Novel basic operational laws for linguistic terms, hesitant fuzzy linguistic term sets and probabilistic linguistic term sets

Personalized movie recommendations based on probabilistic linguistic sentiment and integrated DEMATEL-TODIM methods

With the development of society, online reviews are increasingly becoming a crucial factor in decision-making. Especially for entertainment products such as movies, they are preferred for their affordability and high entertainment factor. Therefore, this paper proposes a movie recommendation model that considers user personalization using a probabilistic linguistic approach based on online reviews. Firstly, the method constructs a quantitative sentiment framework that transforms comments into a multi-granular probabilistic sentiment language. Secondly, we build the decision-making trial and evaluation laboratory (DEMATEL) method for probabilistic linguistic environments to explore interrelationships between product attributes, and improve the distance measure and score function to better integrate probabilistic linguistic information into DEMATEL weight calculations. Furthermore, to account for risk preferences, the model employs the extended TODIM (an acronym in Portuguese for interactive and multicriteria decision making) methodology to determine the ranking of alternatives. Finally, we design Douban movie ranking experiments to demonstrate the validity of the model. Compared with other methods, this paper incorporates the emotional tendency of movie attributes and user preference into the decision-making process leading to more reasonable results.

Linguistic intuitionistic fuzzy multi-attribute bilateral matching considering satisfaction and fairness degree

Aiming at the multi-attribute bilateral matching problem with unknown attribute weights under a linguistic intuitionistic fuzzy environment, a decision method based on TODIM considering satisfaction and fairness degrees is proposed. First, the theories of linguistic intuitionistic fuzzy sets and bilateral matching are given, and the multi-attribute bilateral matching problem under a linguistic intuitionistic fuzzy environment is described. To solve this problem, according to linguistic intuitionistic fuzzy preference matrices, the overall attribute dominances are calculated based on TODIM; considering group consensus, a new method is proposed to calculate attribute weights based on linguistic intuitionistic fuzzy induced ordered weighted averaging (LIFIOWA) operator; then, the overall dominances of bilateral subjects are obtained by aggregating the overall attribute dominances and attribute weights. Furthermore, the overall dominances are standardized to calculate the satisfaction degrees of bilateral subjects; the fairness degrees of bilateral subjects are calculated considering the loss attenuation coefficient. Based on satisfaction degree matrices, fairness degree matrices and bilateral matching matrices, multiple bilateral matching models are established and then solved to obtain the optimal bilateral matching scheme. Finally, an example shows the effectiveness, reliability and accuracy of the proposed method. The research results indicate the following main characteristics of the proposed method: (1) A new method for calculating the unknown attribute weights using LIFIOWA operator is proposed. (2) According to the TODIM idea, a calculation method for fairness degree considering the loss attenuation coefficient is proposed. (3) Considering satisfaction and fairness degrees, multiple bilateral matching models under a linguistic intuitionistic fuzzy environment are established.

Geographic information system-based multi-criteria decision-making analysis for investment assessment of wind-photovoltaic-shared energy storage power stations: a case study of Shanxi Province

As the center of the development of power industry, wind-photovoltaic (PV)-shared energy storage project is the key tool for achieving energy transformation. This research seeks to construct a feasible model for investment appraisal of wind-PV-shared energy storage power stations by combining geographic information system (GIS) and multi-criteria decision-making (MCDM) method. Firstly, a comprehensive criteria system is established from the perspectives of orography, economy, resources, climate, and society, and the evaluation data is described using probabilistic linguistic term sets (PLTSs). Then, to avoid the weight deviation produced by the single weighting approach, a comprehensive weighting model including the best-worst method (BWM) and entropy weight method is provided to calculate the weights of criteria. Next, expert weights are calculated based on trust analysis. Finally, alternatives are ranked by the improved gained and lost dominance score (GLDS) method. To verify the validity of the model, an empirical investigation is carried out in Shanxi Province. The results show that the economy is the primary factor influencing the investment decision. Among all the projects approved by the government, alternative F4 located in Yanzhuang Town, Yuanping City is the best investment object. Furthermore, to illustrate the stability of the result, triple sensitivity analysis and comparative analysis are conducted in Shanxi Province. This study expands the application scope of GIS and MCDM method by first providing support for government and investors to identify optimal investment targets.

