Comparative Linguistic Expressions Research Articles

Managing non-cooperative behaviors in consensus reaching process: A novel multi-stage linguistic LSGDM framework

Large-scale group decision-making (LSGDM) is a complex process involving numerous decision-makers (DMs). However, considering such a large number of DMs increases the complexity of the process. it seems necessary to pay much more attention to aspects such as a proper dimensionality reduction for scalability, consensus processes with automatic feedback, and effective management of non-cooperative DMs. To address such aspects, this paper presents a novel framework for LSGDM, based on Extended Comparative Linguistic Expressions With Symbolic Translation (ELICIT). We first extend the K-means clustering algorithm by incorporating individual assessments and trust relationships to classify DMs into subgroups, enhancing decision-making efficiency. We then develop a feedback mechanism based on two optimization consensus models for ELICIT information, that automatically provides optimal recommendations. An essential aspect of our proposal is the management of non-cooperative behaviors by utilizing the normal distribution to detect and penalize misbehaviors. Furthermore, we introduce a Data Envelopment Analysis (DEA) cross-efficiency method based on ELICIT values to rank all alternatives once an acceptable group consensus degree is reached. The framework’s effectiveness is demonstrated through a practical application case study, accompanied by a parametric analysis. Comparisons with existing LSGDM methods highlight the superiority of our proposal in terms of efficiency.

Average consistency index based consensus model for a group decision making problem dealing with ELICIT expressions

A group decision making (GDM) problem is often modeled by using a reciprocal preference relation (RPR) structure. Linguistic information is widely used in RPRs to depict its components because it facilitates its understanding and management of uncertainty. Among the existing linguistic representation models, the extended comparative linguistic expressions with symbolic translation (ELICIT) model improves the accuracy of computational processes and maintains the comprehensibility and interpretability of the results. Therefore, we introduce a new linguistic RPR (L-RPR) structure using ELICIT information, denoted as ELICIT-RPR, whose elements are uniformed as 2-tuple linguistic intervals to simplify and facilitate computations between ELICIT expressions. In addition, the average consistency index (ACI) of ELICIT-RPR is proposed together an algorithm for improving the ACI values of ELICIT-RPRs based on their best and worst consistency indices. To avoid conflicts and obtain agreed solutions, consensus reaching processes (CRPs) have been widely used in GDM. Thus, a novel CRP based on ACI values is developed using a new distance between linguistic intervals. Finally, a case study and a comparison analysis are presented to demonstrate the validity and applicability of the proposal.

Consensus reaching for social network group decision making with ELICIT information: A perspective from the complex network

Consensus reaching is essential in group decision-making (GDM) since it can mitigate conflicts between expert opinions and promotes the further implementation of decision-making results. Meanwhile, interaction between experts commonly occurs within social networks and in practical GDM problems. Therefore, it neecessary to consider the trust relationship between experts and utilize it to facilitate the consensus-reaching process (CRP). However, most existing social network-based GDM studies mainly use local measures (e.g., degree centrality) to determine the importance of experts, which cannot reflect their actual influence on a global topological structure. To address this issue, we propose a novel consensus-reaching strategy from the perspective of complex network analysis. First, the Extended Comparative Linguistic Expressions with Symbolic Translation (ELICIT) is adopted to flexibly facilitate the expression of experts’ uncertain evaluations. The hybrid centrality is then defined to determine the influence of experts in the social network by considering both node importance and edge weight. Since experts with greater influence have stronger information propagation capabilities, hybrid centrality is utilized to guide the CRP, which can better reflect information flows in the social network. Additionally, the BWM-CRITIC weighting method is developed to reflect the significance and relationship among criteria. Finally, we verify the effectiveness and superiority of the proposed method by means of a case study on a sustainable supplier selection problem.

