Hesitant Fuzzy Linguistic Elements Research Articles

A 2-order additive fuzzy measure identification method based on hesitant fuzzy linguistic interaction degree and its application in credit assessment

To reflect both fuzziness and hesitation in the evaluation of interactivity between attributes in the identification process of 2-order additive fuzzy measure, this work uses the hesitant fuzzy linguistic term set (HFLTS) to describe and depict the interactivity between attributes. Firstly, the interactivity between attributes is defined by the supermodular game theory. According to this definition, a linguistic term set is established to characterize the interactivity between attributes. Under the linguistic term set, the experts employ linguistic expressions generated by context-free grammar to qualitatively describe the interactivity between attributes. Secondly, through the conversion function, the linguistic expressions are transformed into the hesitant fuzzy linguistic term sets (HFLTSs). The individual evaluation results of all experts were further aggregated with the defined hesitant fuzzy linguistic weighted power average operator (HFLWPA). Thirdly, based on the standard Euclidean distance formula of the hesitant fuzzy linguistic elements (HFLEs), the hesitant fuzzy linguistic interaction degree (HFLID) between attributes is defined and calculated by constructing a piecewise function. As a result, a 2-order additive fuzzy measure identification method based on HFLID is proposed. Based on the proposed method, using the Choquet fuzzy integral as nonlinear integration operator, a multi-attribute decision making (MADM) process is then presented. Taking the credit assessment of the big data listed companies in China as an application example, the analysis results of application example prove the feasibility and effectiveness of the proposed method. This work successfully reflects both the fuzziness and hesitation in evaluating the interactivity between attributes in the identification process of 2-order additive fuzzy measure, enriches the theoretical framework of 2-order additive fuzzy measure, and expands the applicability and methodology of 2-order additive fuzzy measure in multi-attribute decision making.

Novel Distance Measures of Multigranular Unbalanced Hesitant Fuzzy Linguistic Term Sets Based on Semantics Intervals.

In the field of qualitative decision making with hesitant fuzzy linguistic term sets (HFLTSs), distance measure (DM) is a significant concept that reflects the degree of difference between HFLTSs. Various DMs among HFLTSs have been proposed, which enhance the applicability of HFLTSs in multicriteria decision making (MCDM) under qualitative hesitation information. However, existing strategies not only have their own pros and cons but also fail to measure linguistic assessments from multiple linguistic term sets with different distributions (i.e., multigranular unbalanced linguistic information). In this article, we first propose a new strict DM between two hesitant fuzzy linguistic elements (HFLEs) based on the Wasserstein distance of their semantics intervals. Then, two novel kinds of DMs (Euclidean and Chebyshev forms) for HFLTSs are proposed and their strictness is proved. Weighted and ordered weighted versions of HFLTSs based on Euclidean form are derived. Afterward, illustrative examples, simulations, and related analyses are given to demonstrate the rationality of the proposals. Finally, two cases are applied to verify the efficiency and practicality of the novel measures in real life.

A hesitant fuzzy SMART method based on a new score function for information literacy assessment of teachers

As two powerful and flexible tools for decision-makers (DMs) to model the complex cognition, the hesitant fuzzy set (HFS) and hesitant fuzzy linguistic term set (HFLTS) allow DMs to express their opinions with several possible membership values or linguistic terms on the objects over each criterion. The aim of this article is to develop a novel score function of the HFS and HFLTS including hesitant degree and fuzzy degree information. For this purpose, the notion of fuzzy degree of the hesitant fuzzy element (HFE) and hesitant fuzzy linguistic element (HFLE) is introduced first. Then, considering both the hesitant degree and fuzzy degree information in expressions, the new score function, namely the Score-H&FD, is designed. Based on which, we extend the classical SMART (simple multi-attribute rating technique) method to the hesitant fuzzy environment. As a result, the hesitant fuzzy SMART (HF-SMART) method is developed in this article. Afterwards, we apply our proposed approach to assess and rank several teachers concerning information literacy. Finally, sensitive analysis and comparative analysis are carried out. The results show that the proposed method in this article has substantial advantages and applicability.

