Probabilistic Linguistic Information Research Articles

Integrated BWM-Entropy weighting and MULTIMOORA method with probabilistic linguistic information for the evaluation of Waste Recycling Apps

Integrated BWM-Entropy weighting and MULTIMOORA method with probabilistic linguistic information for the evaluation of Waste Recycling Apps

Cloud vendor selection for the healthcare industry using a big data-driven decision model with probabilistic linguistic information.

The role of cloud services in the data-intensive industry is indispensable. Cision recently reported that the cloud market would grow to 55 billion USD, with an active contribution of the cloud to healthcare around 2025. Inspired by the report, cloud vendors expand their market and the quality of services to seek growth globally. The rapid growth of the cloud sector in the healthcare industry imposes a challenge: making a rational choice of a cloud vendor (CV) out of a diverse set of vendors. Typically, the healthcare industry 4.0 sees the issue as a large-scale group decision-making problem. Previous studies on a CV selection face certain challenges, such as (i) a lack of the ability to handle multiple users’ views, as well as experts’/users’ complex linguistic views; (ii) the confidence level associated with a view is not considered; (iii) the transformation of multiple users’ views into holistic data is lacking; and (iv) the systematic prioritization of CVs with minimum human intervention is a crucial task. Motivated by these challenges and circumventing them, a new big data-driven decision model is put forward in this paper. Initially, the data in the form of complex expressions are collected from multiple cloud users and are further transformed into a holistic decision matrix by adopting probabilistic linguistic information (PLI). PLI represents complex linguistic expressions along with the associated confidence levels. Later, a holistic decision matrix is formed with the missing values imputed by proposing an imputation algorithm. Furthermore, the criteria weights are determined by using a newly proposed mathematical model and partial information. Finally, the evaluation based on the distance from average solution (EDAS) approach is extended to PLI for the rational ranking of CVs. A real-time example of a CV selection for a healthcare center in India is exemplified so as to demonstrate the usefulness of the model, and the comparison reveals the merits and limitations of the model.

SUSTAINABLE MEDICAL SUPPLIER SELECTION BASED ON MULTI-GRANULARITY PROBABILISTIC LINGUISTIC TERM SETS

The sustainable medical supplier selection (SMSS) is an important issue facing the medical industry in the context of sustainable development, which can be regarded as a typical multi-attribute group decision making (MAGDM) problem. In the MAGDM process, linguistic term set (LTS) is particularly natural and convenient for decision makers (DMs) to express evaluation information. Especially, probabilistic linguistic term set (PLTS) is a very critical and effective tool, which can reflect the importance of different linguistic terms. Due to the different preferences and experience of different DMs, they may use multi-granularity probabilistic linguistic term sets (MGPLTSs) to represent different linguistic information. In this article, in order to study the comparison method of MGPLTSs, a new possibility degree formula is firstly proposed and its properties is proved. Then, in order to build a weight model, a possibility degree-based Best-Worst method (BWM) and a probability degree based-maximizing deviation method are established to calculate the subjective weights and objective weights of attributes, respectively. Where after, a MAGDM method is proposed by combining the ELimination Et Choix Traduisant la REalite (ELECTRE) method with Evaluation based on Distance from Average Solution (EDAS) method in the multi-granularity probabilistic linguistic information environment. Finally, the created MAGDM method is applied to the SMSS, and its effectiveness and advantages compared with other existing methods are verified.

An extended VIKOR method based on particle swarm optimization and novel operations of probabilistic linguistic term sets for multicriteria group decision‐making problem

This paper proposes an extended VlseKriterijuska Optimizacija I Komoromisno Resenje (VIKOR) method based on the particle swarm optimization (PSO) algorithm for solving multicriteria group decision-making problems with probabilistic linguistic information. First, we define the novel operations of probabilistic linguistic term sets and then prove the corresponding properties. Second, we apply a modified PSO algorithm to the consensus reaching process to improve the collective consensus level. In the context of probabilistic linguistic information, each participant can be recognized as a particle moving towards the best position. The consensus level can be regarded as the objective function that is used to construct the fitness function. In the update function, the trust relationship and the similarity measure between experts are exploited to determine the adjustment coefficient. The new consensus model based on PSO can ensure that the ultimate evaluation achieves a high level of consensus. Afterward, we propose the extended VIKOR method to obtain the optimal solution, which not only avoids the loss of decision information, but also considers the separation of each alternative from the positive ideal solution and the negative ideal solution when criteria are interactive. The advantages of the proposed method are highlighted through a numerical example. Finally, we perform a comparative analysis and a sensitivity analysis to reveal the effectiveness and applicability of the method.

