Probabilistic Linguistic Term Sets Research Articles

A fuzzy group decision-making framework for computer network security evaluation with probabilistic linguistic information

The computer network security evaluation is a classical multiple attribute group decision making (MAGDM) problems. Recently, the Exponential TODIM TODIM (ExpTODIM) method has been used to cope with MAGDM issues. The probabilistic linguistic term sets (PLTSs) are used as a tool for characterizing uncertain information during the computer network security evaluation. In this manuscript, the probabilistic linguistic ExpTODIM (PL-ExpTODIM) is built to solve the MAGDM under PLTSs. In the end, a numerical case study for computer network security evaluation is given to validate the proposed method. The main contribution of this paper is constructed: (1) the Exponential TODIM TODIM (ExpTODIM) method is extended to the PLTSs; (2) the probabilistic linguistic ExpTODIM (PL-ExpTODIM) method is defined to solve the MAGDM under PLTSs; (3) In the end, a numerical case study for computer network security evaluation is given to validate the proposed method.

A multi-stage group decision making approach for sustainable supplier selection based on probabilistic linguistic time-ordered incentive operator.

This study proposes a novel multi-stage multi-attribute group decision making method under a probabilistic linguistic environment considering the development state and trend of alternatives. First, the probabilistic linguistic term set (PLTS) is used by decision makers (DMs) to describe qualitative evaluation information. Subsequently, the weights of DMs for different attributes in different periods are determined by the credibility degree, which is combined with the hesitancy degree and the similarity degree. The evaluations of different DMs for alternatives and the evaluations of DMs' intentions to reward or punish are then aggregated. Later, the trend change level and the trend change stability of alternatives are measured through the means of reward and punishment incentives. Additionally, the probabilistic linguistic time-ordered incentive operator is proposed to aggregate the development state evaluation information and development trend evaluation information in different periods, and alternatives are prioritized by the extended TOPSIS method in the probabilistic linguistic environment. Finally, the practical use of the proposed decision framework is validated by using a sustainable supplier selection problem, and the effectiveness and the applicability of the framework are discussed through comparative analysis. The results show that the proposed approach can select suitable sustainable suppliers by considering their development state and trend in multiple stages.

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 group consensus model with prospect theory under probabilistic linguistic term sets

The challenges encountered in the realm of multi-attribute group decision-making (MAGDM) involving probabilistic linguistic term sets (PLTSs) have garnered substantial attention. Within the PLTS context, this study introduces a consensus reaching process (CRP) that iteratively refines the weights assigned to decision-makers (DMs) by leveraging the principles of prospect theory (PT). The primary goal of this iterative weight adjustment process is to enhance the overall decision-making procedure when dealing with PLTSs. To circumvent any data loss during transformation and compute the prospect values of PLTSs directly, a novel transformation formula is developed. Acknowledging the distinct cognitive levels among different DMs, the integration of multiple weights into the consensus process is characterized by its dynamic and iterative nature. Concerning the measurement of consensus, this study employs a method based on the gap between prospect values, which enhances objectivity while overcoming the limitations associated with the distance formula of PLTSs. Furthermore, the feedback mechanism incorporated into the modification process incorporates dynamic adjustment parameters that are tailored to different evaluation values, thereby preventing excessive adjustments that are either too low or too high. By utilizing the newly proposed prospect value function, this research aggregates the group evaluation value and identifies the optimal alternative. In conclusion, this paper concludes with a comparative analysis involving various counterparts, shedding light on the feasibility and validity of the proposed model.

A novel integrated approach based on best–worst and VIKOR methods for green supplier selection under multi-granularity extended probabilistic linguistic environment

With consideration for the extensive resources consumption and environmental degradation being on the rise today, implementing green development strategy to pursue both socioeconomic growth and the coordinated of environment sustainability, has become an increasingly important issue in modern enterprise supply chain operations management. Hence, the appropriate green supplier selection (GSS), viewed as a core issue in green supply chain management (GSCM), requires continuous research in this field to obtain a complete perception on GSS practices. It can be regarded as a multi-attribute group decision-making (MAGDM) problem that involves many conflict and unmeasurable evaluation criteria. In view of the superiority of multi-granularity extended probabilistic linguistic term sets (MGEPLTSs) in modeling such issues on potential ambiguity, complexity and uncertainty in actual GSS practices, we propose a novel integrated MAGDM methodology for GSS problems, by integrating the BWM (best–worst method) with the VIKOR (VIšekriterijumsko KOmpromisno Rangiranje) technique under the MGEPLTSs environment. First, by introducing the multi-granularity and probabilistic linguistic term sets, the MGEPLTSs are proposed to represent and quantify the decision information of GSCM practitioners. Then, the BWM is introduced to the MGEPLTSs environment to compute the weights of decision-making panels and evaluation attributes in GSS problems, by building the fuzzy mathematical programming model, respectively. Finally, we extend a multi-granularity extended probabilistic linguistic VIKOR method to calculate the compromise measure of alternatives considering the group utility maximization and the individual regret minimization, thereby achieving the full ranking of alternatives. A GSS case is conducted to illustrate the feasibility of the proposed approach, and the sensitivity analysis and comparative analysis with other similar approaches are presented to demonstrate its effectiveness and advantages.