An ELICIT information-based ORESTE method for failure mode and effect analysis considering risk correlation with GRA-DEMATEL

Failure mode and effect analysis (FMEA) is one of the most powerful reliability analysis techniques for identifying and preventing potential risks across various fields. Current FMEA methods, while effective, still present several shortcomings. For example, using experts’ subjective pairwise comparisons of risk factors to determine their weights reduces the stability of the result; different relationships among failure modes are often ignored. To improve the performance of FMEA, multi-criteria decision-making (MCDM) methods have been employed to support risk evaluation and prioritization in recent years. This paper proposes a novel FMEA method by exploring several MCDM techniques. First, the Extended Comparative Linguistic Expressions with Symbolic Translation (ELICIT) are utilized to generate group risk assessments under uncertainty. Then, grey relation analysis (GRA) is incorporated into the decision-making trial and evaluation laboratory (DEMATEL) method to objectively determine the weight of risk factors. Afterward, the traditional ORESTE (organísation, rangement et Synthèse de données relarionnelles (in French)) method is generalized to the ELICIT environment to prioritize the failure modes, in which the Besson’s ranking is replaced by deviation measure for more accurate ranking results. Finally, a case study of FMEA for electro-mechanical actuators is presented to illustrate the effectiveness of the proposed method. The results indicate that our approach can express risk information more flexibly, determine the weight of risk factors more objectively, and prioritize failure modes more reasonably.

A Large Scale Group Three-Way Decision-based consensus model for site selection of New Energy Vehicle charging stations

The development of New Energy Vehicles (NEVs) has contributed to the alleviation of environmental pollution in the transportation sector. Although NEVs have some advantages, such as energy saving, being environmentally friendly, and low noise, they are restricted by their cruising range or recharging-related problems. To minimize such disadvantages, an optimal plan for the charging station site is necessary. This paper proposes a Large-Scale Group Decision-Making (LSGDM) method to select the best location for such charging stations. This method involves a large group of experts providing their preferences according to their knowledge and background. To facilitate the elicitation, our method uses Hesitant Fuzzy Linguistic Term Sets (HFLTS) and Extended Comparative Linguistic Expressions with Symbolic Translation (ELICIT) model to improve the elicitation process, guarantee precise computing processes and obtain interpretable results. A social network is then constructed based on experts’ preference similarity and trust relationships, which reflects both their relationship and its strength simultaneously. Afterwards, a social analysis-based clustering process groups the experts, and a Three-Way Decision (TWD)-based Consensus Reaching Process (CRP) is introduced to improve the group’s agreement. Finally, a selection of charging station site case studies is conducted, and a comparative analysis is carried out to illustrate the quality of the proposal.

Consensus-driven methodology to managing diversity and complex linguistic ratings in quality function deployment: An optimization-based approach

Quality function deployment (QFD) is a quality management tool that can effectively transform customer requirements (CRs) into engineering characteristics (ECs) of services or products. It is a crucial process to determine the prioritization of ECs from the assessments of the relationship between CRs and ECs in QFD. This study designs several optimization models to derive the consensual prioritization of ECs from the diverse and complex assessments, in which the assessments of QFD team members are modelled by comparative linguistic expressions (CLEs). First, a consensus-driven optimization model (CDOM) is presented to manage CLEs by transforming them into linguistic distribution assessments. Then, a minimum adjustment element consensus model (MAECM) is developed to derive the consensual assessments by minimizing the number of adjustment elements between the members’ original and adjusted assessments. Following this, a technique for order preference by the similarity to ideal solution (TOPSIS) based method is used to derive the prioritization of ECs from the consensual assessments. A case study regarding the improvement of window services in the Bank of JT Shanghai Branch is proposed to illustrate the implementation of the presented method. The comparative analysis shows that the presented method outperforms previous methods in managing CLEs and consensus.

