Probabilistic Linguistic Preference Relations Research Articles

Additive consistency analysis for nested probabilistic linguistic preference relations and its application in decision making

Additive consistency analysis for nested probabilistic linguistic preference relations and its application in decision making

A quantum probability theory-based method for heterogeneous multi-criteria group decision making with incomplete probabilistic linguistic preference relations considering the interference effect among decision makers

Quantum probability theory (QPT) reveals that decision makers (DMs) can interfere with each other and thus affect the decision result. However, existing methods of heterogeneous multi-criteria group decision making (HMCGDM) seldom consider the interference effect among DMs. This paper defines an interference degree based on the phase angle difference obtained by QPT to address HMCGDM problems in which the alternative and criteria sets provided by DMs may be different. In addition, the incomplete probabilistic linguistic preference relations (InPLPRs) are introduced to express the evaluation information of DMs. Considering that the same linguistic term may has different meanings for DMs, we construct a consistency-driven optimization model based on the personalized individual semantics (PISs) to estimate the missing information in InPLPR on each criterion provided by DMs and the corresponding complete PLPR (CPLPR). Then, for each DM, the individual weights of criteria and the comprehensive CPLPR on all criteria in the individual criteria set can be obtained by an optimization model. Subsequently, a novel QPT-based model is erected to derive the weights of DMs and the ranking order of alternatives. Finally, an example of tourism evaluation and several sensitivity and comparative analyses are offered to examine the applicability of the proposed method.

Trust Risk Test-Based Group Consensus With Probabilistic Linguistic Preference Relations Under Social Networks

Trust Risk Test-Based Group Consensus With Probabilistic Linguistic Preference Relations Under Social Networks

Consistency improvement and local consensus adjustment for probabilistic linguistic preference relations considering personalized individual semantics

To address the challenge of facilitating overall problem solving and improving the overall efficiency of intelligent systems efforts through group decision making (GDM) by experts at all stages of the systems, this paper proposes an approach that focuses on improving consistency and enhancing local consensus. The proposed approach specifically considers the probabilistic linguistic preference relations (PLPRs) and incorporates personalized individual semantics (PISs) of decision makers (DMs). For the consistency procedure, we construct an expectation-additive consistency-driven semantic model to acquire PISs of different DMs. Secondly, the preference relation (PR) which does not satisfy the consistency is improved based on a minimum adjustment model. In particular, according to the expected value with PISs this paper, DMs offer PLPRs can be transformed into fuzzy preference relations (FPRs) correspondently for making decisions. For the FPRs, a virtue consensus measure is explored for the consensus reaching process (CRP) from two levels to combine the average value and variance of pair similarities, which effectively improves the accuracy of the consensus measurement. Next, a collective consensus level is calculated to replace the consensus threshold objectively, and then the DMs and alternative pairs that do not reach consensus are identified locally from two levels. Subsequently, an optimisation model that combines the two objectives is developed to improve the consensus level while ensuring consistency. Finally, our method is applied to a publicly available air quality dataset, and the consensus and ranking results are discussed in comparison with other advanced methods to confirm the superiority of the established method.

Three-way group consensus with experts' attitudes based on probabilistic linguistic preference relations

Intelligent decision-making collaborates with big data analytics to navigate the intricate landscape of the digital economy, orchestrating data-driven strategies to achieve the most favorable results. Through the integration of specific objectives and relevant data, intelligent decision-making involves the modeling, analysis, and realization of decisions. This comprehensive process seamlessly incorporates elements such as constraints, strategies, preferences, and uncertainty, ultimately leading to the autonomous achievement of optimal outcomes. In this context, the probabilistic linguistic preference relation (PLPR) serves as a recently introduced form of linguistic evaluations, offering adaptable expression of expert preference assessments. Within the domain of preferences, consistency emerges as a pivotal consideration. Extremes occur when calculating the additive consistency of PLPR using expectation values. To comprehensively address the trouble, this paper introduces an innovative planning model that employs deviation degrees. The establishment of a consistency threshold is approached objectively using the principle of minimum individual regret and maximum group delight. Once consistency is established, the process advances to consensus reaching process (CRP). During the consensus feedback phase, the infusion of the three-way decision (TWD) theory accounts for distinct expert modification attitudes, while ensuring consistency remains upheld throughout the modification procedure. For clarity, the proposed technique is referred to as the TWD-GC-EA method. Notably, the effectiveness of the designed approach is demonstrated through its application to a real-world scenario. Furthermore, a comparative assessment is conducted against several other consensus methods to validate its efficacy and superiority.