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.

TODIM-VIKOR method based on hybrid weighted distance under probabilistic uncertain linguistic information and its application in medical logistics center site selection

At a time of global epidemic control, the location of the medical logistics distribution center (MLDC) has an important impact on the operation of the entire logistics system to reduce the operating costs of the company, enhance the service quality and effectively control the COVID-19 on the premise of increasing the company's profits. Thus, the research on the location of MLDC has important theoretical and practical application significance separately. Recently, the TODIM and VIKOR method has been used to solve multiple-attribute group decision-making (MAGDM) issues. The probabilistic uncertain linguistic term sets (PULTSs) are used as a tool for characterizing uncertain information. In this paper, we design the TODIM-VIKOR model to solve the MAGDM in PULT condition. Firstly, some basic concept of PULTSs is reviewed, and TODIM and VIKOR method are introduced. The extended TODIM-VIKOR model is proposed to tackle MAGDM problems under the PULTSs. At last, a numerical case study for medical logistics center site selection (MLCSS) is given to validate the proposed method.

On probabilistic linguistic term set operations

In a recent work (Wang et al. 2020), a partial order ⪯, a join operation ⊔ and a meet operation ⊓ of probabilistic linguistic term sets (PLTSs) were introduced and it was proved that L 1 ⊓ L 2 ⪯ L 1 ⪯ L 1 ⊔ L 2 and L 1 ⊓ L 2 ⪯ L 2 ⪯ L 1 ⊔ L 2. In this paper, we demonstrate that its join and meet operations are not satisfy the above requirement. To satisfy this requirement, we modify its join and meet operations. Moreover, we define a negation operation of PLTSs based on the partial order ⪯. The combinations of the proposed negation, the modified join and meet operations yield a bounded, distributive lattice over PLTSs. Meanwhile, we also define a new join operation and a new meet operation which, together with the negation operation, yield a bounded De Morgan over PLTSs.

A multi-criteria group decision-making framework for investment assessment of offshore floating wind-solar-aquaculture project under probabilistic linguistic environment

The offshore floating wind-solar-aquaculture (WSA) system with its advantages such as strong seakeeping ability, considerable power generation, and full utilization of ocean space and water resources will have a bright prospect in the future. In order to accelerate the sustainable development of the energy industry, it is very important to build a reasonable investment decision-making framework. Therefore, this paper aims to build a multi-criteria group decision-making (MCGDM) framework for investment decision-making of this project. Firstly, a comprehensive criteria system has been established. Secondly, probabilistic language term sets (PLTSs) are introduced to describe the uncertainty and fuzziness of decision information. Thirdly, the expert weight determination model is established based on the correlation measure and correlation coefficient of PLTSs, and the PL-fuzzy decision-making trial and evaluation laboratory (DEMATEL) method and the information entropy method are introduced to determine the subjective and objective weights of the criteria. In addition, considering the decision maker's psychological behavior, we choose probabilistic language the interactive and multiple attribute decision-making (TODIM) method to determine the optimal investment alternative. Finally, we apply the proposed framework to a case study. The results illustrate that the alternative A₃ possesses the optimal comprehensive performance with the overall value is 1. Then, we conduct sensitivity analysis and comparative analysis to verify its robustness and feasibility. Scenario analysis in TODIM method showed that it is reasonable to express decision preference by setting different recession coefficients in the actual decision-making environment. This study can provide some reference for decision-makers, and also extend the method of decision-making field.

Probabilistic linguistic evolutionary game with risk perception in applications to carbon emission reduction decision making

Carbon emission reduction, an effective way to facilitate carbon neutrality, has gained increasing attention in government policy and scientific research. However, the establishment of a sustainable carbon emission reduction market is a complex game between governments and enterprises. In addition, it is difficult to obtain precise evaluations of the political and environmental factors in most cases. Irrational enterprises with a profit-seeking nature bring challenges to the strategy selection. To bridge this gap, we propose a probabilistic linguistic evolutionary game to model strategic behavior in carbon emission reduction assistant decision making. First, we introduce a probabilistic linguistic payoff matrix to describe the uncertain payoffs of players. A new distance measure for the probabilistic variables is also proposed to construct the prospect payoff matrix in the prospect theory framework. Then, the evolutionary dynamics and the probabilistic linguistic evolutionary stability of the proposed methods are analyzed. A comprehensive case study for carbon emission reduction with comparisons is presented for validation.