An attitudinal consensus method under uncertainty in 3PRLP selection

To underpin a reverse logistics (RL) outsourcing decision, this study aims to investigate a third-party reverse logistics provider (3PRLP) selection problem under the framework of group decision making (GDM). Group attitude towards distinctive opinions may affect the time and cost on consensus reaching process (CRP). Therefore, an attitudinal consensus method under uncertainty is established and composed of three parts: initialization process, consensus process and selection process. In initialization process, considering each expert’s risk preference, a transformation rule is deployed to compute semantics possibility distribution of general comparative linguistic expressions (GCLEs) based on the numerical counterpart of linguistic assessment. In consensus process, three group attitudes-oriented consensus policies are qualitatively presented, including maximum, indifference and minimum disagreement consensus policies. Considering the feasible interval of attitudinal parameter, a new consensus measure under uncertainty, i.e., attitudinal consensus acceptability index (ACAI), is quantitively defined by stochastic acceptability analysis. To resolve the issue that the consensus degree fails to reach a predefined level, an automatic feedback mechanism is designed, and is supported by a consensus improvement algorithm evolving GCLEs’ possibility distribution. In selection process, to identify the criteria weight, incomplete information such as pairwise comparisons of criteria are characterized by ordinal regression-like linear programming. TODIM (an acronym in Portuguese of interactive and multiple attribute decision making) is extended on fuzzy measure and then acted as rank function in stochastic acceptability analysis to explore the uncertainty of criteria preference. Lastly, 3PRLP selection for an automobile manufacturing firm is conducted to demonstrate the flexibility and practicability of our method along with sensitivity analysis and comparative analysis.

Large-scale group decision-making for prioritizing engineering characteristics in quality function deployment under comparative linguistic environment

Quality function deployment (QFD) is a well-known tool for quality management. With its systematic operation mechanism for translating customer requirements (CRs) into corresponding engineering characteristics (ECs), QFD highly facilitates product/service design and improvement. However, the evolution of the decision-making environment has made the quantification within the traditional QFD operation could hardly able to meet the demanded efficiency as well as the accuracy of the generated results. To cope with the problem, an enhanced large-scale group decision-making method that integrates proportional hesitant fuzzy linguistic term sets (PHFLTSs) and the cumulative prospect theory (CPT) is put forward by this study to determine the ranking priority of ECs in doing QFD. To facilitate QFD team members carry out an easier and more accurate evaluation, they would use comparative linguistic expressions in making judgments, and the comparative linguistic expressions are subsequently transformed into hesitant fuzzy linguistic term sets (HFLTSs). The obtained HFLTSs are transformed into PHFLTSs based on the statistical method under a group decision-making environment for preventing information loss, and, at the same time, improving calculation accuracy. Taking decision-makers’ heterogeneity and risk attitudes into consideration, the CPT method is adopted and extended under the PHFL environment to prioritize the ECs in QFD operation. To illustrate how the proposed large-scale group decision-making-based QFD method is to be applied, a case study about solar photovoltaic cell development is presented. Furthermore, a comparative analysis is conducted to exhibit the effectiveness of the proposed QFD method.

An Influence Network-Based Consensus Model for Large-Scale Group Decision Making with Linguistic Information

The vast majority of the existing social network-based group decision-making models require extra information such as trust/distrust, influence and so on. However, in practical decision-making process, it is difficult to get additional information apart from opinions of decision makers. For large-scale group decision making (LSGDM) problem in which decision makers articulate their preferences in the form of comparative linguistic expressions, this paper proposes a consensus model based on an influence network which is inferred directly from preference information. First, a modified agglomerative hierarchical clustering algorithm is developed to detect subgroups in LSGDM problem with flexible linguistic information. Meanwhile, a measure method of group consensus level is proposed and the optimal clustering level can be determined. Second, according to the preference information of group members, influence network is constructed by determining intra-cluster and inter-cluster influence relationships. Third, a two-stage feedback mechanism guided by influence network is established for the consensus reaching process, which adopts cluster adjustment strategy and individual adjustment strategy depending on the different levels of group consensus. The proposed mechanism can not only effectively improve the efficiency of consensus reaching of LSGDM, but also take individual preference adjustment into account. Finally, the feasibility and effectiveness of the proposed method are verified by the case of intelligent environmental protection project location decision.