Attitude- and cost-driven consistency optimization model for decision-making with probabilistic linguistic preference relation

Probabilistic linguistic term set (PLTS) conveys the preference for a linguistic term by assigning a probability distribution, which can more correctly and flexibly reflect the decision-maker (DM)’s evaluation information and make the decision outcome more scientific and rational. Probabilistic linguistic preference relation (PLPR) allows the DM to represent decision information for pairwise comparison of alternatives with PLTS, allowing a more comprehensive representation of the DM’s valid preferences. Consistency is essential in the preference decision-making process and directly influences the dependability of the final results. Therefore, this paper develops a minimum cost consistency adjustment mechanism based on attitudes and emotions for solving the decision-making problem with PLPR. Firstly, a new PLTS normalization model is proposed to handle the unknown information, considering the DM’s preferred attitude and emotional tone. Secondly, the expected parametric multiplicative consistency index for PLPR is defined, and parameter settings improve the flexibility and relevance of the consistency. Then, the concepts of linguistic hesitancy, probabilistic uncertainty, and probabilistic incompleteness are defined for the PLTS that can reflect the psychological characteristics of DMs’ hesitancy; they are then used to measure hesitation and unit consistency adjustment costs. Next, a new distance measure is established between the two PLTSs to measure the difference between the preference information. Subsequently, a direction-guided minimum cost consistency optimization model with unacceptable consistency is constructed for the PLPR. Finally, the usefulness of the suggested decision-making method with PLPR is tested using a numerical example of talent selection, and parametric sensitivity analysis and comparative analysis are utilized to show the benefits of the suggested methodology.

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.

Simplified probabilistic linguistic preference relation in decision making

Probabilistic linguistic preference relation (PLPR), whose elements are denoted in probabilistic linguistic term sets, provides a flexible tool for experts to express linguistic preferences in pairwise comparisons of objects. However, missing elements in PLPRs often occur owing to the difficulty of providing pairwise comparison values, especially when the number of objects is large. This study introduces a simplified PLPR based on reference objects, which allows for the incompleteness of probabilistic linguistic term sets when deriving the priorities of objects. We also introduce a consistency measure to check the reliability of a simplified PLPR. An illustrative example is provided to demonstrate the efficiency and validity of the simplified PLPR in decision making.

Advances of Probabilistic Linguistic Preference Relations: A Survey of Theory and Applications

Advances of Probabilistic Linguistic Preference Relations: A Survey of Theory and Applications

Managing multi-granular probabilistic linguistic information in large-scale group decision making: A personalized individual semantics-based consensus model

The multi-granular probabilistic linguistic modeling allows decision makers to express cognitive information using multiple linguistic term sets based on their preferences. However, personalized individual semantics (PIS) can lead to different meanings of the same word within the linguistic context. To address this issue and manage consensus in large-scale group decision making, this study proposes a decision framework that employs multi-granular probabilistic linguistic preference relations (MGPLPRs). First, a transformation method is presented to unify different granularity levels of MGPLPRs, thus ensuring the consistency of granularity. Moreover, a consistency-driven optimization model is constructed to generate the numerical scales with PIS for different experts. Thereafter, a two-stage consensus reaching process (CRP) is developed, including both within-cluster and across-cluster CRP, to achieve group consensus. The experts’ original weights are derived from a social network, taking into account the trust relationships among them. A dynamic weighting mechanism is used to update the experts’ weights based on their contributions to group consensus, which better reflects the actual situation than fixed weights. The proposed method is exemplified through a case study of assessing and selecting campus surveillance measures for COVID-19. Finally, the effectiveness and robustness of the proposed framework are verified through comparative analysis and sensitivity analysis.

Group decision-making with multiplicative probabilistic linguistic preference relations based on consistency improvement and upgraded multiplicative DEA cross-efficiency

Multiplicative probabilistic linguistic preference relation (MPLPR) has been widely used by decision-makers (DMs) to tackle group decision-making (GDM) problems. However, due to the complexity of the decision-making circumstance and individual subjectivity of DMs, they often provide inconsistent MPLPRs which often lead to unreasonable decision results. To solve this problem, this paper investigates a novel approach to GDM with MPLPRs based on consistency improvement and upgraded multiplicative data envelopment analysis (DEA) cross-efficiency. First, the concept of sequential consistency of MPLPR is defined. Then, a consistency improvement algorithm is proposed, which can convert any unacceptable consistent MPLPR into an acceptable one. Furthermore, we use geometric averages to transform MPLPR into multiplicative preference relation (MPR). Meanwhile, considering the conservative psychology of DMs, an upgraded multiplicative DEA cross-efficiency model based on the pessimistic criterion is constructed, which can derive the priority vector of MPLPR. Therefore, we can obtain the rational ranking results for all alternatives. Finally, a case analysis of emergency logistics under COVID-19 is provided to illustrate the validity and applicability of the proposed approach.

