Weights Of Experts Research Articles

The Quality-of-Life Measurement with a Stochastic Choice of Parameters of the Weighted Principal Component

The quality of life of the population is a latent category, and due to the impossibility of direct measurement it has to be assessed as an integral indicator of many variables. According to the established methodology, one of the main tools in this case is the first principal component, that is, a linear convolution of variables, which has the property of minimizing the variation of the original characteristics. The fact that parameters’ variation is taken into account with equal weight may cause criticism from economists. The use of a weighted principal component which is free of this drawback can be considered as a development of the initial method. In this case to minimize the total variation, the weighting coefficients of features are set expertly. However, in this case, a logical question arises: won’t expert subjectivity have a significant impact on the final integral indicator, as it happens in the case of simple linear convolution with expert weights? Thus, the purpose of this work is to test the applicability of the weighted first principal component as the main tool in constructing an integral indicator of the population quality of life. In particular, it is necessary to test the hypothesis that the influence of heterogeneity in the weights of expert assessments on the final integral indicator is insignificant. In this case, it would be useful not only to illustrate the presence or absence of this influence, but also to estimate its extent. To do this, the simulation modeling is carried out to assess the latent variable “quality of life of the population”, based on empirical expert weights and macro statistics data. Moreover, in contrast to most works related to the topic, the values of the integral indicator (and, accordingly, the ranking of observations) are presented as an interval estimate. In other words, the result is presented as a random variable where the element of randomness is the subjectivity of the expert choice of weights for the weighted principal component. It turns out that even in this case it is possible to obtain robust and meaningful results that are in good agreement with the conclusions of well-known research in this area.

A Decision-Making Model With Intuitionistic Fuzzy Information for Selection of Enterprise Resource Planning Systems

Involvement of small and medium-scale enterprises is important for developing countries like India. Henceforth, enhancing their competency with the adoption of a suitable enterprise resource planning system (ERPS) is a vital way to enhance their competitiveness. The choice of an appropriate ERPS can be considered as a complex multicriteria decision-making (MCDM) problem where several alternatives (ERPS packages) are assessed based on certain types of characteristics, namely domain knowledge of the supplier, system reliability, service and support, functionality, compatibility, information security, cross-module integration, etc. One critical issue associated with the evaluation of ERPSs is the handling of uncertain information. In this article, we first develop a new methodology to resolve the issue of MCDM problems. In this methodology, the weights of decision experts are systematically calculated with the extended variance approach on intuitionistic fuzzy sets. For calculating the criteria weights, an optimization model based on cross-entropy is proposed, and for the aggregation of the criteria values, a new model called intuitionistic fuzzy improved measurement alternatives and ranking based on the compromise solution is developed, which allows both the vector and linear normalizations and having the advantages of comprising two kinds of aggregation models. Next, an ERPS cloud vendor assessment problem is deliberated with three alternatives (A1: Systems, Applications, and Products (SAP), A2: Oracle Corporation, A3: Microsoft Corporation) and 16 criteria to interpret the reasonableness of the introduced framework. According to the outcomes, SAP is the most suitable alternative. Next, a sensitivity analysis is exhibited with diverse parameter values to inspect the permanence of the presented approach. The advantage of the presented approach is discussed with the comparative investigation.

A Multi-Attribute Group Decision-Making Method Based on Trust Relationship and DEA Regret Cross-Efficiency

In multiattribute group decision-making (MAGDM) problems, the data envelopment analysis (DEA) cross-efficiency method is an effective tool to evaluate each decision-making unit. However, this method usually assumes that the decision-maker (DM) is completely rational, which ignores the risk psychology of the DM in the decision-making process. To compensate for this deficiency, this article proposes an MAGDM method based on trust relationships and DEA regret cross-efficiency. First, we construct a modified model based on the CCR model. Then, we propose the DEA regret cross-efficiency method. This method involves the risk psychology of the DM in the decision-making process. Next, a weighting model is developed to aggregate the cross-efficiency comprehensive utility matrix. Subsequently, we construct trust propagation and trust aggregation models to obtain the weights of experts. Finally, the MAGDM method based on trust relationships and DEA regret cross-efficiency is designed to rank all alternatives. A numerical example is provided to illustrate the superiority and rationality of our proposed method.