A type-1 OWA operator for Extended Comparative Linguistic Expressions with Symbolic Translation

Recently, a new representation model has been proposed to improve the interpretability and accuracy of Computing with Words (CW) processes, the so-called Extended Comparative Linguistic Expressions with Symbolic Translation (ELICIT). It extends the concept of comparative linguistic expressions based on hesitant fuzzy linguistic term sets into a continuous domain by means of the symbolic translation used in the linguistic 2-tuple model. The aggregation of this kind of information is vital when solving decision making problems, but as the field of ELICIT information is still quite new, not many aggregation operators have been defined for it. Therefore, taking into account the need to deal with the fuzzy representation of ELICIT information for its aggregation, we propose the ELICIT type-1 OWA (ELICIT-t1-OWA) operator based on the equivalent α−level type-1 OWA operator to simplify the CW processes by using ELICIT trapezoidal fuzzy representations. The ELICIT-t1-OWA operator will use interval weights induced by an interval-valued linguistic quantifier to aggregate ELICIT expressions and then its properties will be studied. Additionally, a way to deal with both the weights and arguments of the ELICIT-t1-OWA operator is provided in the form of fuzzy numbers. Finally, a decision making model dealing with ELICIT information that carries out the aggregation by using the proposed ELICIT-t1-OWA operator is developed and a numerical example to show its effectiveness is introduced.

Modeling Personalized Individual Semantics and Consensus in Comparative Linguistic Expression Preference Relations With Self-Confidence: An Optimization-Based Approach

Comparative linguistic expression preference relations (CLEPRs) are an effective tool to represent uncertain opinions of decision makers in group decision making (GDM). Nevertheless, multiple self-confidence levels are not considered by existing research on CLEPRs. Thus, this article proposes CLEPRs with self-confidence by considering multiple self-confidence levels and presents a way to measure their consistency level. Meanwhile, personalized individual semantics (PIS), indicating that words mean different things for different people, have been highlighted and investigated in the GDM with linguistic assessment information. Considering PIS in comparative linguistic expressions, this article proposes an optimization model based on the consistency-driven methodology to assess individual semantics in CLEPRs with self-confidence. Particularly, the PIS are described and addressed by setting different numerical scales of linguistic terms for different decision makers. Finally, an optimization-based consensus model is proposed to obtain a consensual collective solution, which seeks to minimize the information loss between the decision makers’ preference relations with self-confidence and corresponding individual preference vectors.

Expertise-based bid evaluation for construction-contractor selection with generalized comparative linguistic ELECTRE III

The process of bid evaluation is subject to indetermination, imprecision, and uncertainty in terms of their alternative-criterion decision appraisals. To address this issue, this paper develops a novel ELECTRE III-based MCGDM approach for bid evaluation, in which generalized comparative linguistic expressions (GCLEs) are used to evaluate bidder performance. The collected GCLEs are further transformed into possibility-distribution-based hesitant fuzzy linguistic-term sets (HFLTSs) to facilitate the qualitative construction of individual expertise. A consensus-reaching process is introduced to promote decisions that are agreed upon by experts and thereby ensure an enhanced state of mutual agreement among the experts. Subsequently, an integrated subjective-objective approach is proposed to calculate criterion weights and to implement an ELECTRE III-based method that incorporates HFLTS possibility distributions, which allows us to treat the indetermination, imprecision, and uncertainty embedded in appraisals of alternative-criterion decisions when evaluating bids. The potential advantages of the proposed approach are validated by a real-life contractor-selection case.

A cohesion-driven consensus reaching process for large scale group decision making under a hesitant fuzzy linguistic term sets environment

Large-scale group decision-making (LSGDM) under uncertainty modelled by comparative linguistic expressions based on a hesitant fuzzy linguistic term set (HFLTS) has recently attracted the interest of many researchers and research, due to the necessity of its function in LSGDM, and the challenges it faces such as the managing of the scalability problem, uncertainty of experts’ opinions and dealing with polarized conflicting opinions. To smooth out such discrepancies and obtain agreed solutions Consensus Reaching Processes (CRPs) for LSGDM have been applied, in which experts are grouped into sub-groups according to the closeness of their opinions to deal with scalability. However, most CRPs for LSGDM are driven by a majority rule, in which larger sub-groups, where there might be internal disagreements, lead the consensus. In such processes, the internal disagreements can produce unsatisfactory solutions. Consequently, the majority view should be complemented by additional mechanisms that also measure the strength of the sub-groups’ opinions. A good measurement of such strength is the cohesion among the sub-group members. Therefore, in this paper, a new cohesion measure for HFLTS based on restricted equivalence functions for measuring the experts’ sub-group cohesiveness is introduced to drive the consensus process together the majority and thus reduce the impact of internal disagreements risen in majority driven CRPs. It is then integrated in a new cohesion-driven CRP approach based on LSGDM to deal with comparative linguistic expressions based on HFLTS. An experimental analysis on different large scale scenarios will show the performance and importance of cohesion in consensus based LSGDM.