Failure Mode and Effect Analysis Based on Probabilistic Linguistic Preference Relations and Gained and Lost Dominance Score Method.

Failure mode and effect analysis (FMEA) is a widely used reliability management technology to evaluate the risk of potential failures in a system, product, or service. Nevertheless, the normal risk priority number (RPN) method has been extensively criticized for many deficiencies in practical applications. To overcome the drawbacks of traditional FMEA, plenty of methods have been suggested in previous studies. But majority of them evaluated the risk factors of each failure mode directly and cannot take group and individual risk attitudes into account. In this article, we put forward a new FMEA approach integrating probabilistic linguistic preference relations (PLPRs) and gained and lost dominance score (GLDS) method. The PLPRs are adopted to describe the risk evaluations of experts by pairwise comparison of failure modes. An extended GLDS method is introduced to derive the risk ranking of failure modes considering both group and individual risk attitudes. Moreover, a two-step optimization model is proposed to determine the weights of risk factors when their weighing information is unknown. Finally, a load-haul-dumper machine risk analysis case is presented to demonstrate the proposed FMEA. It is shown that the approach being proposed in this study provides a practical and effective way for risk evaluation in FMEA.

A novel consensus model with probabilistic linguistic preference relation for the utilization mode selection of renewable energy sources

A novel consensus model with probabilistic linguistic preference relation for the utilization mode selection of renewable energy sources

Unit consensus cost-based approach for group decision-making with incomplete probabilistic linguistic preference relations

In group decision-making, the incomplete probabilistic linguistic preference relation (InPLPR) has been widely studied because it can flexibly reflect the decision psychology of decision makers (DMs). In addition, to help DMs revise their opinions and reach a consensus, a large number of scholars have conducted research on the consensus reaching process. Therefore, this study proposes a group consensus decision approach based on InPLPR, considering consistency, the social trust network (STN), and unit cost consensus adjustment. First, an InPLPR consistency measure formula is proposed, based on which a multi-stage missing value estimation method based on optimal consistency and STN is offered for the missing information problem in InPLPR. Thereafter, the hesitation index and unit consensus cost measurement formulas are presented for incomplete probabilistic linguistic term set. Subsequently, consensus reaching and ranking selection are performed based on the proposed unit minimum cost consensus model. Finally, a numerical example of the future development choice problem for new energy vehicle enterprises is provided to demonstrate the applicability of the decision process, and the advantages of the method are derived through comparative analysis.

Managing uncertain preferences of consumers in product ranking by probabilistic linguistic preference relations

Product recommendation helps reduce the difficulty for consumers to make purchases from overloaded products on e-commerce platforms. However, “ramp-up” problems are common as many consumers have little information on purchases and ratings, making it difficult to predict their preferences. In this study, an interactive process is implemented between consumers and the system to capture consumer preferences. To make it easier for consumers to express their preferences for products with respect to different attributes, we design the interface in terms of linguistic terms and probability that are closest to expression habits, and structure the expressions through probabilistic linguistic preference relations. A consistency checking method and an inconsistency repairing method are presented to make the preference information provided by consumers meet the consistency requirements. We propose a partial ranking method based on attribute aggregation to rank products with preference information from the consumer. To rank products for which the consumer does not provide preference information, we develop a global ranking method by estimating the priorities of different kinds of attribute performance. Two examples of hotel recommendations prove that the proposed product ranking methods are suitable for consumers with clear purchasing demands.

Value-driven preference disaggregation analysis for uncertain preference information

Multiple criteria decision aiding aims to recommend decisions that are consistent with the decision-maker's value system by making trade-offs among multiple criteria to measure the performance of alternatives. A challenge is that decision-makers may be unable to provide certain information about their preferences. This study focuses on the preference disaggregation analysis of uncertain pairwise comparisons between reference alternatives familiar to the decision-maker. Probabilistic linguistic preference relations are introduced to portray uncertain preference information, in which linguistic terms and subjective probabilities are used to express the intensities of preferences and corresponding belief degrees, respectively. The preference information is converted into constraints on value functions by triangular fuzzy numbers, and the value functions compatible with the preference information are estimated by linear programming to model the decision-maker's value system. We conduct a consistency analysis of probabilistic linguistic preference information as well as a robustness analysis of compatible value functions based on Monte Carlo simulations. Based on the data collected from Amazon.com, the proposed model is applied to laptop recommendations where the decision-maker is a single person and treadmill recommendations where the decision-maker is a group. The comparative analysis verifies the effectiveness of the proposed model in dealing with the uncertainties and intensities of preferences.