A novel CODAS approach based on Heronian Minkowski distance operator for T-spherical fuzzy multiple attribute group decision-making

T-spherical fuzzy sets (TSFSs) are more flexible and efficient tools to deal with ambiguous, uncertain and vague information in complex real-world decision-making problems than various extended intuitionistic fuzzy sets. This paper aims to develop a novel T-spherical fuzzy (TSF) Combinative Distance-Based ASsessment (CODAS) based on the Heronian Minkowski distance aggregation operator, this new method can capture interrelationship between input arguments. Some TSF weighted Heronian Minkowski distance (TSFWHMD) aggregation operators with generalization are developed based on Heronian mean and Minkowski-type distance, their properties are discussed as well as their families are analyzed. Furthermore, the TSF MAGDM methodology based on the improved CODAS is designed, where the Minkowski-type distance is used to define the TSF similarity for computing the expert weights and to construct the maximizing deviation method (MDM) for determining the attribute weights, respectively. The TSF ordered weighted Heronian Hamming distance (TSFOWHHD) and TSF ordered weighted Heronian Euclidean distance (TSFOWHED) operators derived from the TSFOWHMD operator are integrated into the CODAS method, which is an improved method for both measuring the deviation of the negative ideal solution from each alternative and capturing the correlation between attributes. Finally, the feasibility and practicality of developed methodology are illustrated with an example of CAE (Computer Aided Engineering) software selection for lithium-ion power battery (LiPB) design, sensitivity analysis and method comparisons are performed to elucidate the reliability and validity of the developed methodology.

Stochastic group preference acceptability analysis for interval-valued multiplicative preference relations based on TODIM method

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.

Probabilistic linguistic q-rung orthopair fuzzy Archimedean aggregation operators for group decision-making

To express uncertain and imprecise information systematically, the concept of probabilistic linguistic q-rung ortho-pair fuzzy set (PLqROFS), which is an advanced version of linguistic intuitionistic fuzzy set and linguistic Pythagorean fuzzy set, considering the instantaneous occurrence of stochastic and non-stochastic-uncertainty. There isn't yet any literature on PLqROFSs that addresses the issue of the relative importance of experts and criteria. The evaluation's findings consequently become irrational. Additionally, the aggregation operators that are currently available on PLqROFSs are too rigid. The primary goal is to resolve these problems by creating a new methodology that makes use of a new flexible aggregation operator. In this paper, a novel integrated framework is suggested to address concerns with group decision-making in PLqROFSs settings by combining the strengths of the power average operator (PAO), the Archimedean operator, and the full consistency method (FUCOM). With the extended variance approach on PLqROFSs, the weight of decision experts is methodically determined in this line. Additionally, the FUCOM on PLqROFSs is used to determine the weight of the criterion. Some probabilistic linguistic q-rung ortho-pair fuzzy Archimedean weighted and power weighted aggregation operators are suggested to aggregate decision experts' preferences. To discuss the viability of the suggested technique, the challenge of choosing a CO2 storage location is given. As alternatives, we have taken into account oilfields, gas fields, basalt formations, and coal resources. Basalt is the best choice, according to the outcome. The stability of our method is demonstrated by the sensitivity analysis of the criteria weights. The comparative analysis demonstrates that, in comparison to the ones already in use, our model is more significant and realistic.

Multiplicative Consistent q-Rung Orthopair Fuzzy Preference Relations with Application to Critical Factor Analysis in Crowdsourcing Task Recommendation

This paper presents a group decision-making (GDM) method based on q-rung orthopair fuzzy preference relations (q-ROFPRs). Firstly, the multiplicative consistent q-ROFPRs (MCq-ROFPRs) and the normalized q-rung orthopair fuzzy priority weight vectors (q-ROFPWVs) are introduced. Then, to obtain q-ROFPWVs, a goal programming model under q-ROFPRs is established to minimize their deviation from the MCq-ROFPRs and minimize the weight uncertainty. Further, a group goal programming model of ideal MCq-ROFPRs is constructed to obtain the expert weights using the compatibility measure between the ideal MCq-ROFPRs and the individual q-ROFPRs. Finally, a GDM method with unknown expert weights is solved by combining the group goal programming model and the simple q-rung orthopair fuzzy weighted geometric (Sq-ROFWG) operator. The effectiveness and practicality of the proposed GDM method are verified by solving the crucial factors in crowdsourcing task recommendation. The results show that the developed GDM method effectively considers the important measures of experts and identifies the crucial factors that are more reliable than two other methods.