A multi-attribute decision making method for TODIM based on mixed correlation coefficients for probabilistic linguistic term sets

In the face of multi-attribute decision problems in complex situations, most traditional multi-attribute group decision methods are based on the assumption that the decision maker is perfectly rational, while in the face of complex decision problems, the decision maker usually has the psychological characteristics of limited rationality and may use more than one linguistic term to describe the decision information when expressing the decision information To this end, this paper selects probabilistic language term sets to describe complex preference information. First, to address the problem that the current probabilistic linguistic term set correlation coefficient cannot appropriately measure the degree of correlation among probabilistic linguistic term sets, this paper proposes a new probabilistic linguistic term set correlation coefficient from three characteristic factors of probabilistic linguistic term sets: mean, variance, and length rate. To integrate the attribute index weights, probabilistic linguistic term set weighted mixed correlation coefficients are proposed. Second, this paper introduces the TODIM method, which can consider the psychological behavior of decision makers, and proposes a TODIM multi-attribute decision making method based on probabilistic linguistic term sets with mixed correlation coefficients. Finally, through an empirical analysis of four Internet listed companies in a new first-tier city in China, this study verifies the rationality and validity of the proposed method. The results show that the mixed correlation coefficient can comprehensively measure the correlation between probabilistic linguistic term sets, which provides an important method for future multi-attribute decision making problems.

The multi-stage evaluation framework for low-carbon development level of rail transit under probabilistic linguistic environment

The scientific evaluation of the low-carbon development level of rail transits is an important prerequisite for their scientific low-carbon transformation, and how to scientifically evaluate it is a problem that needs to be studied. This article first constructs an evaluation index system that includes 4 evaluation attributes and 11 evaluation criteria based on the reality of low-carbon development in rail transit. Then, aiming at the uncertainty of evaluation information and the fluctuation of evaluation results in the evaluation of low-carbon development of rail transits, a multi-stage evaluation model is constructed based on probabilistic linguistic term set, TOPSIS model principle and multi-stage decision theory. The above evaluation index system and evaluation model together constitute a multi-stage evaluation framework for low carbon development level of rail transits. The results of the case study show that the evaluation index system can provide scientific guidance for the low-carbon development level evaluation of rail transits, and the multi-stage evaluation model can improve the robustness and reduce the fluctuation of the evaluation results, so as to improve the scientificity of the evaluation results.

An Extended TODIM Method and Applications for Multi-Attribute Group Decision-Making Based on Bonferroni Mean Operators under Probabilistic Linguistic Term Sets

Due to the complexity and uncertainty of decision-making, probabilistic linguistic term sets (PLTSs) are currently important tools for qualitative evaluation of decision-makers. The asymmetry of evaluation information can easily lead to the loss of subjective preference information for decision-makers, and the existing operation of decision-maker evaluation information fusion operators is difficult to solve this problem. To solve such problems, this paper proposes some new operational methods for PLTSs based on Dombi T-conorm and T-norm. Considering the interrelationships between the input independent variables of PLTSs, the probabilistic linguistic weighted Dombi Bonferroni mean Power average (PLWDBMPA) operators are extended and the properties of these aggregation operators are proposed. Secondly, the PLWDBMPA operator is used to fuse the evaluation information of decision-makers, avoiding the loss of decision information as much as possible. This paper uses social media platforms and web crawler technology to obtain online comments from users on decision-making to obtain the public’s attitude towards decision events. TF-IDF and Word2Vec are used to calculate the weight of alternatives on each attribute. Under traditional group decision-making methods and integrating the wisdom of the public, a novel multi-attribute group decision-making method based on TODIM method is proposed. Finally, the case study of Turkey earthquake shelter selection proves this method is scientific and effective. Meanwhile, the superiority of this method was further verified through comparisons with the PL-TOPSIS, PLWA, SPOTIS and PROMETHEE method.

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.

