Probabilistic Linguistic Preference Relations Research Articles

Personalized individual semantics based consensus reaching process for large-scale group decision making with probabilistic linguistic preference relations and application to COVID-19 surveillance

This paper develops a new personalized individual semantic (PIS) based consensus reaching process (CRP) for large-scale group decision making (LSGDM) with probabilistic linguistic preference relations (PLPRs) and applies to the selection of COVID-19 surveillance plans. Firstly, considering that a linguistic term means different things to different decision makers (DMs), a new definition of distance between probabilistic linguistic term sets (PLTSs) is defined considering the PIS of a DM. Then, a consistency-driven optimization model is built to determine the PIS of linguistic terms in a PLPR of a DM by maximizing the consistency of a PLPR. DMs’ weights can be acquired through a programming model by minimizing the distance between the individual semantic and the collective semantic. Besides, a clustering algorithm based on PIS is devised for dividing DMs into several subgroups with similar semantic. Based on the obtained subgroups, the corresponding moderators can be identified by DMs with unacceptable consensus level (CL). Several minimum preference adjustment models are constructed to obtain the adjusted PLPRs. These models not only can sufficiently consider the willingness of DMs to modify their preferences but also can improve their CLs in CRP. Finally, an illustration example of selection of college COVID-19 surveillance plans is offered to demonstrate the proposed method and to verify the effectiveness of the proposed model.

A self-confidence and leadership based feedback mechanism for consensus of group decision making with probabilistic linguistic preference relation

There are usually multiple stakeholders involved in a group decision-making (GDM) problem. The probabilistic linguistic preference relation (PLPR) is an effective tool to describe the preference of each stakeholder. The probability distribution of linguistic preference can be available from statistics analysis on the questionnaires. In GDM process, the essential step is to execute the consensus reaching process (CRP) that is a dynamic iterative process by utilizing the feedback mechanism to update the preference of identified stakeholders. However, the existing feedback mechanisms with the fixed boundary parameter neglect the individual psychological behavior, leading to false CRP. For which, the personalized feedback mechanism based on self-confidence and leadership is developed to generate recommendation advice for the identified stakeholders, which is the three-step procedure: (1) construct trust relationship network and obtain trust degree among stakeholders; (2) assess individual self-confidence level from professional ability and sociability that are captured by entropy and trust degree, respectively, and (3) identify the opinion leader as reference preference. Furthermore, we analyze the convergence and consistency of identified stakeholders after adopting the feedback recommendation. Then, an example of hydropower development project assessments is illustrated to show the feasibility of the proposed method. Finally, by comparison and analysis with other consensus models, it demonstrates the advantages of the proposed feedback mechanism.

Consistency Adjustment Strategy and Multiplicative DEA Cross-Efficiency for Group Decision-Making with Probabilistic Linguistic Preference Relations

Consistency Adjustment Strategy and Multiplicative DEA Cross-Efficiency for Group Decision-Making with Probabilistic Linguistic Preference Relations

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.

Additive Consistency-Based Decision-Making with Incomplete Probabilistic Linguistic Preference Relations

Additive Consistency-Based Decision-Making with Incomplete Probabilistic Linguistic Preference Relations

Emergency Optimization Decision-Making with Incomplete Probabilistic Information under the Background of COVID-19

At present, the whole world is facing the serious challenge of COVID-19, and it has reached a consensus that taking appropriate measures timely is the key to prevent and control infectious diseases. This paper proposes an algorithm to solve the problem of how to choose the most appropriate alternative from numerous alternatives in the limited time from the perspective of management. First of all, we have compared various data structures for keeping the comparison results of alternatives. After comparisons, we adopt the hesitant fuzzy incomplete probabilistic linguistic preference relation matrix to save the information which can keep the first-hand valuable collected data to the maximum extent; then, we can obtain the missing values with the help of the fault tree analysis method, which can consider both subjective evaluation data and objective historical data simultaneously. Meanwhile, the fault tree analysis method can find development laws with the help of similar infectious diseases that have occurred in the past. The definition of consistency index is also introduced which can measure whether there are contradictions and the degree of contradiction in the decision results. Only those data that meet the consistency requirements can be used for decision-making and then a method is proposed to effectively reduce the degree of inconsistency. The information aggregation method will be adopted subsequently, and we can obtain the ranking of alternatives. An instance with specific execution steps is also introduced to illustrate the feasibility and efficiency of the algorithm proposed in this paper; in the end, several types of comparisons with typical algorithms proposed by other scholars are carried out, and all the experimental results show that the algorithm proposed in this paper is effective and innovative in some aspects.