A large-scale group decision-making method based on improved affinity propagation algorithm and adjustable minimum-cost consensus model in social networks

The rapid development of information technology has made social network large-scale group decision-making (SN-LSGDM) a focus of the field of decision science. Clustering and consensus-reaching process (CRP) are widely used methods in SN-LSGDM. In this paper, we propose an improved affinity propagation (AP) clustering algorithm that fully consider the trust and similarity attributes to obtain clustering results that are more in line with the expert preferences. Furthermore, we propose an adjustable minimum-cost consensus (MCC) model that considers trust-polymerization degree, which takes into account variations in expert weights and cluster diversity. And the cuckoo search (CS) algorithm is utilized to solve the model. Finally, the applicability and advantages of the proposed methods are demonstrated through a case and comparative analysis.

A dual-level multi-attribute group decision-making model considering interaction factors based on CCSD and MARCOS methods with R-numbers

The current body of research on multi-attribute group decision-making (MAGDM) exhibits some limitations, namely the utilization of the single attribute hierarchy and the assumption of attribute independence. This paper presents a novel approach, referred to as the R-DLMAGDM (R-numbers Dual-Level Multi-Attribute Group Decision-Making) model with interaction factors, which integrates the advantages of R-numbers in risk evaluation. The proposed model aims to address the limitations related to attribute hierarchies and the assumption of attribute independence. The first step in the new model involves establishing the entropy model with R-numbers to determine the expert weights. Subsequently, the R-numbers generalized weighted arithmetic average (RNGWAA) operator and the R-numbers generalized weighted geometric average (RNGWGA) operator are introduced to combine the information provided by the experts. Next, the application of the enhanced correlation coefficient and standard deviation (CCSD) method is utilized to ascertain the relative weights of the dual-level attributes using the inverse order concept. Then, the fuzzy cognitive map (FCM) is employed to evaluate the interrelationships among components in order to derive the final attribute weights. Additionally, the paper discusses the implementation of the R-DLMAGDM model for the assessment of risk in a virtual supply chain in the metaverse. The evaluation process entails the prioritizing of five different alternatives based on four Level 1 criteria and seven Level 2 criteria. The model’s flexibility and validity are showcased through the execution of comprehensive sensitivity analysis and three-dimensional comparative analysis.

A hybrid generalized TODIM approach for sustainable 3PRLP selection in electronic manufacturing industry

Under the pressure of globalization, environmental protection/resource consumption, and the intensification of market competition, various industries have recognized the significant importance of sustainable supply chain management (SCM), in which reverse logistics (RL) has attracted many concentrations from governments to enterprises and the public. However, it is relatively difficult to operate RL autonomously for most electronic manufacturing companies whose core businesses and competition advantages are not in logistics operations because of limited resources and professional skills. Therefore, it is a good choice to escape from the predicament by selecting an appropriate third-party reverse logistics provider (3PRLP) with professional skills for outsourcing and accomplishing the RL business. Generally, evaluation and selection of a 3PRLP is regarded as a multi-attribute group decision-making (MAGDM) process, in which four aspects, namely, the evaluation attributes system, weight of experts and attributes, preference information representation and alternative ranking method have impacts on the decision-making results. Therefore, this paper constructs an MAGDM framework named generalized TODIM (TOmada de DecisãoInterativa e Multicritério, Portuguese acronym for Interactive multicriteria decision-making) under a hybrid information environment, which includes crisp numbers, interval numbers and fuzzy linguistic terms, for solving the problem. It provides a useful reference for manufacturing enterprises to find out the optimal 3PRLP from many alternatives. In particular, the use of different information forms for different evaluation attributes can not only facilitate decision makers to provide their judgments, but also effectively retain the original decision information as much as possible. Utilization of the generalized TODIM method is helpful for considering the risk attitudes and psychological preference behaviors of decision-makers. Finally, to demonstrate the feasibility and effectiveness of the proposed method, a case study relates to select a sustainable 3PRLP in an electronic manufacturing company was conducted. The findings show that the company should pay more attention to the attributes related to social responsibility, service quality and cost when selecting alternative 3PRLP under the sustainable SCM environment. It also provides useful suggestions for 3PRLP themselves to improve their competitiveness from these aspects. Moreover, the sensitivity and comparative analysis demonstrated the necessity and superiorities of comprehensively considering weights of experts and attributes, adopting hybrid information formats, and taking into account the risk attitudes and psychological preference behaviors of decision-makers during the evaluation and selection process.

Large-scale group-hierarchical DEMATEL method for complex systems.