Probabilistic linguistic fuzzy cognitive maps: applications to the critical factors affecting the health of rural older adults

Background

Achieving healthy ageing has become the only way for China to alleviate the pressure of ageing, especially in rural areas. However, the factors affecting the health of rural older adults are numerous and complex. It is important to identify the critical factors that affecting the health of older adults in rural areas and provide decision-making support for targeted health interventions.

Methods

To overcome some limitations of existing works, an extended probabilistic linguistic fuzzy cognitive map model is proposed in this paper as a useful tool for modeling the cause-effect relationship between factors. The proposed model integrates the advantages of probabilistic linguistic term sets and fuzzy cognitive maps. In the end, to rank and identify the critical factors affecting the health, a novel similarity measure based on Euclidean distance and Z-mapping function is proposed.

Results

The proposed model can effectively deal with the uncertainty of experts and reflect different opinions of groups well. In terms of representing uncertainty and ambiguity, the proposed method outperforms other models in modeling complex systems. In the real-world case analysis, we find that education is the most important factor affecting the health of rural older adults, followed by previous occupational experiences, psychology, and physical exercise, among other things. Intergenerational relationship has become another important factor affecting the health of rural older adults in China as the development of Chinese society.

Conclusions

From a macro perspective, social economic status, living environment, lifestyle, and health management, are the variables that have the greatest impact on the health of rural older adults. As a result, providing more precise health interventions with the characteristics of factors influencing health is a crucial guarantee for preserving and improving the health of rural older adults in China.

Supplementary Information

The online version contains supplementary material available at 10.1186/s12911-022-02028-9.

A probabilistic linguistic opinion dynamics method based on the DeGroot model for emergency decision-making in response to COVID-19

Emergency decision-making entails a multi-criteria problem with a short period and urgent events, which creates difficulties for decision makers to undertake an optimal decision. To ensure the validity and rationality of decision results, the probabilistic linguistic term set is adopted to represent the evaluation information of experts because it can assign different probabilities or importance to different linguistic terms, which is closely related to human cognition. In addition, to portray the dynamic changes in the emergency decision-making process, this study develops a new dynamics method based on the DeGroot model with probabilistic linguistic information. First, to simulate the transition matrix of probabilistic linguistic opinions, the basic operational rules are defined based on the transformation function and expectation function. Next, three forms of influence matrices incorporating similarity, self-persistence, and authority degrees are constructed, and the consensus conditions of the models are discussed. Then, considering the social networks and incomplete trust relationships between experts, a fourth trust-based influence matrix is devised. A case study of emergency decision-making for assessing response plans to COVID-19 is performed to verify the feasibility and effectiveness of the dynamic method. Furthermore, a sensitivity analysis is conducted. Finally, comparisons with classical methods are performed to illustrate the superiorities of the proposed algorithms.

Primary node election based on probabilistic linguistic term set with confidence interval in the PBFT consensus mechanism for blockchain

This study proposes a primary node election method based on probabilistic linguistic term set (PLTS) for the practical Byzantine fault tolerance (PBFT) consensus mechanism to effectively enhance the efficiency of reaching consensus. Specifically, a novel concept of the probabilistic linguistic term set with a confidence interval (PLTS-CI) is presented to express the uncertain complex voting information of nodes during primary node election. Then, a novel score function based on the exponential semantic value and confidence approximation value for the PLTS-CI, called Score-ESCA, is used to solve the problems of comparing different nodes with various voting attitudes. This method helps select the node with the highest score by utilizing complex decision attitudes, making it an accurate primary node election solution. Furthermore, the feasibility of our proposed method is proved by both theoretical analysis and experimental evaluations.