EVALUATION OF GOVERNMENT INVESTMENT USING NESTED PROBABILISTIC LINGUISTIC PREFERENCE RELATIONS BASED ON GRAPH THEORY

Government investment, as a major government function, is closely related to national development and economic growth. It plays a key role to maximize the benefits of this fund, which requires the government to choose the optimal investment plan. Considering the complex and uncertain decision-making environment, we propose the nested probabilistic linguistic preference relation (NPLPR) based on the nested probabilistic linguistic term sets (NPLTSs), to express preference information from the qualitative and quantitative angle. According to graph theory, we define a consistency index and an acceptable consistency of NPLPR to measure the additive consistency. Based on which, we establish a novel algorithm for unacceptable consistent NPLPR to meet the acceptable consistency. Finally, projects in government investment are evaluated by the proposed decision-making method, and some comparative analyses, discussions, and implications are provided from three angles. This study provides a new perspective for scholars to make scientific and rational decisions with the help of technological and economic development in various fields.

Risk assessment in project management by a graph-theory-based group decision making method with comprehensive linguistic preference information

Risk assessment is a vital part in project management. It is possible that experts may provide comprehensive linguistic preference information in distinct forms with respect to different aspects of the risk assessment problem in investment management. It is a challenge to model and deal with comprehensive linguistic preference assessments in multiple forms given by experts. In this regard, this paper defines the generalised probabilistic linguistic preference relation (GPLPR) to represent different forms of linguistic preference information in a unified structure. Then, a probability cutting method is proposed to simplify the representation of a GPLPR. Afterwards, a graph-theory-based method is developed to improve the consistency degree of a GPLPR. A group decision making method with GPLPRs is then proposed to carry on the risk assessment in project management. Discussions regarding the comparative analysis and managerial insights are given.

The Research on Consistency Checking and Improvement of Probabilistic Linguistic Preference Relation Based on Similarity Measure and Minimum Adjustment Model

In the process of decision making, the probabilistic linguistic term set (PLTS) is a useful tool to express the evaluation information provided by decision makers (DMs). On the basis of PLTS, the probabilistic linguistic preference relation (PLPR) has been proposed, which can well describe the uncertainty of preferences when experts conduct pairwise comparison between any two alternatives. The consistency analysis is an essential process to check whether the preferences are reasonable and logical. For the consistency checking and improvement of PLPR, some methods have been developed to conduct the work. However, the previous methods seldom consider whether the information of original preferences is distorted after the adjustment of inconsistency preferences, and the adjustment processes are complicated in much of the literature. To overcome the defects of existing methods, we developed a novel PLPR consistency analysis model, and this paper mainly contains two sections. On the one hand, a new consistency index and the consistency checking method are proposed based on similarity measure, respectively. On the other hand, based on the idea of minimum adjustment, we constructed an optimization model to improve the consistency level and develop the process of decision making on the basis of consistency analysis. A numerical example about talent recruitment is given to verify the feasibility of the proposed method. We have a comparative analysis with Zhang’s method from many aspects including the decision results, consistency checking and improvement, as well as adjusted preferences, adjustment costs and consistence threshold. At length, the conclusion of this research is that the proposed consistency analysis model is superior to the previous method on the determination of adjustment parameter, as well as the adjustment cost and the retention of original preferences. To show the effectiveness and superiority, we have a comparative analysis with other approaches. At length, the conclusion of this study is drawn.

Managing consistency and consensus measures and adjustment strategies in group decision making with probabilistic linguistic preference relations

The use of probabilistic linguistic preference relations (PLPRs) in pairwise comparisons enhances the flexibility of quantitative decision making. To promote the application of probabilistic linguistic term sets (PLTSs) and PLPRs, this paper introduces the consistency and consensus measures and adjustment strategies to guarantee the rationality of preference information utilized in the group decision making process. First of all, a novel entropy-based similarity measure is developed with PLTSs. Hereafter an improved consistency measure is defined on the basis of the proposed similarity measure, and a convergent algorithm is constructed to deal with the consistency improving process. Furthermore, a similarity-based consensus measure is developed in a given PLPR, and the consensus reaching process is presented to deal with the unacceptable consensus degree. The proposed consistency improving and consensus reaching processes follow a principle of minimum information loss, called a local adjustment strategy. In particular, the presented methods not only overcome the deficiencies in existing studies but also enhance the interpretation and reduce the complexity of the group decision making process. Finally, the proposed consistency measure and improving process, as well as consensus measure and reaching process are verified through a numerical example for the medical plan selection issue. The result and in-depth comparison analysis validate the feasibility and effectiveness of the proposed methods.