Existing Decision-Making Trial and Evaluation Laboratory (DEMATEL) methods are mostly suitable for simple systems with fewer factors, and lack effective integration of expert knowledge and experience from large-scale group populations, resulting in a potential compromise of the quality of the initial direct relation (IDR) matrix. To make DEMATEL better suited for the identification of critical factors in complex systems, this paper proposes a hierarchical DEMATEL method for large-scale group decision-making. Considering the limitations of expert knowledge and experience, a method based on expert consistency network for constructing the expert weight matrix is designed. The expert consistency network is constructed for different elements, and the weights of experts in different elements are determined using the clustering coefficient. Following the principles of the classic DEMATEL method, the steps for identifying key elements in complex systems using the large-scale group-hierarchical DEMATEL method are summarized. To objectively test the effectiveness and superiority of the decision algorithm, the robustness of the algorithm is analyzed in an interference environment. Finally, the superiority of the proposed method and algorithm is verified through a case study, which demonstrating that the proposed decision-making method is suitable for group decision-making in complex systems, with high algorithm stability and low algorithm deviation.

A study on the sustainable development of regional water resources-socio-economic-ecological environment-tourism industry: survey evidence from the Yellow River Basin, China

High-quality development of socio-economic, ecological environment, tourism industry and natural resources in the Yellow River Basin is a major strategic task for national development. High-quality development in the Yellow River Basin still has a lot of room for improvement, so it is important for the coupled and coordinated development of water resources-socio-economic-ecological environment-tourism industry in the Yellow River Basin region. In this study, we focus on the major strategic issues of high quality development in the Yellow River Basin in the context of the above-mentioned background and the current forms and policies of sustainable development in China, and conduct research on the theory and methods of assessing the sustainable development of regional water resources-socio-economic-ecological environment-tourism industry. However, by analyzing the existing research literature on sustainable development assessment, we find that most of them focus on a single area or two combinations of modal development studies, and focus on exploring micro-coupling mechanisms, so the generality of macro policy support is rather mediocre, which we fill this gap through this study. The study relies on an innovative macroscopic research perspective that draws pioneeringly on the quality function deployment (QFD) theory in the field of product quality management in marketing, which, it is worth stating, allows for a framework of research perspectives from a systematic and holistic perspective. In this framework, we will propose a G1-entropy value method for indicator importance (weight) assessment. It is worth stating that the G1 method used in this paper is different from the traditional G1 method in that we will introduce the identity information weights of experts to improve the reliability of the subjective assignment method. We will also construct an indicator system for studying the regional sustainable development issues in the Yellow River Basin on this basis, so as to complete the ranking and analysis of the nine provinces and the importance of indicators in the Yellow River Basin. This study will provide a comprehensive theoretical basis for Chinese government and related departments to formulate policies for the high-quality development of water resources, socio-economic, ecological environment and tourism industry in the Yellow River Basin, and also provide theoretical and empirical references for the analysis and assessment of similar international regional sustainability cases.

An integrated linguistic Pythagorean fuzzy decision-making approach for risk analysis of offshore wind turbine

The evaluation of risk factors within the context of condition-based maintenance (CBM) for offshore wind turbines has been a challenging issue. In this paper, a novel risk analysis method that combines the fuzzy weighted with zero inconsistency (FWZIC) technique and the DEMATEL method under the linguistic Pythagorean fuzzy environment is proposed. Firstly, 75 risk factors linked to offshore wind turbines are identified by leveraging analysis and prior literature, which are modeled using linguistic Pythagorean fuzzy sets (LPFSs) to facilitate the complexity of expert opinions in the face of uncertainty. Then, the hybrid expert weight calculation method and the FWZIC-based criteria weight calculation method are introduced to determine the weights of the experts and the criteria while considering uncertainty. Next, the extended DEMATEL method under the linguistic Pythagorean fuzzy environment is adopted to determine the significance and influence of the pinpointed risk factors, and an illustrative cause–effect diagram is crafted to dissect the interconnections between these factors. Through this intricate analysis, the cause factors and effect factors specific to offshore wind turbines are identified, and the results obtained from the proposed method are validated through sensitivity analysis and comparative analysis. The results of this study could provide valuable recommendations and references for the implementation of CBM in offshore wind turbines.