Cosine similarity measures between q-rung orthopair linguistic sets and their application to group decision making problems

The q-rung orthopair linguistic set (q-ROLS), a combined version of linguistic term sets and q-rung orthopair fuzzy set, is an efficient mathematical tool to accomplish the imprecise information while solving the decision-making problems. Under this environment, we propose additional operations and relations to deal with the decision information, and some properties are well proved. Furthermore, we propound some cosine similarity measures and weighted cosine similarity measures for q-ROLSs based on the traditional cosine similarity measures with a brief study of related properties. In the proposed similarity measures, various linguistic scale functions are utilized in order to take into account the semantics of linguistic terms. Besides this, we employ the stated q-rung orthopair linguistic similarity measures to multi-criteria group decision making problems, in which the weights of DMs are delineated by the projection of individual decisions on the ideal decision results. At last, a numerical example is used to demonstrate the practicality of the suggested technique, and its efficacy is validated by comparison with prevailing techniques. The suggested method’s sensitivity and stability analyses are also provided.

A DEMATEL-Based Method for Linguistic Multiple Attributes Group Decision Making Using Strict t-Norms and t-Conorms

To evaluate fuzzy information precisely, researchers and practitioners are apt to use linguistic variables to model vague or uncertain contexts in natural language. In this paper, some new operation laws for continuous linguistic terms using strict t-norms and t-conorms are defined. Significantly, these operation laws have some desirable properties and are closed on the restricted continuous linguistic term set. On the basis of these new linguistic operation laws, a series of triangular t-(co)norm-based linguistic generalized power geometric operators are developed. In order to consider the interactive influence and interrelationship of decision makers (DMs) and attributes, a decision-making trial and evaluation laboratory (DEMATEL)-based method for linguistic multiple attributes group decision making (MAGDM) is proposed. In the method, the weighting information for DMs and attributes are dependent on the initial direct-relation matrices among DMs and attributes, respectively. Finally, a numerical example is provided. In comparison with the existing methods, two aspects of the DEMATEL-based method for linguistic MAGDM in the work can be highlighted: the underlying operators for linguistic terms using strict t-norms and t-conorms that are closed on the set of the restricted continuous linguistic term set; and the techniques in determining the weighting information, with which the weighting information for DMs and attributes are determined by the interactive influence and interrelationship among DMs or attributes.

Diagnosis and prediction of failures in maintenance systems using fuzzy inference and Z-number method

In this research, a timely diagnosis and prediction mechanism for drill failure are provided to improve the maintenance process in drilling through fuzzy inference systems. Failures and decisions are based on information and reliability as well, and that affects the quality of decision-making. We apply the potential of if-then rules and a new approach called Z-number that considers fuzzy constraints and reliability at the same time. Exerting Z-number in this research took maximum advantage of reducing uncertainty for predicting failures. Additionally, this research has a practical aspect in maintenance systems by using if-then rules that rely on Z-number. The proposed approach can cover the expert idea during drill operation time simultaneously. This approach also helps experts encounter ambiguous situations and formulate uncertainties. Experts or drill operators can consider key factors of drilling collapse along with the reliability of these factors. The proposed approach can be applied to a real-life situation of human inference with probability for the purpose of predicting failures during drilling. Hence, this method has excellent flexibility for implementation in various maintenance systems.

Decision-making based on probabilistic linguistic term sets without loss of information

Probabilistic linguistic term set (PLTS) provides a much more effective model to compute with words and to express the uncertainty in the pervasive natural language by probability information. In this paper, to avoid loss of information, we redefine the classical probabilistic linguistic term sets (PLTSs) by multiple probability distributions from an ambiguity perspective and present some basic operations using Archimedean t-(co)norms. Different from the classical PLTSs, the reformulated PLTSs are not necessarily normalized beforehand for further investigations. Moreover, the multiple probability distributions based PLTSs facilitate the incorporation of the different attitudes of the DMs in their score values and the deviation, and thus the comparisons. Then the Decision-Making Trial and Evaluation Laboratory (DEMATEL) method is extended to the reformulated PLTS frame by incorporating probability information. With these newly developed elements in the reformulated PLTSs, a DEMATEL based multiple attributes decision-making is proposed. The illustrative example and comparison analysis show that the method over the reformulated PLTSs is feasible and valid, and has the advantage in processing without any information loss (i.e., without normalization) and fully exploration of the DMs-preference and knowledge.

