Hesitant Fuzzy Linguistic Sets Research Articles

Combinative-distance-based assessment approach for the evaluation of artificial intelligence cloud platforms using probabilistic linguistic hesitant fuzzy sets

With the rapid expansion of artificial intelligence (AI) and machine learning, the evaluation of AI cloud platforms has become a critical research topic. Given the availability of many platforms, selecting the best AI cloud services that can satisfy the requirements and budget of an organization is crucial. Several solutions, each with its advantages and disadvantages, are available. In this study, a combinative-distance-based assessment approach was proposed in probabilistic linguistic hesitant fuzzy sets (PLHFSs) to accommodate the multiple characteristics of group decision-making. The original data were normalized using a standardized process that integrated numerous methodologies. Furthermore, under PLHFSs, the statistical variance approach was used to generate the weighted objective of the vector of assessment criteria. Finally, an AI cloud platform evaluation and comparison analysis case study was used to validate the feasibility of this method.

Undergraduate Teaching Audit and Evaluation Using an Extended ORESTE Method with Interval-Valued Hesitant Fuzzy Linguistic Sets

Undergraduate teaching audit and evaluation (UTAE) plays a substantial role in the teaching quality assurance and monitoring of universities. It achieves the goal of selecting the best university for promoting the quality of higher education in China. Generally, the UTAE is a complex decision-making problem by considering competing evaluation criteria. Moreover, the evaluation information on the teaching quality of universities is often ambiguous and hesitant because of the vagueness existing in human judgments. Previous studies on UTAE have paid subtle attention towards the managing of linguistic expressions and the performance priority of universities. The interval-valued hesitant fuzzy linguistic sets (IVHFLSs) can effectively describe uncertainty, hesitancy, and inconsistency inherent in decision-making process. The ORESTE (organísation, rangement et Synthèse de données relarionnelles, in French) is a new outranking decision-making method which can show detailed distinctions between alternatives. Therefore, in this study, we propose a new UTAE approach based on the VHFLSs and ORESTE method to resolve the prioritization of universities for selecting the optimal university to benchmark. Specifically, the presented method handles the hesitant and uncertain linguistic expressions of experts by adopting the IVHFLSs and determines the ranking of universities with an extended ORESTE approach. Finally, a practical UTAE example illustrates the feasibility the proposed approach and a comparison analysis provides grounding for the superiority of the integrated approach. When the obtained results are evaluated, U2 has been determined as the best university. The results indicate the good performance of the proposed UTAE approach in evaluating and improving the teaching quality of universities.

Matrix games involving interval-valued hesitant fuzzy linguistic sets and its application to electric vehicles

Game theory has been successfully applied in a variety of domains to deal with competitive environments between individuals or groups. The matrix games involving fuzzy, interval fuzzy, and intuitionistic fuzzy numbers exclusively examine the numeric components of an issue. However, several researchers have also examined various extensions of conventional game theory, considering the ambiguous situations for payoffs and goals. In many real-life scenarios, qualitative information is often critical in expressing the payoffs of a matrix game. Thus, the present work contributes to the field of matrix games where the payoffs have been quantified via qualitative variables, termed interval-valued hesitant fuzzy linguistic sets. The mathematical formulation and solution concept for matrix games involving interval-valued hesitant fuzzy linguistic numbers is designed by utilizing an aggregation operator supported by linguistic scale function and solving them by employing score function. Finally, the proposed approach is validated by applying it to electric vehicle sales.

Sub-catchment-based urban flood risk assessment with a multi-index fuzzy evaluation approach: a case study of Jinjiang district, China

Urban flood risk assessment requires attention in inland areas with intensifying climate change and an increasing probability of extreme precipitation. This study describes the developments and testing of a sub-catchment-based multi-index fuzzy evaluation approach that can provide adaptation guidance for municipal decision-makers at a local level. We first built a comprehensive flood risk assessment system considering three categories: hazard, urban system, and social environment. The proposed evaluation system includes hybrid uncertain information that involves random indicator sources and hesitant fuzzy judgments from experts. The storm weather management model combined with geographic information system tools was then applied to obtain random indicators. Subsequently, hesitant fuzzy linguistic sets and the Euclidean distance method were adopted to solve the problem of uncertainty and vagueness from subjective hesitant information. Therefore, the aggregation method provides a beneficial way to assess flood risk in a hybrid uncertain environment. In addition, the proposed approach was applied to the Jinjiang district in an inland city in the P. R. of China. This supports efforts to prioritize locally tailored policies and practical measures for higher-risk sub-catchments within large urban systems.