Evaluate the locations for smart waste bins using BWM and WASPAS methods under a probabilistic linguistic environment

The decreasing resources of the earth and the deterioration of the environment are offering new challenges for handling waste management practices. The establishment of the smart waste bins plays an important role in promoting the development of waste classification and treatment fundamentally. We developed the evaluation system for the location selection problem of smart waste bins. Considering the uncertainty in the location selection of smart waste bins, the probabilistic linguistic term sets (PLTSs) are selected to express the evaluation information. Because of the excellent performance in weight-determing, the best worst method (BWM) is chosen to get the weight of criteria. While the weighted aggregated sum product assessment (WASPAS) method could handle both the qualitative and quantitative information, which are considered to derive the final ranking of the alternatives. This paper proposed a new group multi-criteria decision making approach integrating the BWM and the WASPAS with probabilistic linguistic information. Finally, in the empirical example, a sensitivity analysis shows that the proposed method is stable, a comparison analysis with PL-TOPSIS, PL-VIKOR, and PL-TODIM reflects its effectiveness and rationality, and the managerial implication verifies its usefulness and practicability, which also give guide to the company, government and resident.

A Maximum Consensus Improvement Method for Group Decision Making Under Social Network with Probabilistic Linguistic Information

A Maximum Consensus Improvement Method for Group Decision Making Under Social Network with Probabilistic Linguistic Information

Clustering analysis and punishment‐driven consensus‐reaching process for probabilistic linguistic large‐group decision‐making with application to car‐sharing platform selection

AbstractProbabilistic linguistic large‐group decision‐making (LGDM) is becoming a hot topic in the field of decision science. In general, clustering and consensus‐reaching are the two important processes to deal with LGDM problems. Traditional clustering methods are mainly based on opinion similarity measures and cannot directly control the number of decision makers (DMs) that can be contained in a cluster. Situations of noncooperative behavior toward consensus may be encountered during the consensus‐reaching process. This paper first proposes a distance‐to‐center clustering algorithm to classify the large group. The most important characteristic of the algorithm is that it is based on similarity measures of probabilistic linguistic information, and specifies the upper and lower limits on the number of DMs in the cluster. Then, a novel weight‐determining method is developed that considers the size, external consensus level, and inner consensus level of a cluster. A punishment‐driven consensus model is designed to manage opinion differences and noncooperative behaviors. Finally, the proposed clustering algorithm and consensus model are applied to a case study of car‐sharing platform selection. The results and comparative analysis reveal the potential application and effectiveness of this study.

How to process local and global consensus? A large-scale group decision making model based on social network analysis with probabilistic linguistic information

With the rapid development of societal and technological paradigms, large-scale group decision making becomes an emerging topic. In conventional group decision making methods, it is often assumed that all experts are independent. However, with the expansion of social media, experts usually have some relationships and get together for some reasons such as the academic relationship, working relationship or common interests. In these cases, experts are no longer independent individuals. To address the issue, this study introduces a large-scale group decision making model based on the social network analysis. In this model, experts can provide trust values on other experts. Due to the scale and complexity of the large-scale group decision making problems, the dimensional reduction, which uses community detection to classify experts into local communities, is deemed essential. Based on this process, the whole group can be divided into two layers. The first layer is the global network containing all communities, and the second layer is the local network within a community. This study develops a model to address large-scale group decision-making problems considering the local and global consensus in two layers simultaneously. This model allows experts to use probabilistic linguistic preference relations to express their cognitive complex evaluation information. An illustrative example is presented to show the usefulness of the proposed model.