Interactive algorithms for normalized probabilistic linguistic preference relations in view of the disjunctive probability based consistency and consensus analysis

This paper investigates decision making with normalized probabilistic linguistic preference relations (NPLPRs). Consistency analysis is indispensable for deriving the reasonable ranking. After recalling previous research, we find that all previous concepts cannot fully define consistent NPLPRs. As a fundamental topic of decision making with preference relations, it is necessary to further study the consistency of NPLPRs. For this purpose, an interactive algorithm for deriving disjunctive probabilistic additive linguistic preference relations (DP-ALPRs) is provided, by which an additive consistency concept for NPLPRs is defined. When NPLPRs are unacceptably consistent, models for obtaining acceptably additively consistent NPLPRs are built. Considering the situation where only incomplete NPLPRs are obtained, a disjunctive probability and additive consistency based interactive algorithm for ascertaining missing judgments is provided. Meanwhile, we discuss group decision making (GDM) with NPLPRs and offer a distance measure based formula to determine the weights of the decision makers. In addition, the method defines a consensus index and builds models for improving the consensus level. Under the additive consistency and consensus discussions, an interactive algorithm for GDM with NPLPRs is proposed. Finally, the new method is applied to select green raw material suppliers to illustrate the application and compared with several previous ones.

A comparative analysis of probabilistic linguistic preference relations and distributed preference relations for decision making

When a decision-maker prefers to compare different alternatives in pairs to handle real situations, there are many different expression styles that can be used. Two representative expression styles are the probabilistic linguistic preference relation (PLPR), which originates from the fuzzy linguistic approach and the distributed preference relation (DPR), which originates from the evidential reasoning approach. Although these two expression styles look quite similar, their meanings, operations, and relevant decision making processes are significantly different. This presents the decision-maker with the challenge of selecting either PLPRs or DPRs in different real cases. To address this issue, this paper provides a detailed analysis of the similarities and differences between PLPRs and DPRs. The analysis is conducted from five perspectives, including modeling of decision making problems, handling of uncertainty, consistency between preference relations, information aggregation, and elicitation process. An engineer selection problem for an automobile manufacturing enterprise is investigated to demonstrate how to appropriately select PLPRs or DPRs to model and analyze decision making problems in real situations with consideration for the preferences of decision-makers.

Evaluation of marine ranching resources and environmental carrying capacity from the pressure-and-support perspective: A case study of Yantai

The pressure on the resources and environment of marine ranching has been increasing due to its large-scale construction and rapid development. Marine ranching resources and environmental carrying capacity (RECC) are important for the sustainable development of marine ranching. This paper constructs a marine ranching RECC evaluation index system based on the analysis of the marine ranching RECC system from the pressure-and-support perspective. Also, on the basis of the determination of index weights using the probabilistic linguistic preference relation (PLPR) method, a model to calculate the marine ranching RECC index is introduced and applied to analyzing the RECC states of 11 marine ranching enterprises in Yantai, China. Based on the obtained results, the following conclusions are drawn. First, the RECC of 11 marine ranching enterprises in Yantai is in a severe state on the whole. Second, the average RECC performance of national marine ranching enterprises is better than that of the provincial marine ranching enterprises. Third, both the pressure and support levels of most marine ranching enterprises in Yantai are relatively low. Finally, there are certain main obstacle indexes in each subsystem that limit the RECC level. This study helps a comprehensive understanding of marine ranching RECC status in Yantai and provides an important reference for the scientific construction and management of marine ranching in China.

