of an optimal third-party reverse logistics provider. • Give a concept of acceptable incomplete triangular fuzzy multiplicative preference relations. • Design a graph-based algorithm to estimate the unknown elements in TFMPRs. • Obtain the optimal normalized triangular fuzzy multiplicative weight vector. • A method of determining expert's weight vector is put forward. [ABSTRACT FROM AUTHOR]

When building consensus in group decision making (GDM) under uncertainty, an important yet rarely studied issue is to find the Pareto solutions of multi-objective optimization model. This paper reports a two-objective (2Ob) optimization driven consensus model in GDM by describing the bipolarity of judgements through intuitionistic multiplicative preference relations (IMPRs). First, it is realized that the inherent property of IMPRs is the hesitancy degree. A novel inconsistency index of IMPRs is proposed by combining the effects of hesitancy degree and inconsistency of boundary matrices. Second, the compatibility measure between two IMPRs is utilized to quantify the consensus level (CL) of decision makers. The threshold of acceptable group CL is found to decrease with the order of IMPRs for the first time. A 2Ob optimization model is constructed by minimizing group inconsistency degree and group CL, respectively. Third, the method of equipping two flexibility degrees to each expert is proposed for optimizing individual IMPRs. It is interesting to find that the constructed granularity matrix is different from interval-valued IMPRs. A multi-objective particle swarm optimization algorithm is adopted to obtain a set of Pareto solutions to GDM problems. Case studies are carried out to illustrate the proposed consensus reaching model. The results help to identify how to provide flexible decisions in GDM under some complexity and uncertainty of a practical problem. • The consistency degree of IMPRs is measured by proposing a novel index. • The threshold of group CL is examined to be dependent on the order of IMPRs. • Two flexibility degrees are proposed to construct a two-objective consensus model. • A MOPSO algorithm is used to derive Pareto solutions of GDM problems. [ABSTRACT FROM AUTHOR]

The increasing complexity of decision-making environments has led to a rise in the involvement of decision-makers (DMs) in group decision-making problems. Clustering is widely used in large-scale group decision-making (LSGDM) to categorize DMs into smaller groups. Ensuring reasonable decision-making results requires providing explanations for the generated groups during the clustering process. To address the clustering problem in LSGDM within uncertain linguistic environments, this paper proposes a conceptual clustering method based on the linguistic concept lattice. The method efficiently manages comparable and incomparable linguistic information. To achieve interpretable clustering results for DMs, attribute and expert induction matrices are first introduced. Cluster stability analysis is then employed to automatically determine the optimal number of clusters. Second, linguistic truth-valued aggregation operators are proposed to aggregate the linguistic evaluation information of DMs in each cluster. In addition, a consensus reaching process is conducted within each cluster, and a feedback mechanism is established to iteratively update clusters when consensus cannot be reached. Finally, numerical examples and comparative analyses are presented that verify the effectiveness of the proposed approach in effectively addressing the LSGDM problem within uncertain linguistic environments. • Using conceptual clustering for the LSGDM problem. • Linguistic concepts are provided as explanations for the clustering results. • The comparable and incomparable linguistic information is handled in LSGDM. • A novel linguistic concept lattice-based LSGDM approach is proposed. [ABSTRACT FROM AUTHOR]

Among many decision problems, interval-valued multiplicative preference relation (IMPR) is widely utilized due to its ability to express uncertain information. A new approach to solve group decision making (GDM) with IMPRs is proposed in this paper, named stochastic group preference acceptability analysis with TODIM (SGPAA-TODIM) method, by combining TODIM method (an acronym in Portuguese of Interactive and multi-criteria Decision Making) with stochastic multi-criteria acceptability analysis (SMAA-2). It effectively circumvents information loss and considers the weight and risk preferences of experts. Firstly, the stochastic multiplicative preference relation is defined through stochastic simulation employing a certain density function, and its priority weight vector is determined using the logarithmic least squares method (LLSM). Then, the priority preference comprehensive matrix is proposed by extracting information of priority vectors. Moreover, the novel SGPAA-TODIM method is developed to analyze the stochastic parameter spaces, with the optimal rank determined based on the analysis of acceptability degrees associated with dominance rank. Finally, to demonstrate the validity and applicability of the proposed method, numerical examples are given. • The stochastic MPR is proposed through stochastic simulation. • The priority preference comprehensive matrix is defined for aggregating the priority vectors. • A novel method to solve group decision making problem. • Three examples are provided to show the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]