Value-Driven Multiple Criteria Sorting with Probabilistic Linguistic Information Considering Uncertain Assignment Examples

Multiple criteria sorting (MCS) dedicates to assigning alternatives to one of the predefined ordered categories according to their evaluation information on multiple criteria. The utility (value) function-based sorting is a popular MCS procedure, which requires decision-makers to express their preferences through assignment examples. By taking the assignment examples as reference alternatives, the additive value function, as the preferred model of a decision maker, can be built using the preference disaggregation technique. However, the existing literature hardly considered people’s hesitancy when determining assignment examples, and ignored applying linguistic evaluation information on qualitative criteria. To fill these research gaps, this study proposes a value-driven MCS procedure with probabilistic linguistic information considering uncertain assignment examples. Specifically, the probability linguistic term set, as a flexible information representation tool, is introduced to express the hesitancy of decision-makers regarding assignment examples and the performance of alternatives on qualitative criteria. Besides, to comprehensively reflect the preference of a decision-maker, a weighted additive value function is proposed based on the preference disaggregation technique to calculate the comprehensive scores of alternatives in which the weights are determined by the best-worst method. Finally, a case study on the sorting of down coats for sale demonstrates the applicability and superiority of our proposed method.

An improved DPoS consensus mechanism in blockchain based on PLTS for the smart autonomous multi-robot system

Due to the development of robot technology, smart autonomous multi-robot systems face different security problems such as data loss and vulnerabilities. However, the robot information stored in blockchain can be more transparent and effective at ensuring the security of the robot system due to the decentralization, tamper-proof and anonymity of blockchain. In the architectural composition of blockchain, Delegated Proof of Stake (DPoS) consensus mechanism is playing a critical role with more decentralization, lower energy consumption and faster confirmation speed. Similar to the board voting, the holders cast a certain number of delegates to perform verification and block generating on their behalf in DPoS. In order to improve the efficiency and flexibility of DPoS consensus mechanism, we propose an improved DPoS consensus mechanism based on the Probabilistic Linguistic Term Set (PLTS) for the smart autonomous multi-robot system. By adding voting options for nodes, the Voting Algorithm with Probabilistic Linguistic Information (VAPLI) calculates the score and deviation degree of each node after tabulating the voting results. The selection of a delegate is based on the comparison of the score and deviation degree. Finally, we explore the model implementation of the improved DPoS consensus mechanism, and verify its feasibility and effectiveness using examples.

A probabilistic linguistic dominance score method considering individual semantics and psychological behavior of decision makers

Psychological behavior could play a key role in many decision-making situations, therefore introducing it into the decision-making process might lead to better decisions being made. In those decision-making problems with uncertainty that are modelled by probabilistic linguistic information, the semantics of such information could be interpreted in different ways by different decision makers (DMs). Consequently, this paper aims at developing a prospect theory (PT) based on the gained and lost dominance score (GLDS) method for probabilistic linguistic multi-attribute group decision-making (MAGDM) to consider both individual semantics and DMs’ psychological behavior. As such, a new similarity degree is introduced to determine DMs’ weights and two programming models are constructed to obtain the individual numerical scales of linguistic terms and optimal individual weights of attributes. Then, the DMs’ psychological behavior is reflected by defining the individual prospect gained and lost dominance scores of alternatives on the basis of PT. The individual prospect dominance scores of alternatives are aggregated into collective prospect dominance scores of alternatives and the collective ranking of alternatives is then generated. Finally, an emission reduction device supplier selection example is analyzed and comparison analyses show the superiority and effectiveness of the proposed method.

Improved Failure Mode and Effect Analysis: Implementing Risk Assessment and Conflict Risk Mitigation with Probabilistic Linguistic Information

Failure mode and effect analysis (FMEA) is a system reliability analysis technique that has been widely used in various industries to reduce the failure risk of products, systems, and services. However, traditional FMEA methods have limitations in managing the complex uncertain environment as well as the aggregation and weight allocation of FMEA attributes. Complex real-world problems usually involve multiple decision-makers. Individual perceptions and subjective factors are likely to lead to the differences in opinion, and even the conflict risk, which can ultimately become a challenge to achieve a highly recognized solution. This paper proposes an improved FMEA method to implement the risk assessment, which integrates probabilistic linguistic information and conflict risk mitigation. Probabilistic linguistic term sets (PLTSs) are used to describe the risk assessments, and a comprehensive method is applied to determine the weights of the FMEA attributes. Several new operations and distance measures related to PLTSs are defined. Then, a conflict risk mitigation model is developed to reduce the differences among decision-makers’ FMEA risk assessments. Finally, a case study on global production base selection is presented to illustrate the feasibility and effectiveness of the proposed method. Comparative analysis and discussion verify features and advantages of the method.