A nondominated selection procedure with partially consistent non-reciprocal probabilistic linguistic preference relations and its application in social donation channel selection under the COVID-19 outbreaks

A non-reciprocal fuzzy preference relation (NrFPR) can express partial relations of alternatives, including indifference relations, preference relations and incomparability relations, but cannot depict linguistic preference intensities. A probabilistic linguistic preference relation (PLPR) can represent preference intensities in forms of probabilities and linguistic terms, but the incomparability relations of alternatives were not defined in a PLPR. Given that the NrFPR and PLPR can overcome each other’s drawbacks, this study proposes the non-reciprocal probabilistic linguistic preference relation (NrPLPR). Six conditions are given to express the partial relations of alternatives. Since the P-cut of probabilistic linguistic term sets (PLTSs) is effective in the operations of PLTSs without information loss, we construct the P-cut matrix of an NrPLPR by an adaptive P-determination method. Afterwards, nine rules are provided to define the partially consistent NrPLPR. To repair the inconsistent NrPLPR, a two-stage consistency repairing process, containing the linguistic information and probability repairing stages, is introduced. In addition, a non-reciprocal probabilistic linguistic nondominated selection procedure is proposed to rank alternatives. A case study on selecting social donation channels under the COVID-19 outbreaks is given to demonstrate the applicability of the proposed method. A comparative analysis is done to show the effectiveness of the proposed method.

An optimisation-based method to conduct consistency and consensus in group decision making under probabilistic uncertain linguistic preference relations

The use of probabilistic uncertain linguistic preference relations (PULPRs) enriches the flexibility of decision makers (DMs) in group decision making (GDM). However, the GDM models under PULPRs are mainly focussed on the consensus reaching process rather than the individual consistent improvement. The goal of this paper is to manage the consistency and consensus in GDM based on PULPRs, and provide a feasible method for minimising the preference information loss by optimisation model. First, according to DMs’ psychological preferences (optimistic, pessimistic, and neutral characteristics), we proposed a conversion function to fit uncertain linguistic terms in PULPRs, which may be transformed into probabilistic linguistic preference relations. Second, to preserve as much as possible the original preference information of DMs, a consensus model based on optimisation is established, which not only obtains the acceptable group consensus but also guarantees that the consistency level of individuals is acceptable. Finally, we validated the proposed method through a case study of an investment project selection for central enterprises’ poverty alleviation fund. The proposed method provides a new way to deal with GDM problems under PULPRs, and help DMs to reach a certain level of consensus on basis of acceptable consistent level of individuals.

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.

A Target-Oriented Multiple-Attribute Decision-Making Approach Based on Probabilistic Linguistic Preference Relations

While the approach to multiple-attribute decision-making (MADM) is widely used in a variety of fields, including models with fuzzy sets and corresponding extensions, it cannot solve target-oriented decision problems with both selective and targeted alternatives. Therefore, this study provides the first description of a target-oriented MADM problem and proposes a novel decision framework. An attribute value function for target orientation is defined by integrating range and frequency values derived under cumulative prospect theory and range-frequency theory. A Choquet integral with discrete fuzzy measures is then used to integrate attribute values and determine comprehensive values for selective alternatives. In this determination of comprehensive values, a parameter estimation model is also established, with its input assumed to be the pairwise comparison judgment matrix with probabilistic linguistic preference relation. This model as well as its transformation aims at determining the parameters of both the attribute value function and fuzzy measures. Finally, the process of target-oriented MADM is summarized, and an illustrative example is provided to demonstrate the applicability of the proposed techniques.