An Improved ELECTRE II-Based Outranking Method for MADM with Double Hierarchy Hesitant Fuzzy Linguistic Sets and Its Application to Emergency Logistics Provider Selection

An Improved ELECTRE II-Based Outranking Method for MADM with Double Hierarchy Hesitant Fuzzy Linguistic Sets and Its Application to Emergency Logistics Provider Selection

A note on “Pythagorean uncertain linguistic hesitant fuzzy weighted averaging operator and its application in financial group decision making”

Shakeel et al. (Soft Comput 24: 1585–1597, 2020) proposed the concept of a Pythagorean uncertain linguistic hesitant fuzzy set (PULHFS), some arithmetic operations of Pythagorean uncertain linguistic hesitant fuzzy sets (PULHFSs), an approach for comparing PULHFSs and a Pythagorean uncertain linguistic hesitant fuzzy weighted averaging (PULHFWA) operator as well as it extensions. Also, using the proposed comparing approach and the proposed aggregation operators, Shakeel et al. proposed a method for solving multi-attribute group decision making (MAGDM) problems. In future other researchers may use Shakeel et al.’s work in their research work. However, it is observed that the approach for comparing PULHFSs and aggregation operators, proposed by Shakeel et al. (Soft Comput 24: 1585–1597, 2020), are not appropriate. Hence, the method for solving MAGDM problems, proposed by Shakeel et al., is also not appropriate. The aim of this note is to make the researchers aware of the inappropriateness of Shakeel et al. work. Furthermore, point out that to resolve the inappropriateness of Shakeel et al. work (Soft Comput 24: 1585–1597, 2020) is a challenging open research problem.

A Personalized Comprehensive Cloud-Based Method for Heterogeneous MAGDM and Application in COVID-19

This paper proposes a personalized comprehensive cloud-based method for heterogeneous multi-attribute group decision-making (MAGDM), in which the evaluations of alternatives on attributes are represented by LTs (linguistic terms), PLTSs (probabilistic linguistic term sets) and LHFSs (linguistic hesitant fuzzy sets). As an effective tool to describe LTs, cloud model is used to quantify the qualitative evaluations. Firstly, the regulation parameters of entropy and hyper entropy are defined, and they are further incorporated into the transformation process from LTs to clouds for reflecting the different personalities of decision-makers (DMs). To tackle the evaluation information in the form of PLTSs and LHFSs, PLTS and LHFS are transformed into comprehensive cloud of PLTS (C-PLTS) and comprehensive cloud of LHFS (C-LHFS), respectively. Moreover, DMs’ weights are calculated based on the regulation parameters of entropy and hyper entropy. Next, we put forward cloud almost stochastic dominance (CASD) relationship and CASD degree to compare clouds. In addition, by considering three perspectives, a comprehensive tri-objective programing model is constructed to determine the attribute weights. Thereby, a personalized comprehensive cloud-based method is put forward for heterogeneous MAGDM. The validity of the proposed method is demonstrated with a site selection example of emergency medical waste disposal in COVID-19. Finally, sensitivity and comparison analyses are provided to show the effectiveness, stability, flexibility and superiorities of the proposed method.

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.

Selecting Personnel with the Weighted Cross-Entropy TOPSIS of Hesitant Picture Fuzzy Linguistic Sets

Personnel selection is a key important role for the human resource department of organization, and hesitant picture fuzzy linguistic sets (HPFLSs) elaborated the advantages of both hesitant linguistic set and picture fuzzy set, which is more flexible and effective to solve the decision-making problems of personnel selection than other extension of fuzzy linguistic sets (FLSs). Cross-entropy, as effective measurement tools, is wildly used under fuzzy multicriteria decision-making (FMCDM) environment; thus, in order to elaborate the advantages of both cross-entropy and HPFLSs under FMCDM environment, the cross-entropy definition of HPFLSs is firstly given in this paper. Meanwhile, several novel cross-entropy measures between two HPFLSs are introduced, and their related properties are proved. Then, an approach based on the weighted cross-entropy measures and TOPSIS under hesitant picture fuzzy linguistic environment is proposed. Finally, the proposed method is applied to the real personnel’s selection, and the ranking results show that the proposed methods are practical and effective.

