Linguistic Preference Relations Research Articles

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

A two-stage consensus model based on personalized individual semantics under linguistic preference relations with self-confidence

Linguistic preference relations with self-confidence (LPRs-SC) are the preference relation that can reflect the decision maker’s (DM) confidence psychology and has received widespread attention for their simple form and multiple information. Currently, arithmetic studies of LPRs-SC are conducted separately for preference relations and self-confidence. In addition, personalized individual semantics (PIS) is an important tool in large-scale decision-making to reflect the differences in the semantic understanding of DMs. However, the confidence level in LPRs-SC limits the preference relation to a certain extent and the linguistic representations of these two components are usually different. This means that it is not only necessary to propose an arithmetic rule that can express the restrictive relationship between the two but also to construct a model that can extract the PIS of preference relation and confidence respectively. Besides, we constructed a two-stage consensus reaching process (CRP) based on the specificity of the LPRs-SC structure when enhancing group harmony. The process takes self-confidence as an independent source of information, delineates the adjusted categories in detail, and builds an adjustment model accordingly. Finally, the example and comparative analyses verify the merits of the proposed PIS in terms of consistency enhancement and CRP in terms of speed and accuracy harmonization.

Constructing order-2 information granules of linguistic expressions with the aid of the principle of justifiable granularity

To capture collective opinions/evaluations in a collection of individual linguistic expressions, this study proposes an approach to construct order-2 information granules by extending the numerical data-based principles of justifiable granularity to a linguistic data-based one. First, the two key criteria of the principle of justifiable granularity, namely coverage and specificity, are formally defined in the context of order-2 information granules. Second, three order-2 information granules construction models by maximizing the product of coverage and specificity are developed for coping with one-dimensional direct linguistic expressions, linguistic preference relations, and multi-dimensional direct linguistic expressions, respectively. Third, considering that the developed order-2 information granules construction models exhibit a non-linear uncertain objective function and equality constraints, the constrained multi-swarm PSO without velocity is improved with the use of the ε constrained handling technique for effectively solving the models. Case studies on the considered three types of linguistic expressions show the applicability of the proposed models and ensuing algorithm. The superiority of the improved algorithm in handling the proposed models is demonstrated by comparison with the original one. The effectiveness of the proposed models in terms of abnormal corrective ability and balance of coverage and specificity is verified by comparing with a family of Top-n methods. The originality of this study lies in the construction of an operational entity, namely order-2 information granule, that reflects the group opinion without specifying the formalism of individual linguistic expressions, which provides an effective and efficient way to aggregate ubiquitous linguistic information for subsequent computation, reasoning and decision-making.

Measuring Additive Consistency of Linguistic Preference Relations in a Personalized-Individual-Semantics Context: A Systematic Investigation With Axiomatic Design

Measuring Additive Consistency of Linguistic Preference Relations in a Personalized-Individual-Semantics Context: A Systematic Investigation With Axiomatic Design

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.

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.

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.

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.

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.

A statistical approach to large-scale group decision making with incomplete hesitant fuzzy linguistic information by incorporating risk attitude

In response to the lack of information and the arguments among the decision-makers (DMs) in large-scale group decision making (LSGDM), this study proposes a method that integrates decision risk and risk attitude into LSGDM with hesitant fuzzy linguistic preference relations (HFLPRs) based on statistical estimation. Firstly, the DMs are arranged into several subgroups via their risk attitudes. Next, the whole or part of the five-number summary for subgroups from incomplete information provided by DMs are collected. After that, the optimization model and Monte Carlo simulation are utilized to obtain mean and standard deviation estimators of the decision information, and the mean estimator is regarded as the evaluation information of subgroup. Then, the hesitant fuzzy linguistic term sets (HFLTSs) with different number of linguistic variables are normalized according to their risk attitudes and confidence interval. Meanwhile, the number of members in subgroups and the decision risk level of subgroups are combined to determine the weights of subgroups. Moreover, a minimum deviation model is derived to rank alternatives. Finally, a case study, sensitivity analysis and comparison are used to guarantee the rationality and availability of the proposed method.

Fuzzy C-means clustering with hesitant fuzzy linguistic preference relation

With the advancement of technology and growing social demand, large scale group decision making has gained significant importance in the field of decision making. Clustering analysis plays a crucial role in enhancing the efficiency of large scale group decision making processes. Linguistic evaluation is more in line with people’s cognitive and expressive habits. The hesitant fuzzy linguistic term set (HFLTS) offers more flexibility in expressing evaluation information. This paper is dedicated to designing a fuzzy C-means clustering model that is specifically applicable for the hesitant fuzzy linguistic preference relation (HFLPR). The objective function of the model is built based on the dissimilarity between HFLPRs and the initial cluster centers to obtain the fuzzy membership matrix and cluster centers. Since initializing cluster centers is a crucial step to produce a reasonable cluster result, three methods are proposed for generating initial centers for HFLPRs. The first and second methods are improvements over existing approaches that dealt with the clustering problem with numerical values. The third approach considers both the preference relation of preferring an alternative and the distribution of the actual preference relations. Based on this, a fuzzy C-means clustering algorithm with HFLPR is designed to obtain the cluster centers and membership matrix for there types of initializing clustering centers. Finally, based on the quality and speed of clustering, a numerical example and comparative analyses illustrate that the proposed clustering algorithm is efficient and effective.