Hesitant Fuzzy 2-Dimension Linguistic Programming Technique for Multidimensional Analysis of Preference for Multicriteria Group Decision Making

The hesitant fuzzy 2-dimension linguistic element (HF2DLE) allows decision makers to express the importance or reliability of each term included in a hesitant fuzzy linguistic element as a linguistic term. This paper investigates a programming technique for multidimensional analysis of preference for hesitant fuzzy 2-dimension linguistic multicriteria group decision making. Considering the flexibility of HF2DLEs in expressing hesitant qualitative preference information, we first adopt HF2DLEs to depict both the evaluation values of alternatives and the truth degrees of alternative comparisons. To calculate the relative closeness degrees (RCDs) of alternatives, the Euclidean distances between HF2DLEs are defined. Based on RCDs and preference relations on alternatives, the group consistency and inconsistency indices are constructed, and a bi-objective hesitant fuzzy 2-dimension linguistic programming model is established to derive the criteria weights and positive and negative ideal solutions. Since the objective functions and partial constraint coefficients of the established model are HF2DLEs, an effective solution is developed, through which the RCDs can be calculated to obtain the individual rankings of alternatives. Furthermore, a single-objective assignment model is constructed to determine the best alternative. Finally, a case study is conducted to illustrate the feasibility of the proposed method, and its effectiveness is demonstrated by comparison analyses.

A generalized TODIM-ELECTRE II based integrated decision-making framework for technology selection of energy conservation and emission reduction with unknown weight information

Energy conservation and emission reduction (ECER) has become an indispensable trend of green life. How to choose a suitable technology for ECER under complex decision-making scenarios has become a key issue faced by traditional industrial enterprises. In this paper, a new integrated decision-making framework is established for technology-selection problems. Firstly, to describe complex linguistic information more accurately and reduce information loss, this framework employs the double hierarchy hesitant fuzzy linguistic term sets (DHHFLTSs) to describe the performance of alternatives. To avoid data redundancy and simplify the computation, we improve the operations of double hierarchy hesitant fuzzy linguistic elements (DHHFLEs) and propose a new comparison method for DHHFLEs. Secondly, based on the proposed normalized projection-based difference measurement, a novel method is proposed to derive the weights of experts regarding each criterion, the group decision-making method based on the best-worst method is also utilized to derive the criteria’s weights via consistent pairwise comparisons. Further, an integrated generalized TODIM (an acronym in Portuguese of interactive and multiple attribute decision making)-ELECTRE II (Elimination and Choice Translating Reality II) method is established to rank alternatives, which has the advantages of dealing with the non-compensatory problem of criteria and considering risk-aversion behavior of experts simultaneously. Subsequently, a case study of emission-reduction technology investment is provided to manifest the practicality and reliability of the given framework. Finally, the preponderance and effectiveness of the proposed method are illuminated through a comparative analysis with several existing representative methods.

A multi-attribute decision-making framework for Chinese medicine medical diagnosis with correlation measures under double hierarchy hesitant fuzzy linguistic environment

In order to meet the increasingly complex and changeable decision-making needs, the double hierarchy hesitant fuzzy linguistic term set (DHHFLTS) expresses linguistic information through two independent linguistic term sets, which is a powerful tool for expressing complex linguistic information. Therefore, the research on the DHHFLTS has great theoretical and practical significance. Considering that correlation measures are not only the theoretical basis for solving linguistic decision-making problems, but also the cornerstone of many multi-attribute decision-making (MADM) methods. Therefore, this paper is devoted to the research on the correlation measure of DHHFLTSs. Based on the equivalent transformation functions of the double hierarchy hesitant fuzzy linguistic element (DHHFLE), we propose the mean and hesitancy degree of DHHFLEs and the mean and variance of DHHFLTSs. Then, this paper proposes the hesitancy degree-based correlation and correlation coefficient of DHHFLTSs. In addition, on the one hand, considering that hesitation is a key feature of the DHHFLTS, this paper gives the upper and lower bounds of the above correlation coefficient. On the other hand, taking into account the weighting factors in the actual problem, the weighted correlation coefficient and the ordered weighted correlation measure are proposed. Then, a general framework for applying the correlation measures proposed in this paper to practical MADM problems is given. Finally, taking the diagnosis of traditional Chinese medicine as an example, it proves that this method is scientific and feasible, and compares and analyzes this method with the existing related correlation measure methods.