Multi-attribute decision making method based on probabilistic linguistic term sets and its application in the evaluation of emergency logistics capacity

The occurrence of public health emergency will cause huge economic losses and casualties, which posed a huge threat to the economic and social development. In response to the emergency, a large amount of emergency relief supplies will be transported to the affected areas. Faced with this public health emergency of international concern, the concept of emergency logistics capacity and the evaluation model based on probabilistic linguistic term sets are proposed. In this paper, the emergency logistics capability evaluation is transformed into user demand evaluation, and the importance of each index of emergency logistics capability is determined by using Quality Function Deployment (QFD) and prospect theory. Under the probabilistic language information environment, a multi-attribute decision making method is established by using TODIM method. Finally, an example is given to verify the feasibility of the proposed method.

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.

The optimal emergency decision-making method with incomplete probabilistic information

Emergencies often occur irregularly, such as infectious diseases, earthquakes, wars, floods, the diffusion and leakage of chemically toxic and harmful substances, etc. These emergencies can bring huge disasters to people, even worse, the time left for people to make critical decisions is usually very limited. When an emergency occurs, the most important thing for people is to make reasonable decisions as soon as possible to deal with the current problems, otherwise, the situation may deteriorate further. The paper proposes an emergency decision-making algorithm under the constraints of the limited time and incomplete information, the research is mainly carried out from the following aspects, firstly, we use the data structure of the hesitant fuzzy probabilistic linguistic set to collect the basic data after careful comparison, which has three advantages, (1) considering the hesitation in the decision-making process, each evaluation information is allowed to contain multiple values instead of just one value; (2) each evaluation value is followed by a probability value, which further describes the details of the evaluation information; (3) the data structure allows some probability information to be unknown, which effectively expands the application scope of the algorithm. Secondly, the maximization gap model is proposed to calculate unknown parameters, the model can distinguish alternatives with small differences. Thirdly, all the evaluation information will be aggregated by the dynamic hesitant probability fuzzy weighted arithmetic operator. Subsequently, an instance is given to illustrate the effectiveness and the accuracy of the algorithm proposed in the paper. Finally, the advantages of the proposed algorithm are further demonstrated by comparing it with other outstanding algorithms. The main contribution of the paper is that we propose the maximization gap model to obtain the unknown parameters, which can effectively and accurately distinguish alternatives with small differences.

Dynamic Pythagorean fuzzy probabilistic linguistic TOPSIS method with psychological preference and its application for COVID-19 vaccination

The probabilistic linguistic term set (PLTS) has been widely used in multiple criteria group decision making (MCGDM) problems where the linguistic information is uncertain and hesitant. To reflect the different preferences and uncertainties, we propose a new PLTS with probability in the form of Pythagorean fuzzy set (PFS), called Pythagorean fuzzy probabilistic linguistic term set (PFPLTS). In addition, considering the information integrity, uncertainty and DMs' preferences, the operation and aggregation operators for PFPLTS are introduced. Then, the weight method based on minimum deviation and dual ideal point-vector projection is proposed, which considers the time-varying characteristics of the weights and combines multi-dimensional influencing factors. Next, the psychological distance measure is proposed by dividing the psychological space into multiple vectors. Based on the proposed dynamic weight method, three psychological distance measures and TOPSIS method, we develop a dynamic Pythagorean fuzzy probabilistic linguistic TOPSIS method with psychological distance (Psy-TOPSIS), the psychological index ranges from 1 to 40. Finally, a practical case, site selecting of COVID-19 vaccination center, is given and compared with three approaches to illustrate the effectiveness and practicality of PFPLTS and the proposed decision-making method.

Hesitant fuzzy multi-attribute decision making based on binary connection number of set pair analysis

To objectively evaluate the influence of hesitant fuzziness on the ranking of alternatives in multi-attribute decision making with hesitant fuzzy or probabilistic hesitant fuzzy information, the binary connection number of set pair analysis is applied to hesitant fuzzy multi-attribute decision making. The hesitant or probabilistic hesitant fuzzy set is transformed to the binary connection number. A hesitant fuzzy multi-attribute decision making model based on binary connection number is then established. Binary connection number theory is utilized to obtain the hesitant fuzzy center and decision-making suggestions about the alternative ranking under different hesitant fuzzy conditions. Experimental examples show that the hesitant fuzzy multi-attribute decision making model based on binary connection number has a certain versatility. It can determine the optimal scheme under the influence of hesitant fuzziness on the alternative ranking and contains the results of the same hesitant fuzzy decision-making problem using other methods, which helps in targeted decision making according to different hesitant fuzzy conditions.