Consensus model based on probability K-means clustering algorithm for large scale group decision making

Nowadays, the increasing complexity of the social environment brings much difficulty in group decision making. The more uncertainty exists in a decision-making problem, the more collective wisdom is needed. Therefore, large scale group decision making has attracted a lot of researchers to investigate. Since the probabilistic linguistic terms have impressive performance in expressing DMs’ opinions, this paper proposes a novel method for large scale group decision making with probabilistic linguistic preference relations. More specifically, (1) a probability k-means clustering algorithm is introduced to segment DMs with similar features into different sub-groups; (2) an integration method is proposed to construct the collective probabilistic preference relation that retains initial information to the most extent; (3) taking the personality of each DM into account, a consensus model is constructed to improve the rationality and efficiency of consensus reaching process. Several simulation experiments are designed to analyze the influence factor in the feedback mechanism and make some comparative analysis with the existing method. Finally, an illustrative example of contractor selection is conducted to verify the validity of the proposed method.

Consistency and consensus improvement models driven by a personalized normalization method with probabilistic linguistic preference relations

Probabilistic linguistic preference relation (PLPR) provides an effective and flexible tool with which preference degrees of decision-makers can be captured when they vacillatingly express linguistic preference values among several linguistic terms. Individual consistency and group consensus are two important research topics of PLPRs in group decision making (GDM). Considering the problems associated with these two topics, this study proposes a novel GDM framework with consistency-driven and consensus-driven optimization models based on a personalized normalization method for managing complete and incomplete PLPRs. First, existing limitations of the traditional normalization method for probabilistic linguistic term sets (PLTSs) managing ignorance information are specifically discussed. Given the potential valuable information hidden in PLTSs, a personalized normalization method is newly proposed through a two-stage decision-making process with a comprehensive fusion mechanism. Then, based on the proposed normalization method for PLTSs, consistency-driven optimization models that aim to minimize the overall adjustment amount of a PLPR are constructed to improve consistency. Moreover, the developed models are extended to improve consistency and estimate the missing values of an incomplete PLPR. Subsequently, a consensus-driven optimization model that aims to maximize group consensus by adjusting experts’ weights is constructed to support the consensus-reaching process. Finally, an illustrative example, followed by some comparative analyses is presented to demonstrate the application and advantages of the proposed approach.

Local adjustment strategy-driven probabilistic linguistic group decision-making method and its application for fog-haze influence factors evaluation

Unlike other linguistic modellings, probabilistic linguistic term sets can express clearly the importance of different linguistic variables. The notion of Probabilistic Linguistic Preference Relations (PLPRs) constitutes an extension of linguistic preference relations, and as such has received increasing attention in recent years. In group decision-making (GDM) problems with PLPRs, the processes of consistency adjustment, consensus-achieving and desirable alternative selection play a key role in deriving the reliable GDM results. Therefore, this paper focuses on the construction of a GDM method for PLPRs with local adjustment strategy. First, we redefine the concepts of multiplicative consistency and consistency index for PLPRs, and some properties for multiplicative consistent PLPRs are studied. Then, in order to obtain the acceptable multiplicative consistent PLPRs, we propose a convergent consistency adjustment algorithm. Subsequently, a consensus-achieving method with PLPRs is constructed for reaching the consensus goal of experts. In both consistency adjustment process and consensus-achieving method, the local adjustment strategy is utilized to retain the original evaluation information of experts as much as possible. Finally, a GDM method with PLPRs is investigated to determine the reliable ranking order of alternatives. In order to show the advantages of the developed GDM method with PLPRs, an illustration for determining the ranking of fog-haze influence factors is given, which is followed by the comparative analysis to clarify its validity and merits.

A novel probabilistic linguistic decision-making method with consistency improvement algorithm and DEA cross-efficiency

Probabilistic linguistic term set (PLTS) is highly useful for decision-makers (DMs) to describe qualitative and uncertain information in the decision-making process. This paper proposes a novel probabilistic linguistic decision-making method with consistency improvement algorithm and data envelopment analysis (DEA) cross-efficiency. Firstly, we put forward the concept of order consistency of probabilistic linguistic preference relation (PLPR). The order consistency is helpful for DMs to make quick and efficient decision in certain situations. Then, based on the defined multiplicative consistency of PLPR, we develop a consistency improvement algorithm to transform the unacceptable multiplicative consistent PLPRs into the acceptable ones. Furthermore, a DEA model is established to derive the priority weight vector of alternatives from the acceptable multiplicative consistent PLPR. Meanwhile, for the alternatives that have equal priority weights, we use a DEA cross-efficiency model to further differentiate and obtain the final ranking of alternatives. Finally, a numerical example of emergency logistics distribution selection is given to illustrate the effectiveness and applicability of the proposed method.