Induced OWA Operator for Group Decision Making Dealing with Extended Comparative Linguistic Expressions with Symbolic Translation

Nowadays, decision making problems have increased their complexity and a single decision maker cannot handle these problems, with a more diverse and comprehensive view of them being necessary, which results in group decision making (GDM) schemes. The complexity of GDM problems is often due to their inherent uncertainty that is not solved just by using a group. Consequently, different methodologies has been proposed to handle it, in which, the use of the fuzzy linguistic approach stands out. Among the multiple fuzzy linguistic modeling approaches, Extended Comparative Linguistic Expressions with Symbolic Translation (ELICIT) information has been recently introduced, which enhances classical linguistic modeling that is based on single terms by providing linguistic expressions in a continuous linguistic domain. Its application to decision making is quite promising, but it is necessary to develop enough operators to accomplish aggregation processes in the decision solving scheme. So far, just a small number of aggregation operators have been defined for ELICIT information. Hence, this paper aims at providing new aggregation operators for ELICIT information by developing novel OWA based operators, such as the Induced OWA (IOWA) operator in order to avoid the OWA operator needs of reordering its arguments, because ELICIT information does not have an inherent order due to its fuzzy representation. Our proposal not only consists of extending the definition of an IOWA operator for ELICIT information with crisp weights, but it is also proposed a type-1 IOWA operator for ELICIT information in which both weights and arguments are fuzzy as well as the use of ELICIT information constructing the order inducing variable to reorder the arguments. Additionally, the use of ELICIT information in GDM demands the ability to manage majority based decisions that are better represented in the IOWA operator by linguistic quantifiers. Hence, a majority-driven GDM process for ELICIT information is proposed, which it is the first proposal for fulfilling the majority solving process for GDM while using ELICIT information. Eventually, an illustrative example and a brief comparative analysis are presented in order to show the performance of the proposal and its feasibility.

A Consensus Model for Extended Comparative Linguistic Expressions with Symbolic Translation

Consensus Reaching Process (CRP) is a necessary process to achieve agreed solutions in group decision making (GDM) problems. Usually, these problems are defined in uncertain contexts, in which experts do not have a full and precise knowledge about all aspects of the problem. In real-world GDM problems under uncertainty, it is usual that experts express their preferences by using linguistic expressions. Consequently, different methodologies have modelled linguistic information, in which computing with words stands out and whose basis is the fuzzy linguistic approach and their extensions. Even though, multiple consensus approaches under fuzzy linguistic environments have been proposed in the specialized literature, there are still some areas where their performance must be improved because of several persistent drawbacks. The drawbacks include the use of single linguistic terms that are not always enough to model the uncertainty in experts’ knowledge or the oversimplification of fuzzy information during the computational processes by defuzzification processes into crisp values, which usually implies a loss of information and precision in the results and also a lack of interpretability. Therefore, to improving the effects of previous drawbacks, this paper aims at presenting a novel CRP for GDM problems dealing with Extended Comparative Linguistic Expressions with Symbolic Translation (ELICIT) for modelling experts’ linguistic preferences. Such a CRP will overcome previous limitations because ELICIT information allows both fuzzy modelling of the experts’ uncertainty including hesitancy and performs comprehensive fuzzy computations to, ultimately, obtain precise and understandable linguistic results. Additionally, the proposed CRP model is implemented and integrated into the CRP support system so-called A FRamework for the analYsis of Consensus Approaches (AFRYCA) 3.0 that facilitates the application of the proposed CRP and its comparison with previous models.