Assessing the impact of healthcare service risks on healthcare demand under evolving economic and social structures: An improved GLDS decision making method considering risk attitudes

Faced with backward and uneven economic conditions and an irrational and increasingly inequitable social structure, healthcare disparities are widening and the healthcare inequalities are expanding. This can lead to an increasing public demand for healthcare services, posing unprecedented risk, such as resource shortages, quality deterioration and rising healthcare costs. By identifying, managing, and optimizing the aforementioned risks within the healthcare system, it helps the healthcare system better address the challenges of expanding healthcare demands under evolving economic and social structure. To achieve this, this paper employs failure mode and effects analysis (FMEA) to identify severe failure modes in healthcare services. However, traditional FMEA methods possess limitations in assessing the dynamics of trust relationships and interaction effects among experts within social networks. Therefore, this paper proposes an improved gained and lost dominance score (GLDS) based social network decision-making method considering risk attitudes for FMEA to prioritize failure modes in healthcare services. First, transform linguistic risk assessment information from an interdisciplinary team of experts based on probabilistic linguistic term sets handle uncertain efficiently. Meanwhile, experts’ influence is reflected by an extended PageRank algorithm with trust degrees based on social networks analysis. Next, an improved GLDS method considering the differentiated risk attitudes of individuals and groups is developed to prioritize failure modes. Especially, to solve the problems of soft preference and incomparability relation among failure modes, which are ignored by the traditional GLDS method, a conflict analysis is established to determine the preference, indifference, and incomparability relations. Finally, the practicality of the proposed method is illustrated by the healthcare service risk case in the emergency department and the effectiveness of the developed method is validated by comparison and sensitivity experiments. The results suggest that failure to update labels showing patient severity promptly is the most dangerous. In addition, it would be more economically efficient to analyze the non-comparable failure modes facing different risk factors.

A novel approach to employment quality evaluation of college graduates with probabilistic linguistic MAGDM

With the continuous extension and deepening of college education reform, the research on the future employment of college students and the evaluation of employment quality has become a major focus topic. The traditional evaluation system for the employment quality of college graduates is relatively outdated and unitary, lacking a vision of the future development status of college graduates, as well as an effective understanding and mastery of the overall feedback and evaluation of the entire employment market for college graduates. Moreover, most colleges and universities mainly focus on the level of competence that college graduates should achieve five years after graduation from college in terms of talent cultivation goals, The lack of specific evaluation work for long-term employment tracking of graduates has resulted in universities being unable to grasp and understand the degree of fit and matching between the comprehensive abilities of university graduates and the future employment market, and thus unable to provide effective feedback and summary of talent cultivation and innovation strategies. Therefore, it is imperative to comprehensively innovate the employment quality evaluation system and methods for college graduates. The employment quality evaluation of college graduates is a classical multiple attribute group decision making (MAGDM) problems. Recently, the TODIM and VIKOR method has been used to cope with MAGDM issues. The probabilistic linguistic term sets (PLTSs) are used as a tool for characterizing uncertain information during the employment quality evaluation of college graduates. In this manuscript, the probabilistic linguistic TODIM-VIKOR (PL-TODIM-VIKOR) method is built to solve the MAGDM under PLTSs. In the end, a numerical case study for employment quality evaluation of college graduates is given to validate the proposed method.

A novel FMEA approach based on probabilistic linguistic best-worst method and TOPSIS with application to marine diesel fuel injection system

The failure mode and effect analysis (FMEA) is an effective tool to analyze risks and potential effects of complex systems, and it is one of the most widely used risk analysis methods for complex systems as there often exists various factors that could affect the operation of the complex systems. Conventional FMEA methods have been limited to using crisp values to represent the assessments, which has been criticized for having many deficiencies. Marine diesel fuel injection system is an important part of marine diesel engine, and its failure could directly affect the performance of the marine diesel engine and even impact the safe operation of the ship. However, little attention has been paid to the FMEA of the marine diesel fuel injection system. To this end, this paper presents a novel FMEA method based on the best-worst method (BWM) and TOPSIS method with probabilistic linguistic term set (PLTS). Firstly, the PLTS is used to represent the uncertain and linguistic judgments of experts. Then, the BWM is extended with PLTS to determine the weights of different elements for FMEA, and the TOPSIS is extended with PLTS to assess and rank different failure modes. Finally, a case study on marine diesel fuel injection is presented, and the most critical failures are identified for improvement measures. The results show that the proposed method could help managers and engineerings identify the most important failure modes for marine diesel fuel injection system.