A novel process to determine consensus thresholds and its application in probabilistic linguistic group decision-making

When solving group decision-making (GDM) problems, the proper values of consensus thresholds are vital for consensus checking and improving. Decision makers are usually not confident to select a proper threshold. In the linguistic setting, this paper presents a new process to support the determination of consensus thresholds. A new concept, namely random consensus index, is presented to serve as a reference object so that the risk preference of a decision maker could be induced by comparing the quality of the information in hands with the averaging quality of randomly generated information. In this sense, admissible consensus thresholds could be determined automatically, and decision makers are not necessary to focus on the detail of consensus measures. Furthermore, the process is applied to the GDM problems with probabilistic linguistic preference relations, and a new GDM approach is presented. Different from the existing contributions, the consensus is measured by the probability of a set of preference relations being with acceptable consensus, and then the consensus is improved by revising the involved probability distributions. All the involved parameters are intuitive and interpretable. A case study, regarding the departure audit in China, demonstrates that the proposed GDM approach is effective even if the original preferences of experts are with low consistency and consensus.

An inverse prospect theory-based algorithm in extended incomplete additive probabilistic linguistic preference relation environment and its application in financial products selection

Selecting financial products is one of the most fundamental investment activities to both individuals and companies, and therefore it is very important to establish an efficient and practical method for financial products selection. To address the challenge of the complicated decision-making environment and decision makers’ expression habits for the selection of financial products, this paper develops the incomplete additive probabilistic linguistic preference relation to depict decision makers’ preferences. Considering that, when decision makers express their opinions using probabilistic linguistic preference relation, it is possible that the sum of the value of the probability information is more than 1, this paper also extends the concepts of probabilistic linguistic term set, additive probabilistic linguistic preference relation and incomplete additive probabilistic linguistic preference relation to improve and ensure their practicability. Moreover, an “inverse prospect theory-based” algorithm is proposed to choose proper financial products. The algorithm processes the original incomplete additive probabilistic linguistic preference relation by using the inverse functions of the prospect theory at first. Then, a priority weights deriving model is established based on the extended concepts. Finally, the numerical case and analysis is presented as the evidences to the conclusion that the proposed algorithm is practical and robust.

A novel weight‐derived method and its application in graduate students' physical health assessment

In multiattribute decision making, the analytic network process (ANP) is an important methodology to derive the subjective weights of attributes when the dependence and feedback relations exist between attributes, and the number of attributes should be no more than seven in a comparison matrix. To reduce the dimensions of attributes, we propose a hybrid hesitant fuzzy linguistic factor analysis method to cluster the attributes into main factors. The method takes multiple forms of decision-making information into consideration, such as single linguistic terms, hesitant fuzzy linguistic terms, and numeric values. Meanwhile, the objective weights of the main factors are obtained as well. As for the subjective weights of main factors, the incomplete probabilistic linguistic ANP is developed after improving the incomplete probabilistic linguistic preference relation with multiplicative consistency. At last, the final weights of the main factors are calculated by combining the objective and subjective weights. A questionnaire survey about assessing the weights of the main factors influencing graduate students' physical health is designed to explain the application of the proposed methodology. To sum up, the main importance and contributions of this study are as following: (1) developing a hybrid hesitant fuzzy linguistic factor analysis method and incomplete probabilistic linguistic ANP, (2) proposing a novel weight-derived method from both objective and subjective perspectives, and (3) applying it to graduate students' physical health assessment.