Third-party reverse logistics provider selection: A computational semantic analysis-based multi-perspective multi-attribute decision-making approach

In the era of circular economies, governments and consumers are increasingly aware of environmental protection, which encourages enterprises to devote more attention to reverse logistics (RL). However, the limited resources and technical limitations of most manufacturing companies have motivated them to outsource their RL activities to professional third-party RL providers (3PRLPs). Optimal 3PRLP selection is instrumentally valuable in RL outsourcing practices because it has the potential to increase enterprises’ economic profitability and to improve their long-term development. Generally, 3PRLP selection is treated as a multiple-attribute decision-making (MADM) problem. To this end, this paper aims to build a multi-perspective MADM (MPMADM) framework to offer systematic decision support for enterprises to select the optimal 3PRLPs. Attribute assessments in the proposed framework take the form of generalized comparative linguistic expressions (GCLEs), which can be transformed into hesitant fuzzy linguistic term set (HFLTS) possibility distributions with semantic analysis in order to enhance information quality and reliability. Expert weights are then assigned in the use of an optimization model based on the correlation consensus measurement. Afterwards, the two-stage aggregation paradigm for computing with HFLTS possibility distributions is used to gather assessments at expert and attribute levels to compile overall assessments of each alternative 3PRLP. Compared with existing studies, our proposal considers environmental and social sustainability for attribute system establishment and introduces GCLEs for 3PRLP selection, which offer greater flexibility for experts to articulate their evaluations. In addition, the two-stage aggregation paradigm eliminates distortion and loss of information and provides decision makers with the capability to control the outcome’s precision. Moreover, the proposed expert weight determination approach is conducive to generating reliable weight vectors. Several illustrative examples, sensitivity analysis, and comparative analysis further demonstrate the flexibility and practicability of our proposal.

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.

Bid evaluation in civil construction under uncertainty: A two-stage LSP-ELECTRE III-based approach

Increasing growth and development of building industry and civil engineering motivates enterprises to advance bid evaluation process in an effort to ameliorate building quality and diminish construction cost. The selection of qualified construction contractor has been generally formulated and addressed as a multi-attribute group decision-making problem. However, few existing studies have taken the reasoning logic pattern in human cognition process and the compensatory among attributes into account. Therefore, a two-stage logic scoring of preference-ELECTRE III-based approach is established for the management and manipulation of bidder selection. In a bid to facilitate expert evaluation articulation, alternative-attribute assessments in this approach take the form of generalized comparative linguistic expressions, which are subsequently converted into possibility-distribution-based hesitant fuzzy linguistic term set via the similarity measure-based generation approach to enhance information quality and reliability. Then, nonlinear optimization-based direction rules are introduced to advance the automatic minimum-distance-based consensus reaching model and based on which, the individual semantic-embedded assessments are algorithmically adjusted to reach acceptable consensus. Furthermore, the expert and attribute importance degrees are extracted from both semantic and formal logic aspects, and the modified individual assessments are gathered by integrating the two-stage logic scoring of preference aggregation structure and the ELECTRE III method. The present approach provides a solution to bid evaluation problems considering the reasoning logic pattern in human cognition process and the compensatory among attributes. A practical case study and a comparative analysis are performed to demonstrate the feasibility and effectiveness of the established multi-attribute group decision-making approach.

A consensus reaching process dealing with comparative linguistic expressions for group decision making: A fuzzy approach

A consensus reaching process dealing with comparative linguistic expressions for group decision making: A fuzzy approach

Transforming and decision-making based on probabilistic linguistic term sets with comparative linguistic expressions and incomplete assessments

The probabilistic linguistic term sets (PLTSs) are widely used in decision-making, due to its convenience of evaluation, and allowances of probability information. However, there are still some cases where it is not convenient to give an evaluation using the PLTS gramma. Sometimes the evaluators can only give a comparative relationship between alternatives, sometimes evaluators may have difficulty understanding all the alternatives and cannot give a complete assessment. Therefore, we propose a method to transform the comparative linguistic expressions (CLEs) into PLTSs, and the comparison objects of CLEs are alternatives evaluated by PLTSs. And the probability distribution has been adjusted to make the transformation more in line with common sense. Then, a method to correct the deviation is proposed, allowing alternatives to be compared in the case of incomplete assessment. Combining the above two methods, we propose a decision-making method when both CLEs and incomplete assessments coexist. With the study in this paper, the limitations of PLTS-based evaluation and decision-making are reduced and the flexibility of using PLTS is improved.