Large-scale consensus with endo-confidence under probabilistic linguistic circumstance and its application

In real decision-making problems, decision makers (DMs) usually select the most potential project from several ones. However, they unconsciously show different confidence levels in decision-making process because they come from various backgrounds and have different experiences, etc., which affects the decision results. Moreover, the probabilistic linguistic term set, which not only includes the linguistic expressions used by DMs in their daily life but also contains the probability for each linguistic term, can well portray the real perceptions of DMs for the projects. Furthermore, large-scale consensus has gradually been a popular way to effectively solve complex decision-making problems. To sum up, in this paper, we are dedicated to constructing a large-scale consensus model considering the confidence levels of DMs under probabilistic linguistic circumstance. Firstly, the endo-confidence is defined and measured by DM’s probabilistic linguistic information. Then, the DMs are clustered according to the similarities of both evaluation information and the endo-confidence levels. Both evaluation of the non-consensus cluster and evaluation integrated by the clusters with higher endo-confidence level than this non-consensus cluster are used as the reference to adjust its evaluation information. Then, a case study and the comparative analysis are carried out. Finally, some conclusions and future work are given.

The two-person and zero-sum matrix game with probabilistic linguistic information

Game theory establishes mathematical models of strategic interactions among rational decision-makers. In many situations, the crisp values of payoffs are difficult to obtain while the probabilistic linguistic information is easy to collect. However, the existing research on matrix game did not consider the probabilistic linguistic information. To bridge this gap, this study takes the probabilistic linguistic information as the input of a two-person and zero-sum matrix game, and addresses the vague information by triangular membership functions. Such a two-person and zero-sum matrix game with probabilistic linguistic information is a useful technique for multiple criteria analysis. In addition, it outputs the same form of information as the inputs to increase the interpretability compared with other uncertain matrix games. An illustrative example about the forest management is provided to show the validity and advantages of the two-person and zero-sum matrix game with probabilistic linguistic information.

Assessment of cloud vendors using interval‐valued probabilistic linguistic information and unknown weights

Assessment of cloud vendors using interval‐valued probabilistic linguistic information and unknown weights

Probabilistic reliable linguistic term sets applied to investment project selection with the gained and lost dominance score method

Probabilistic linguistic term sets (PLTSs) are an effective tool in keeping with the habits of decision makers (DMs). However, in multi-criteria group decision making (MCGDM) problems, it is necessary to deal with the information reliability problem because of the difference of the DMs’ knowledge backgrounds and knowledge structures. Therefore, this paper proposes a novel concept called probabilistic reliable linguistic term sets. Based on which, some basic operations, comparison laws, distance measures, similarity measures and aggregation operators are defined. After that, we propose the probabilistic reliable linguistic gained and lost dominance score method to cope with MCGDM problems, and we further apply the proposed method to solve an investment project selection problem about lucky bag machine. Finally, we make some comparative analyses to verify the effectiveness and highlight the strength of the proposed method compared with four methods, i.e., the aggregation-based method, the TOPSIS method under probabilistic reliable linguistic environment, the gained and lost dominance score (GLDS) method with probabilistic linguistic information and the GLDS method with hesitant linguistic information.