MABAC method based on cumulative prospect theory for MCGDM with dual probabilistic linguistic term set and applications to sustainable supplier selection

Dual probabilistic linguistic term set (DPLTS) is a new proposed decision-making environment. It uses probabilistic form to represent the appraisal of the alternative from decision makers. There are few methods to deal with DPLTS according to the literature proposed up to now. The purpose of this article is to proposed a new improved Multi-Attribute Border Approximation Area Comparison (MABAC) method extended by cumulative prospect theory (CPT) and combined with DPLTS to address the multi-criteria group decision-making (MCGDM) problem of sustainable supplier selection. In order to make the decision procedure containing more fuzzy information, we also improved the equation of distance between DPLTSs with system of rectangular coordinates. This new improved MABAC method is combined with CPT and it is semi-objective method. Not only in the procedure of calculating distance between alternatives and border approximation area, but also in the procedure of determining the weights of attributes. At the end of this paper, the comparison of this new method with other proposed DPLTS methods, such as Correlation Coefficient Method and DPLTS-TODIM-CRITIC Method, demonstrates the availability and difference.

A fuzzy decision support model for online review-driven hotel selection by considering risk attitudes of customers

Online hotel reviews provide a vital information source for customers to select an optimal hotel, but a large amount of vague and unstructured information increases the difficulty of decision-making. From the perspective of customers’ risk attitudes, this paper proposes a novel fuzzy decision support model for hotel selection based on online reviews. Firstly, the useful information from online reviews is extracted by attribute extraction and sentiment analysis, and then this information is aggregated into the Probabilistic Linguistic Term Set (PLTS) by considering the weight of each review. Secondly, the improved linguistic scale functions are constructed from the perspective of customers’ risk attitude to convert PLTS into quantitative information. Thirdly, an integrated attribute weighting method is presented based on objective weights of the statistical measure and subjective weights of the Analytic Hierarchy Process (AHP) technique. Fourthly, an extended Combinative Distance-based Assessment (CODAS) method is developed to evaluate the performances of hotels. The effectiveness of the proposed model is verified by the practical case from TripAdvisor.com and the comparative analysis with the existing methods.

A Probabilistic Linguistic Three-Way Decision Method With Regret Theory via Fuzzy c-Means Clustering Algorithm

Aiming at multi-attribute decision-making (MADM) problems with probabilistic linguistic term sets (PLTSs), and considering the effective rationality of a decision-maker (DM) in complex decision environments, this paper proposes a probabilistic linguistic three-way decision (TWD) method based on the regret theory (RT), namely PL-TWDR. First, a probabilistic linguistic attribute weight determination method is developed that considers probabilistic linguistic information entropies and the weighted total deviation of all objects from the negative ideal solution (NIS). Then, a new group satisfaction index is designed to replace the utility function in RT, which overcomes the limitation of the RT calculation in PLTSs. Second, the fuzzy c-means (FCM) algorithm is extended to PLTSs for obtaining equivalent objects under different clusters and calculate conditional probabilities in corresponding TWD models, which makes up for the shortage of the PLTS evaluation matrix when dividing equivalence classes. Third, RT is introduced into PLTSs to rank objects according to utility perception values. At the same time, a new TWD model constructed by average utility perception values is used to realize object domains in probabilistic linguistic environments. Finally, the proposed method is applied to realistic cases, and the effectiveness and superiority of the PL-TWDR method are verified via comparative analysis and sensitivity analysis in terms of other nine popular decision-making methods.

A trust-based quantum probabilistic linguistic multi-criteria group decision making model considering interference effect

In group decision-making (GDM), there exist cognitive and realistic uncertainties and humans exhibit hesitation and ambiguity. Using probabilistic linguistic term sets (PLTSs) can better adapt to the above challenges. However, the current PLTS-based methods rarely take the subjectivity and behavior of experts into account, especially the influence of trust relations and subjective beliefs. This paper combines the trust network and the quantum probability theory (QPT) in GDM, and proposes a new probabilistic linguistic multi-criteria group decision-making (MCGDM) model considering the trust relationships and the interference effects between experts. Firstly, probabilistic linguistic evaluations and trust information are collected. Then, the entropy-weight method based on PLTS is proposed to determine criterion weights. A new mixed multi-path trust transfer aggregation operator that integrates both the path length and the path quality is defined, to establish a complete trust network and measure the expert weight. Thirdly, because of the certain interference between experts, a quantum-like Bayesian network framework is built to aggregate the opinions of experts. During the process, the system is in a superposition state, and personal opinions are regarded as interfering wave functions, affecting the final results. Finally, an example of the prevention and control of COVID-19 in a city is used for verification and sensitivity and comparison analyses are provided to verify the effectiveness of the method.