Interval-Valued Hesitant Fuzzy Linguistic Multiattribute Decision-Making Method Based on Three-Parameter Heronian Mean Operators

Numerous variants have been proposed for sets of linguistic terms and the interval-valued hesitant fuzzy set (IVHFS). In particular, the interval-valued hesitant fuzzy linguistic set (IVHFLS) is more suitable for defining the hesitancy and inconsistency inherent in the human cognitive processes of decision making. A key aggregation operator is Heronian mean (HM), based on which the correlation among aggregated arguments can be captured. However, the existing HM operators partially overlook the correlation among more than two arguments and lack the properties of idempotency and reducibility. In this work, the limitations of HM operators are first analyzed. Then, two new HM variants are introduced: three-parameter weighted Heronian mean (TPWHM) and three-parameter weighted geometric Heronian mean (TPWGHM). Thus, the reducibility, idempotency, monotonicity, and boundedness properties are proven for the two computational procedures, and unique situations are mentioned. Furthermore, two more elaborate operators are also introduced which are called the interval-valued hesitant fuzzy linguistic TPWHM (IVHFLTPWHM) and the interval-valued hesitant fuzzy linguistic TPWGHM (IVHFLTPWGHM). The main properties, as well as unique situations of these two computational procedures, are discussed. Finally, the introduced methods are clarified by illustrative examples. In addition, the parameter effects on the decision-making outcomes are discussed and comparisons with other reference methods are made.

A Two-Sided Stable Matching Model of Cloud Manufacturing Tasks and Services considering the Nonlinear Relationship between Satisfaction and Expectations

To improve the satisfaction of both service demanders (SDs) and service providers (SPs) in the matching of cloud manufacturing (CMfg) tasks and services, a two-sided stable matching model of CMfg tasks and service considering the nonlinear relationship between satisfaction and expectations is proposed. As the expectations of SDs and SPs are difficult to be quantified directly, an evaluation method based on interval-valued hesitant fuzzy linguistic sets (IVHFLSs) is first presented. Next, a nonlinear model of satisfaction and expectations is built to quantify the satisfaction, which achieves accurate quantification of satisfaction. Then, a two-sided stable matching model of CMfg tasks and service is built, which takes the satisfaction of SDs and SPs as the optimization goals and considers the individual rationalities and blocking pairs. Finally, an adaptive genetic algorithm (AGA) is designed to solve the proposed two-sided matching model. A practical application and comparison analysis is used to verify the effectiveness and superiority of the research.

New method for dependence assessment in human reliability analysis based on linguistic hesitant fuzzy information

Human reliability analysis (HRA) is a proactive approach to model and evaluate human systematic errors, and has been extensively applied in various complicated systems. Dependence assessment among human errors plays a key role in the HRA, which relies heavily on the knowledge and experience of experts in real-world cases. Moreover, there are ofthen different types of uncertainty when experts use linguistic labels to evaluate the dependencies between human failure events. In this context, this paper aims to develop a new method based on linguistic hesitant fuzzy sets and the technique for human error rate prediction (THERP) technique to manage the dependence in HRA. This method handles the linguistic assessments given by experts according to the linguistic hesitant fuzzy sets, determines the weights of influential factors by an extended best-worst method, and confirms the degree of dependence between successive actions based on the THERP method. Finally, the effectiveness and practicality of the presented linguistic hesitant fuzzy THERP method are demonstrated through an empirical healthcare dependence analysis.

How to realize the effect of air pollution control? A hybrid decision framework under the fuzzy environment

Air pollution control is important work and realizing the effect of treatment has a significance on follow-up policy-making and perfection of closed-loop management. Based on the principle of post control, the article constructs a comprehensive decision-making framework for air pollution control effect evaluation. Firstly, considering the impact of sustainable development, the evaluation index system is established from environmental, social and economic aspects. Secondly, the improved hesitant fuzzy linguistic set, fuzzy analytical network process and cloud fuzzy synthetic evaluation are employed as core methods to determine the air pollution control effect. Then, the decision framework is applied in a case study and the result shows that the effect of air pollution control in the region is at a good level. Further, the stability and applicability of the framework are proved through sensitivity and comparative analysis. Finally, suggestions to improve the effectiveness of air pollution control are put forward.