The risk evaluation of PPP projects: A technique based on probabilistic linguistic terms with weakened hedges

Risk management is a significant part of the success of a public-private partnership (PPP) project. There are four phrases for the process of risk management: Constructing a risk management environment, identifying risk factors, evaluating risk factors, and allocating risk factors. After identifying risk factors, it is imperative to analyze and evaluate critical risk factors, which can help participants formulate strategies to allocate risk factors, and thus alleviate the possible adverse results. The objectives of analyzing and evaluating risk factors focus on two aspects: The possibilities of risk occurrence and the degrees of risk loss. On behalf of determining the critical risk factors effectively, we take the probability degree and linguistic expressions into consideration to manifest experts’ perspectives. We consider critical risk factors in terms of the probabilistic linguistic terms with weakened hedges from the evidential reasoning approach view. The linguistic terms with weakened hedges are applied to express the degree of risk risk loss, and the possibilities of risk occurrence collect from the probabilities of linguistic terms with weakened hedges. First, the commonality function and plausibility function are applied to correct the possibilities of risk occurrence for linguistic terms with weakened hedges. Next, we build a risk evaluation model from experts’ risk propensity and risk perceptions. Moreover, a case study of the risk analyzing and evaluating process of a PPP project is applied to illustrate the availability and effectiveness of the proposed model. We contrast the introduced model with other approaches. Finally, the advantages of this model intend to improve the linguistic terms with weakened hedges for the probabilistic linguistic terms with weakened hedges and evaluate risk factors considering the evidence reasoning approach.

Representing a probabilistic linguistic term set with an interval type-2 fuzzy set and the application in green supplier selection

The use of probabilistic linguistic term sets (PLTSs) means the process of computing with words. The existing methods computing with PLTSs mainly use symbolic model. To provide a semantic model for computing with PLTSs, we propose to represent a PLTS by using an interval type-2 fuzzy set (IT2FS). The key step is to compute the footprint of uncertainty of the IT2FS. To this aim, the upper membership function is computed by aggregating the membership functions of the linguistic terms contained in the PLTS, and the lower membership function is obtained by moving the upper membership function downward with the step being total entropy of the PLTS. The comparison rules, some operations, and an aggregation operator for PLTSs are introduced. Based on the proposed method of computing with PLTSs, a multi-criteria group decision making model is introduced. The proposed decision making model is then applied in green supplier selection problem to show its feasibility.

Projection-based probabilistic linguistic multi-criteria decision-making method for new energy project selection

The development of new energy industry is a pressing issue due to the deterioration of the environment. The selection of new energy projects is a critical problem for decision makers. Incomplete and uncertain information appears in the process of new energy project selection. Compared with other linguistic expressions, probabilistic linguistic term set (PLTS) simultaneously reflects all possible linguistic terms and their corresponding weights, which conforms to the cognitive habits of people. Thus, a multi-criteria decision-making framework under PLTS environment is constructed for energy project selection. Firstly, a normalised projection model of PLTS, which considers the distance and the angle between two objects, is proposed to overcome the limitations of distance measurement. Secondly, a comprehensive weight-determination method combining the maximum deviation and expert scoring methods is developed to calculate the weight vector of the criteria. Furthermore, a projection-based VIKOR (Višekriterijumska optimizacija i kompromisno rešenje) method is established to select new energy projects, which can reflect the preferences of decision makers for group utility and individual regret. Finally, a numerical study on new energy project selection is performed to determine the validity and applicability of this method. Sensitive and comparative analyses are also conducted to reflect the rationality and feasibility of the method.