Consistency improvement under incomplete hesitant fuzzy linguistic preference relations in large-scale group decision-making

This paper studies a large-scale group decision-making method (LSGMD) based on incomplete hesitant fuzzy linguistic preference relations (IHFLPRs) and proposes an improved model for additive consistency of hesitant fuzzy linguistic preference relations (HFLPRs). Additionally, consistency control and fuzzy C-means (FCM) clustering are utilized to enhance efficiency and reliability. Firstly, a model is proposed to address the issues of missing elements in IHFLPRs and insufficient additive consistency in HFLPRs, aiming to more accurately reflect decision makers’ preference relationships towards candidate alternatives. Subsequently, the FCM method is employed to cluster decision experts’ preference information and obtain the overall preference information. Finally, the rationality and accuracy of our proposed method are demonstrated through a case study and comparative analysis.

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.

A social network analysis-based model for failure mode and effect analysis under linguistic preference relation environment

Failure mode and effect analysis (FMEA) is a proactive risk analysis technique widely used to improve the reliability and safety of complex systems in various industries. Generally, FMEA is a multidisciplinary team activity in which the trust relationships among experts have an influence on the risk assessment process and the risk priority of failure items. Furthermore, it is significant to obtain the risk ranking result of failure items with a high consistency degree in the group FMEA. Therefore, in this study, we aim to develop a new FMEA model based on double hierarchy hesitant linguistic preference relations to derive the risk priority of failure items considering experts' social network. First, the risk assessments of experts are described by using the double hierarchy hesitant linguistic preference relations via pairwise comparisons of failure items. Second, the relative weights of FMEA experts are derived based on their trust relationships in social network and the consistency of failure risk evaluations. Third, consistency checking and repairing algorithm are performed to address experts’ self-contradictory opinions, and the risk priority of failure items is determined in line with their risk degrees. Finally, a practical risk evaluation case is provided to demonstrate the applicability of the proposed FMEA model, and a comparative analysis is conducted to illustrate its effectiveness and advantages.

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

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

A novel Group Decision Making method with the prediction selection rate

Methods on the basis of the consensus reaching process are prevalent in Group Decision Making (GDM), which typically forces some evaluators to revise initial opinions in order to reach group consensus without being able to precisely reflect original viewpoints. Furthermore, in case the correct opinion is embedded in the hand of the minority, existing methods may not reach the correct consensus. With the aim to tackle these observations, a novel approach of the Positive and Negative Prediction Selection Rate (PNPSR) is proposed on the basis of the Pythagorean Fuzzy Preference Relation (PFPR) which enables to present individuals’ opinions in a pairwise manner using the linguistic preference relation. The PFPR expressed opinions then serve as input for the computation of the proposed PNPSR, the minimum of which is subsequently selected as the correct one. Finally, the full ranking of the alternatives can be calculated through the proposed iterative algorithm. In the process, the evaluators’ original opinions are not required to modify, and the correct result can be achieved when the minority evaluators provide the correct opinions. Experimental results demonstrate the efficacy of the proposed approach in comparison with two state-of-the-art methods.

An indirect multicriteria group decision-making method with heterogeneous preference relations and reliabilities of decision-makers

This study proposes a new indirect method to solve multicriteria group decision-making (MCGDM) problems with heterogeneous preference relations and decision-makers’ reliabilities. To unify the heterogeneous preference relations, the transformation of multiplicative preference relations (MPRs), fuzzy preference relations (FPRs), intuitionistic fuzzy preference relations (IFPRs), and linguistic preference relations (LPRs) into distributed preference relations (DPRs) is analyzed. As consistency among DPRs is constructed under the assumption that decision-makers are bounded rationality, the abstract transformation of MPR, FPR, IFPR, and LPR into DPR is defined, and its reality depends on the preferences of decision-makers. Two important properties of abstract transformation, namely, internal consistency and restricted max-max transitivity, were theoretically verified. The reliabilities of decision-makers are involved in MCGDM by estimating the reliability of each criterion to improve solution quality. Based on the four types of abstract transformations, a process for analyzing MCGDM problems with heterogeneous preference relations and decision-makers’ reliabilities is developed. The proposed method is used to analyze a new business selection problem for an enterprise located in Changzhou, Jiangsu, China to demonstrate its applicability and validity.

Coming to Consensus on Classification in Flexible Linguistic Preference Relations: The Role of Personalized Individual Semantics

Coming to Consensus on Classification in Flexible Linguistic Preference Relations: The Role of Personalized Individual Semantics

A Large-Scale Group Decision-Making Approach to Assess Water Resource Sustainability with Double-Level Linguistic Preference Relation

With the rapid development of science and technology and the continuous progress of society, water resource sustainability has attracted much attention. The assessment process of water resource sustainability has become a hot topic. Because professional models cannot ensure the accuracy of evaluation results, expert judgment techniques are used to perform the assessment process. Meanwhile, to eliminate the biases and consider people’s cognitive processes in complex decision making, this study utilizes a large group of experts to evaluate the sustainability of water resources, which is called a large-scale group water resource sustainability assessment (LGWRSA). This study proposes the double-level linguistic preference relation (DLLPR) to enable experts to present more reasonable and intuitive linguistic opinions. Based on the DLLPR, this study presents a clustering method, a weighting method, and a comprehensive adjustment factor determination method. To prevent minority opinions and non-cooperative behaviors from interfering with the decision-making process and to make the decision-making process develop in an accurate and objective direction, a consensus model is developed to modify minority opinions and suggestions and manage non-cooperative behaviors. After a sufficient number of experts reach a consensus through the method proposed in this article, a more accurate evaluation result can be obtained. Finally, an actual LGWRSA problem is established to derive water resource sustainability expectations for four provinces, which validates the effectiveness of the proposed method. A comparative analysis is performed to illustrate the benefits of these methods and present their shortcomings.