A new risk evaluation methodology based on FMEA, MULTIMOORA, TPOP, and interval-valued hesitant fuzzy linguistic sets with an application to healthcare industry

Purpose The healthcare system is regarded as one of the most critical service industries. The surgical unit is the heart of hospitals in that any failures directly affect the safety of patients, so they should be managed thoroughly. It is an intricate multi-attributes decision-making problem with uncertainty. Uncertain information in the form of fuzzy sets theory has been applied widely to describe the different aspects of system uncertainty. This study aims to present a new methodology to manage the healthcare system failures due to the multi-attributes decision-making process. Design/methodology/approach This study introduces a new risk evaluation methodology by failure mode and effect analysis (FMEA) and MULTIMOORA method. Group decision-making process in this methodology is presented under uncertain information in the form of interval-valued hesitant fuzzy linguistic sets (IVHFLSs). IVHFLSs encompass both qualitative and quantitative interpretation of experts to reflect their preferences, as well the ability and flexibility of derivation of linguistic information by several linguistic terms increase. To avoid the different ranking order of MULTIMOORA approaches, a new interval multi-approaches multi-attribute methodology, namely, technique of precise order preference (TPOP), is extended to provide precise ranking order. Findings The application and precision of proposed integrated IVHFL-MULTIMOORA methodology with TPOP is examined in a case study of healthcare systems. The results indicate the superiority of proposed methodology to prioritize and assess the failures as well as handling system uncertainty. Originality/value This study addresses the challenges of an organization to prioritize potential failures by implementing FMEA method. Moreover, this paper contributes to making the manager's ability in decision-making. The value of this study can be discussed in two aspects. First and foremost, this study provides a new FMEA-based methodology to rank failures precisely. The results prove that the proposed methodology is more robust to changes of different ranking order methods, applied by FMEA. On the other hand, using the capability of IVHFLSs allows collecting accurate information in an ambiguous and uncertain environment.

An integrated multi-criteria decision making approach with linguistic hesitant fuzzy sets for E-learning website evaluation and selection

Network teaching has been widely developed under the influence of COVID-19 pandemic to guarantee the implementation of teaching plans and protect the learning rights of students. Selecting a particular website for network teaching can directly affects end users’ performance and promote network teaching quality. Normally, e-learning website selection can be considered as a complex multi-criteria decision making (MCDM) problem, and experts’ evaluations over the performance of e-learning websites are often imprecise and fuzzy due to the subjective nature of human thinking. In this article, we propose a new integrated MCDM approach on the basis of linguistic hesitant fuzzy sets (LHFSs) and the TODIM (an acronym in Portuguese of interactive and multi-criteria decision making) method to evaluate and select the best e-learning website for network teaching. This introduced method deals with the linguistic assessments of experts based on the LHFSs, determines the weights of evaluation criteria with the best–worst method (BWM), and acquires the ranking of e-learning websites utilizing an extended TODIM method. The applicability and superiority of the presented linguistic hesitant fuzzy TODIM (LHF-TODIM) approach are demonstrated through a realistic e-learning website selection example. Results show that the LHF-TODIM model being proposed is more practical and effective for solving the e-learning website selection problem under vague and uncertain linguistic environment.

An Integrated Decision-Making Model for Analyzing Key Performance Indicators in University Performance Management

University performance has an important effect on the social influence of universities. With increasing emphasis placed on higher education, it is important to improve and optimize university performance management. However, the performance of university management is affected by numerous indicators in practice, and it is difficult for administrators to optimize all of them because of resource restriction. To address this concern, in this paper, we design a novel integrated model by combining linguistic hesitant fuzzy sets (LHFSs) with the decision-making trial and evaluation laboratory (DEMATEL) method to identify key performance indicators (KPIs) for improving the level of university performance management. Specifically, the LHFSs are utilized to express the hesitant and vague interrelationship assessment of performance indicators provided by experts. A modified DEMATEL is adopted to visualize the causal relationship between performance indicators and determine critical ones. Moreover, we introduce a gray relation analysis (GRA)-based method to derive experts’ weights when their weight information is unknown. Finally, a comprehensive university in Shanghai, China, is employed as an example to illustrate the practicability and availability of the proposed linguistic hesitant fuzzy DEMATEL model.