Incomplete interval-valued probabilistic uncertain linguistic preference relation in group decision making

In group decision making (GDM), due to complexity of various factors, decision makers (DMs) often provide incomplete preference relations (PRs) in preference matrix. Interval-valued probabilistic uncertain linguistic term set (IVPULTS) is a flexible and accurate tool to depict evaluation information of experts. In this paper, we mainly propose a new concept pertaining to interval-valued probabilistic uncertain linguistic preference relation (IVPULPR) that applies the IVPULTS to preference relations. Firstly, some new basic theoretical concepts of IVPULTS are developed including ordered IVPULTS, normalization method and new expectation function. Secondly, we establish several goal programming models to estimate the unknown elements in incomplete IVPULPR and propose the expected additive consistency of IVPULPR. To improve the consistency level, two optimization models are constructed based on the idea of minimum adjustment. Thirdly, we derive the experts’ weights in terms of information uncertainty, where a new method to measure information uncertainty of IVPULTS is proposed. For the sake of improving group consensus, we construct a group consensus index (GCI) and two optimization models depending on the adjustment mechanism of expert weight. Finally, a complete GDM framework with incomplete IVPULPR is devised based on the analysis of IVPULPR consistency and group consensus. Through an experiment analysis by using an UCI dataset, we find that the proposed GDM model can not only precisely express fuzzy preference information of DMs, but also ensure achievement of acceptable consistency and group consensus under the condition of not changing the initial preference as much as possible.

Risk assessment based on failure mode and effects analysis (FMEA) and WASPAS methods under probabilistic double hierarchy linguistic term sets

Failure mode and effects analysis (FMEA) is regarded as an efficient tool in identifying and eliminating system failures and important tool in safety and reliability analysis. However, the traditional FMEA method has some drawbacks, for example, in the process of risk assessment, traditional FMEA method usually ignores the influence factors of weight. Simultaneously, when represent risk assessment information, crisp numbers and fuzzy sets cannot represent complex linguistic information forms accurately. Moreover, the traditional FMEA method ranks risk failures through simple product. Thus, based on these disadvantages, this paper aims to present an improved FMEA method combines with the Weighted Aggregates Sum Product Assessment (WASPAS) method and weight determination method to address the risk assessment problems under probabilistic double hierarchy linguistic (PDHL) environment. In assessment process, the probabilistic double hierarchy linguistic term sets (PDHLTSs) can indicate the probability distribution as a linguistic tool to describe the information reasonably and precisely. The contribution s of this paper can be incarnated as below. Firstly, the PDHLTSs are utilized to provide the linguistic information of failure modes and construct risk evaluation model in risk assessment. Secondly, FMEA method is combined with WASPAS method to overcoming some drawbacks existing in traditional FMEA such as without consideration of the weight of three aspects in Severity (S), Occurrence (O) and Detection (D) and too simple to evaluate the risk factors using Risk Priority Number (RPN) values. Meanwhile, in response to the issue of traditional FMEA method neglecting expert weights, weight determination method is established based on the SNA method under the PDHL context. Additionally, the FMs are ranked through the multi-attribute decision-making method WASPAS, and the final risk ranking result is obtained. Finally, the proposed method is applied to the marine risk assessment faced in the development of marine economy. Based on the assessment results, suggestions are given for the risk problems. In addition, we also carried out sensitivity analysis and accuracy analysis on the evaluation results. At the same time, comparison analysis with existing methods is given to illustrate the superiority of the proposed method.

Resisting the Edge-Type Disturbance for Link Prediction in Heterogeneous Networks

The rapid development of heterogeneous networks has proposed new challenges to the long-standing link prediction problem. Existing models trained on the verified edge samples from different types usually learn type-specific knowledge, and their type-specific predictions may be contradictory for unverified edge samples with uncertain types. This challenge is termed edge-type disturbance in link prediction in heterogeneous networks. To address this challenge, we develop a disturbance-resilient prediction method ( DRPM ) comprising a structural characterizer, a type differentiator, and a resilient predictor. The structural characterizer is responsible for learning edge representations for link prediction. Concurrently, the type differentiator distinguishes type-specific edge representations to generate diverse type experts while maximizing their link prediction performances on specific types. Furthermore, the resilient predictor evaluates the reliability weights of different type experts to develop a resilient prediction mechanism to aggregate discriminable predictions. Extensive experiments conducted on various real-world datasets demonstrate the importance of the explainable introduction of the edge-type disturbance and the superiority of DRPM over state-of-the-art methods.