An integrated model for occupational health and safety risk assessment based on probabilistic linguistic information and social network consensus analysis

As a critical activity in occupational risk management, the occupational health and safety risk assessment (OHSRA) aims at assessing occupational hazards in the workplace and prioritizing them to ensure employees’ safety and reduce occupational risk to an acceptable level. In this paper, we develop a new integrated OHSRA model for the risk evaluation and prioritization of occupational hazards based on probabilistic linguistic information and social network consensus analysis. The probabilistic linguistic term sets are applied to handle the hesitant risk evaluations of occupational hazards provided by experts. A combinative distance-based assessment technique is introduced for determining the risk priority of the identified occupational hazards. Additionally, the social network consensus analysis with minimum adjustment distance is used to help individual experts reach consensus. Finally, a healthcare case study is implemented for illustrating the developed OHSRA model and its effectiveness is validated with a sensitivity analysis and a comparative analysis.

A multi-subgroup decision-making method for design selection based on subjective reports and objective physiological index data

Selecting an optimal product design scheme requires considering multiple criteria and engaging the wisdom of crowds. However, existing studies regarding design selection rarely considered the participation of group wisdom, and few studies considered subjective reports and physiological index data comprehensively for evaluation. This study developed a multi-subgroup decision-making method based on the participation of designers, experts, and customers. Multi-modal aggregation strategies are applied to aggregate subjective evaluations of both individuals and groups represented in probabilistic linguistic term sets (PLTSs), objective eye movement, and Electroencephalogram feature data. Specifically, a probabilistic linguistic information aggregation operator based on the Choquet integral is proposed to aggregate the values of subjective criteria with correlations, and the double normalization-based multi-aggregation method is then applied to aggregate objective criteria values, which can avoid information loss in the normalization and aggregation. Finally, the Choquet integral-based Borda operator is developed to integrate the evaluation results of multiple subgroups. An example of evaluating intelligent shared vehicle design schemes is presented to validate the proposed method.

A dynamic emergency response decision-making method considering the scenario evolution of maritime emergencies

In order to reduce the losses caused by maritime emergencies, it is crucial to select an alternative for timely response after the occurrence of maritime emergencies. However, maritime emergencies involve uncertainty, complexity, and information incompleteness within the scenario evolution process, making it difficult for decision-makers to evaluate with crisp numbers in a completely rational situation. Moreover, decision-makers need to dynamically adjust the emergency response based on the changing scenario. In response, this paper proposes a novel dynamic emergency response decision-making method that not only deals with the problem of fuzzy decision-making under bounded rationality, but also ameliorates the effects of early evaluations within the dynamic adjustment process on later decisions. Specifically, the decision-makers’ evaluations of alternatives in a hesitant fuzzy environment are represented as probabilistic linguistic term sets (PLTSs). Subsequently, a new dissimilarity measure for the PLTSs based on the Jensen-Shannon divergence is proposed and combined with prospect theory (PT), which describes the decision-makers’ psychological behavior. From this, a new static rating calculation method is developed. Furthermore, a static rating-based, dynamic rating method that can reflect the historical evolution of alternatives is put forward to rank alternatives in order to determine the best response option. Finally, an example of a maritime accident is applied to illustrate the feasibility of the proposed method, and a comparative analysis is performed to validate its effectiveness as a decision-making support tool for maritime emergency managers.

A method for product appearance design evaluation based on heterogeneous data

The eye-tracking and electroencephalogram data, as physiological information, have been viewed as effective supplements to subjective reporting for guiding the product appearance design. In this context, how to combine heterogeneous information is a challenging question. This study proposes different methods to determine subjective and objective weights of criteria regarding the self-reporting, eye-tracking, and electroencephalogram data for the evaluation of product appearance design. We introduce the probabilistic linguistic term set with interval uncertainty (IUPLTS) to represent complex self-reporting data, and develop a method to aggregate IUPLTSs. An algorithm is proposed to fuse physiological data on the data layer and feature layer. To combine the obtained heterogeneous information, we define an objective weighting method that examines the differences in indicator data and the correlation between indicators, and then use a level difference maximization model to fuse subjective and objective weights. To ensure the stability of decision-making results for the problem involving a large number of indicators, we use the Measurement of Alternatives and Ranking according to the Compromise Solution (MARCOS) to rank alternatives. An example regarding the evaluation of automobile appearance design schemes is presented to show the validity and practicality of the proposed method. The prototype support system of the proposed method has been developed and is freely available at https://github.com/BitSecret/DAQQSO.