A Novel Multi-Criteria Group Decision-Making Approach Based on Bonferroni and Heronian Mean Operators under Hesitant 2-Tuple Linguistic Environment

Ambiguous and uncertain facts can be handled using a hesitant 2-tuple linguistic set (H2TLS), an important expansion of the 2-tuple linguistic set. The vagueness and uncertainty of data can be grabbed by using aggregation operators. Therefore, aggregation operators play an important role in computational processes to merge the information provided by decision makers (DMs). Furthermore, the aggregation operator is a potential mechanism for merging multisource data which is synonymous with cooperative preference. The aggregation operators need to be studied and analyzed from various perspectives to represent complex choice situations more readily and capture the diverse experiences of DMs. In this manuscript, we propose some valuable operational laws for H2TLS. These new operational laws work through the individual aggregation of linguistic words and the collection of translation parameters. We introduced a hesitant 2-tuple linguistic weighted average (H2TLWA) operator to solve multi-criteria group decision-making (MCGDM) problems. We also define hesitant 2-tuple linguistic Bonferroni mean (H2TLBM) operator, hesitant 2-tuple linguistic geometric Bonferroni mean (H2TLGBM) operator, hesitant 2-tuple linguistic Heronian mean (H2TLHM) operator, and a hesitant 2-tuple linguistic geometric Heronian mean (H2TLGHM) operator based on the novel operational laws proposed in this paper. We define the aggregation operators for addition, subtraction, multiplication, division, scalar multiplication, power and complement with their respective properties. An application example and comparison analysis were examined to show the usefulness and practicality of the work.

Expected consistency-based model and multiplicative DEA cross-efficiency for group decision-making with incomplete distribution linguistic preference relations

Faced with complex decision problems, distribution linguistic preference relation (DLPR) is an effective way for decision-makers (DMs) to express preference information. However, due to the complexity of the decision-making environment, DMs may not be able to provide complete linguistic distribution for all linguistic terms in DLPRs, which results in incomplete DLPRs. Therefore, in order to solve group decision-making (GDM) with incomplete DLPRs, this paper proposes expected consistency-based model and multiplicative DEA cross-efficiency. For a given incomplete DLPRs, we first propose an optimization model to obtain complete DLPR. This optimization model can evaluate the missing linguistic distribution and ensure that the obtained DLPR has a high consistency level. And then, we develop a transformation function that can transform DLPRs into multiplicative preference relations (MPRs). Furthermore, we design an improved multiplicative DEA model to obtain the priority vector of MPR for ranking all alternatives. Finally, a numerical example is provided to show the rationality and applicability of the proposed GDM method.

A review on fuzzy preference modeling methods for group decision-making

With the rise of group decision-making and the increasingly complex decision-making environment, preference modeling for decision makers has become more and more important, and many preference modeling methods have emerged. Based on the fuzzy theory, researchers have proposed a large number of preference models to express the subjective uncertainty of decision makers. These methods based on fuzzy theory are collectively referred to as fuzzy preference modeling methods. The fuzzy sets preference model is the first practice of fuzzy theory used in the field of preference modeling, and it is still widely used by researchers until now. Subsequently, based on fuzzy theory, the researchers also proposed linguistic term sets and cloud model. These methods have different representation domains, and are applicable to different decision-making environment. In this paper we give a review of classical fuzzy preference modeling methods and its latest extensions and variants. After the presentation of comparative analyses on the existing methods, we figure out some current challenges and possible future development directions in the field of fuzzy preference modeling.

A new EDAS method for probabilistic linguistic information based on evidence theory and its application in evaluating nursing homes

With the sharp increase in the elderly population and the gradual invalidation of traditional long-term care style, the supply-demand contradiction for nursing homes services appears. A suitable evaluation mechanism is very useful to resolve the contradiction. The evaluation process can be seen as a multiple criteria decision making (MCDM) problem. Because some criteria are subjective and the evaluation process usually needs more than one decision maker (DM), probabilistic linguistic information is suitable to express DMs’ opinions. Therefore, we propose a novel EDAS method with probabilistic linguistic information based on D-S evidence theory for evaluating nursing homes. First, a new score function for probabilistic linguistic term set (PLTS) is put forward in order to compare PLTSs and use EDAS method conveniently. Then, a novel uncertainty measure based on D-S evidence theory is proposed to obtain the criteria weights. Furthermore, a novel EDAS method for PLTSs based on cobweb area model is put forward to reduce the effect of some extreme values influencing the decision result. Finally, our method is applied to a real case of evaluating nursing homes in Nanjing city, and the effectiveness of our method is illustrated by comparing the traditional decision methods.