Social network trust relationship environment based advanced ovarian cancer treatment decision-making model: An approach based on linguistic information with experts’ multiple confidence levels

Advanced ovarian cancer is the deadliest gynecologic cancer in World. The survival rate is not significant, and it depends on how well cancer responds to treatment. Generally, the treatment decision depends on Gynecologic oncology experts, which treatment is best for the patient. However, a Gynecologic oncology expert’s limited rationality and personality traits strongly impact a patient’s treatment decision. In addition, according to the American Cancer Society, a patient’s treatment decision may change if Gynecologic oncology experts change. To solve this kind of medical problem, we design a group decision-making model (GDM) based on linguistic preference relations (LPRs) with multiple confidence levels like confidence and doubting levels of experts to analyse experts’ treatment decision opinions digitally for improving the survival rate of patients. In a GDM, consistency analysis and obtaining expert weights are two keys. Hence, this paper design an LPRs with confidence and doubting levels (LPRs-CDLs) based GDM model under a unique consistency improvement algorithm and Pythagorean linguistic trust relations social network analysis driven expert weight determination. First, we define the additive consistency of LPRs-CDLs based on minimum confidence and maximum doubting levels. Second, a consistency reaching process (CRP) algorithm with convergence theorem is offered to improve the consistency of experts’ opinion decisions. Third, develop a trust propagation model based on Pythagorean linguistic trust relations under a social network environment for expert’s weights determination. Then, a social network trust relationship-based GDM model with LPRs-CDLs information is presented to the advanced ovarian cancer patient’s treatment final decision. Finally, we show the rationality of this study with some comparative analysis.

Dependence assessment in human reliability analysis based on cloud model and best-worst method

Dependence assessment, which is to assess the dependence level of human errors, is an essential part of human reliability analysis, which could be affected by the complexity and uncertainty of the real world. In this paper, a novel dependence assessment method based on cloud model and best-worst method (BWM) is proposed. Firstly, the influential factors used to measure the dependence level are identified. Then, the social network trust graph of different experts is constructed, and the weights of different experts are determined. Next, the cloud model is adopted to represent the linguistic judgments of experts, where the linguistic judgments are transferred into cloud models, and the assessments of different experts are combined. Finally, based on the dependence level of each factor, the final dependence assessment result is obtained. Two numerical examples are presented to show that the proposed method can effectively provide reliable assessment results under uncertainty. In conclusion, the proposed method provides a novel and effective way for dependence assessment in human reliability analysis.

The optimization model of whole process engineering consulting consortium members based on Z-number

At present, there are very few enterprises with whole-process engineering consulting capability and qualification. To carry out consulting work in a consortium is a necessary way to meet the actual situation of the industry and promote whole-process consulting quickly, and the selection of consortium members is the key issue. First of all, this paper summarizes the construction principle of the index system of consortium member selection, and describes the index system. Aiming at the consortium member selection model, on the basis of comprehensive consideration of 9 indicators, the evaluation value of Z-Numbers fuzzy numbers is obtained by using seven-point language terms, the index weight and expert weight are obtained by using the sequential method and entropy weight method, and the data are processed to get the alternative enterprise evaluation matrix. Fuzzy TOPSIS method suitable for Z-Numbers was introduced to solve the positive ideal solution closeness degree of each enterprise, so as to rank the alternative enterprises.

Three-way group consensus method based on probabilistic linguistic preference relations with acceptable inconsistency

In the realm of addressing consensus challenges within group decision-making (GDM) that encompass individual preferences, this article presents an innovative approach. This article introduces a three-way group consensus methodology grounded in probabilistic linguistic preference relations (PLPRs) that ensures an acceptable level of inconsistency by applying the three-way decision (TWD) principle. This methodology is referred to as the TWD-GC-AIC approach. The TWD-GC-AIC approach consists of two core components, each dedicated to distinct aspects: ensuring the internal consistency of individual expert preference relations and achieving consensus within the expert group. The first component is dedicated to enhancing the consistency of individual expert preferences. This process commences with the determination of expert weights and the development of a novel aggregation formula. Subsequently, the consistency metric is refined through the incorporation of a newly devised distance formula. Once the predefined consistency threshold is reached, this study seamlessly integrates a planning model with an iterative algorithm. This integration serves a dual purpose: minimizing adjustment costs while retaining as much of the original information provided by the experts as possible. In the consensus-reaching phase, known as the consensus reaching process (CRP) of the expert group, this study employs iterative algorithms that incorporate TWD within the feedback mechanism. This strategic approach aims to comprehensively consider the emotional attitudes of the experts when adjusting the evaluation information, ultimately leading to a more informed and rational final decision outcome. Finally, this paper empirically validates the effectiveness and efficiency of the TWD-GC-AIC method, particularly in scenarios involving probabilistic linguistic term sets (PLTSs). The method is applied to a practical example and rigorously benchmarked against various other consensus methodologies to assess its performance.