Interactive multi-criteria group decision-making with probabilistic linguistic information for emergency assistance of COVID-19

This paper develops a new method for interactive multi-criteria group decision-making (MCGDM) with probabilistic linguistic information and applies to the emergency assistance area selection of COVID-19 for Wuhan. First, a new possibility degree for PLTSs is defined and a new possibility degree algorithm is devised to rank a series of probabilistic linguistic term sets (PLTSs). Second, some new operational laws of PLTSs based on the Archimedean copulas and co-copulas are defined. A generalized probabilistic linguistic Choquet (GPLC) operator and a generalized probabilistic linguistic hybrid Choquet (GPLHC) operator are developed and their desirable properties are discussed in details. Third, a tri-objective nonlinear programming model is constructed to determine the weights of DMs. This model is transformed into a linear programming model to solve. The fuzzy measures of criterion subsets are derived objectively by establishing a goal programming model. Fourth, using the probabilistic linguistic Gumbel weighted average (PLGWA) operator, the collective normalized decision matrix is obtained by aggregating all individual normalized decision matrices. The overall evaluation values of alternatives are derived by the probabilistic linguistic Gumbel hybrid Choquet (PLGHC) operator. The ranking order of alternatives is generated. Finally, an emergency assistance example is illustrated to validate the proposed method of this paper.

Probabilistic linguistic term ordered weighted distance operator and its applications in public Eco-environment satisfaction evaluation

ABSTRACT This thesis aims to propose a novel distance operator, the probabilistic linguistic term ordered weighted distance (PLTOWD) operator, which enriches the distance theory in probabilistic linguistic term circumstances. The PLTOWD operator is an efficient tool to deal with qualitative evaluation information and their corresponding probabilities or importance degrees. Moreover, some of its desired properties and different families of the PLTOWD operator are discussed. Meanwhile, the extensions of the PLTOWD operator are also investigated. Then, a method of multiple attribute group decision making (MAGDM) in probabilistic linguistic term information is proposed on the basis of the PLTOWD operator. Finally, a numerical evaluation example in public Eco-environment satisfaction is developed to illustrate the practicability and effectiveness of the given method. Some discussions and comparisons are carried out according to the case results.

Consistency and trust relationship-driven social network group decision-making method with probabilistic linguistic information

Unlike other linguistic modelings, probabilistic linguistic terms can clearly describe the importance of different linguistic terms. With respect to group decision-making (GDM) problems, it is convenient for experts to express their evaluation opinions with probabilistic linguistic preference relations (PLPRs), which can transform experts’ quantitative descriptions into qualitative probabilistic linguistic terms. The processes of consistency-adjustment and expert weights determination play a key role in GDM. Therefore, this paper aims at the design of a novel probabilistic linguistic GDM method with consistency-adjustment algorithm and trust relationship-driven expert weight determination model. First, we redefine the multiplicative consistency of PLPRs, which only involves changing the probabilities of linguistic terms. A new distance between PLPRs is presented to calculate the consistency index. Then, we propose a convergent consistency-adjustment algorithm to improve the consistency of a PLPR to an acceptable consistency level. Subsequently, a trust relationship-driven expert weight determination model is developed to derive the experts’ weights in a social network environment. Finally, a probabilistic linguistic GDM method is designed to determine the reliable ranking of alternatives. The advantages and applicability of the proposed method are illustrated by a case study concerning an evaluation of logistics service suppliers and associated comparative analyses.

Risk ranking of wind turbine systems through an improved FMEA based on probabilistic linguistic information and the TODIM method

The technology of wind power is being widely developed worldwide. Ensuring the reliable operation of wind turbine systems is of significance. A popular tool to identify the potential risk of an engineering system is the failure mode and effect analysis (FMEA) method. However, when conducting a FMEA in a complex and uncertain environment, experts may find it challenging to select an appropriate linguistic term for the evaluation. The probabilistic linguistic term sets (PLTSs) are a useful fuzzy set to help experts in describing their assessment. However, different experts may assign different semantic values to the same linguistic terms, and this aspect has not been extensively examined in the existing studies. Therefore, considering the psychological behaviour of experts and the semantics of linguistic terms in the risk ranking process, an improved FMEA based on the probabilistic linguistic information and TODIM (an acronym in Portuguese of interactive and multicriteria decision making) method was developed to identify the risks in wind turbine systems. Furthermore, to demonstrate the utility of the proposed model, it was applied in a floating offshore wind turbine system. The effectiveness and the validity of the model were verified by comparing with some other methods.