A risk assessment framework of seawater pumped hydro storage project in China under three typical public-private partnership management modes

• Establish unique risk criteria systems of seawater pumped hydro storage under three typical PPP management modes. • Comprehensively evaluate the current risk degree of seawater pumped hydro storage in China. • An improved linguistic hesitant fuzzy sets based cloud model framework is established for risk assessment. • Risk response strategies of seawater pumped hydro storage project in China is proposed. Along with the rapid development of pumped hybrid storage in China, the shortage of inland resources has become a serious problem that restricts its further development. Fortunately, seawater pumped hybrid storage (S-PHS) processes the advantages in saving cost of lower reservoir construction and making full use of coastal resources, which has attracted great attention in China. In view of the characteristics of expanding sources of infrastructure investment funds and improving financial stability of both public and private sectors, varied public-private partnership (PPP) modes are introduced to promote the construction of S-PHS power plant. However, due to lack of experience, high investment, long payback period, and so forth, S-PHS project still holds great uncertain risks in the aspects of economy, environment, technology, etc. Therefore, this paper will study on the risk assessment of S-PHS project under three typical PPP management modes by linguistic hesitant fuzzy sets based cloud model. Result shows that the risk level of S-PHS project locates between “Middle High” and “High”, and PPP-S-PHS processes relatively low risk degree, of which the BOT-S-PHS is the lowest. Moreover, corresponding risk response measures for PPP-S-PHS project are proposed for helping risk prevention and further smooth implementation of PPP-S-PHS project in China.

Evaluation model of surrounding rock stability based on fuzzy rock engineering systems (RES)-connection cloud

The factors affecting the stability of surrounding rock have fuzzy randomness, and their evaluation indicators not only show boundary ambiguity and interval discreteness but also have complex interactions. In order to reflect the distribution characteristics and interaction relationship of the indicators, and improve the accuracy of surrounding rock stability evaluation, a stability evaluation model of surrounding rock based on a fuzzy Rock Engineering Systems (RES)-connection cloud is proposed. The research showed that the introduction of linguistic hesitant fuzzy sets improves RES, resulting in experts’ compilation completely retained. Through cloud theory transformation, the subjectivity can be further weakened, and the credibility of indicator weight can be effectively improved. The two-dimensional cloud cause-effect map can reflect the indicator interaction relationship more intuitively and accurately. The joint state is found to be the most dominant parameter, and groundwater seepage is found to be the least dominant parameter. Furthermore, the connection cloud can overcome the defects of traditional cloud model which assumes the indictor follow normal distribution. Comparing the engineering application results with the matter-element extension method and the fuzzy set method, the feasibility of the present model is verified.

A Novel Multicriteria Group Decision-Making Approach with Hesitant Picture Fuzzy Linguistic Information

In real-life group decision-making environment, different decision-makers (DMs) might be hesitant to provide their evaluation by more than two linguistic terms with positive, neutral, negative, and refusal information (e.g., attitude for support, neutral, oppose, and refusal) for criteria of alternative. In order to solve such kinds of decision-making problems, a novel definition of hesitant picture fuzzy linguistic sets (HPFLSs) is introduced, and the HPFLS-based methods are developed. Considering the operation laws appeared in previous papers are not well suitable for HPFLS operation, the novel operation laws of HPFLSs are developed. Then, two aggregation operators of HPFLSs are developed, including hesitant picture fuzzy linguistic weighted average operator (HPFLSWA) and hesitant picture fuzzy linguistic weighted geometric operator (HPFLSGA). Meanwhile, the related proofs are given in detail. Additionally, the comparison method of score and accuracy functions is provided to rank the alternative. Finally, a real-life case of teaching performance evaluation is used to verify the proposed methods. The same case-based comparisons are further conducted between the proposed method and previous methods. The results showed that the proposed method can well overcome the lack of operation rules appeared in previous multicriteria group decision-making (MCGDM) methods and demonstrate effectiveness.

Green Supplier Evaluation and Selection with an Extended MABAC Method Under the Heterogeneous Information Environment

With the increasing awareness of global environmental protection, green production has become a significant part for enterprises to remain in a competitive position. For a manufacturing company, selecting the most suitable green supplier plays an important role in enhancing its green production performance. In this paper, we develop a new green supplier evaluation and selection model through the combination of heterogeneous criteria information and an extended multi-attributive border approximation area comparison (MABAC) method. Considering the complexity of decision context, heterogeneous information, including real numbers, interval numbers, trapezoidal fuzzy numbers, and linguistic hesitant fuzzy sets, is utilized to evaluate alternative suppliers with respect to the selected criteria. A maximizing consensus approach is constructed to determine the weight of each decision-maker based on incomplete weighting information. Then, the classical MABAC method is modified for ranking candidate green suppliers under the heterogeneous information environment. Finally, the developed green supplier selection model is applied in a case study from the automobile industry to illustrate its practicability and efficiency.