A consensus measure for group decision making with hesitant linguistic preference information based on double alpha-cut

The hesitant fuzzy linguistic term set, which is characterized by a set of possible linguistic terms, becomes a useful tool to describe the complex cognitions of experts. In many cases, it is much more flexible for experts to provide evaluation information via pairwise comparisons rather than give their evaluation information on options directly. In this regard, the hesitant fuzzy linguistic preference relation (HFLPR) whose elements are hesitant fuzzy linguistic elements was introduced. Besides, to make a reasonable decision, a group of experts are usually involved in practice and thus how to reach an agreement among experts whose perceptions are represented by HFLPRs turns to be significantly important. To meet this challenge, in this study, we propose a novel consensus measure for group decision making with HFLPRs. Firstly, we define an alpha-cut-based method to calculate the similarities among different hesitant fuzzy linguistic evaluations and then develop an alpha-cut-based consensus measure for group decision making with HFLPRs. By converting the linguistic terms of hesitant fuzzy linguistic elements into numerical values of 0 or 1, the consensus measure can be simplified. Finally, to illustrate the effectiveness of the method, we apply it to a practical case study. A comparative analysis is provided to demonstrate the advantages and significance in practical applications of the proposed method.

Probabilistic double hierarchy linguistic term set and its use in designing an improved VIKOR method: The application in smart healthcare

Double hierarchy hesitant fuzzy linguistic term set (DHHFLTS) can be used to express complex linguistic information by combining two hierarchy linguistic term sets with 2-tuple linguistic structures. In decision-making processes, experts’ assessment information may often be represented by some possible double hierarchy hesitant fuzzy linguistic elements (DHHFLEs) or some DHHFLEs with probability information, and we cannot ignore these probabilities when they are directly provided or aggregated by the experts’ assessments. As we are aware that representing probability information is a new improvement and challenge for DHHFLTSs, this paper defines a novel and more general concept named probabilistic double hierarchy linguistic term set (PDHLTS). Then, to propose some more reasonable operations and a distance measure of PDHLTSs, we develop an adjustment method to ensure that two PDHLTSs have same probability distribution. Additionally, this paper develops an extended probabilistic double hierarchy linguistic VIKOR method by improving the traditional VIKOR method. Moreover, the advantages and practicality of the proposed method are demonstrated by applying it to solve a practical multiple criteria decision-making problem involving smart healthcare. Finally, we make some comparative analyses, as well as discussing possible directions for future studies.

Selecting a Public Service Outsourcer Based on the Improved ELECTRE II Method with Unknown Weight Information under a Double Hierarchy Hesitant Linguistic Environment

In present-day society, government public service outsourcing has become an irreversible trend due to the gradually increasing public pursuit of service quality and efficiency. To better meet the needs of the public and effectively improve the quality of service, it has been a crucial issue for government departments to choose the most desirable one from a series of public service outsourcers (PSOs) with distinct characteristics. In this paper, to deal with such decision problems, we propose the improved elimination and choice translating reality (ELECTRE) II method with unknown weight information under the double hierarchy hesitant fuzzy linguistic (DHHFL) environment to accurately and effectively select the best PSO. Firstly, aiming at the shortcomings of the original comparison method for double hierarchy hesitant fuzzy linguistic elements (DHHFLEs), we define the hesitant deviation degree (HDD) for DHHFLEs and, based on this, further propose a new comparison method for comparing DHHFLEs more reasonably. Secondly, inspired by the classical power average (PA) operator proposed by Yager, a new method is introduced to determine the weights of experts with respect to each attribute, based on the support degree between attributes. Afterwards, an improved ELECTRE II method is proposed to address the problem of PSO selection. A numerical case about e-government outsourcer selection is given to demonstrate the enforceability of the method. Finally, comparisons between previous methods and our method are carried out to illustrate the effectiveness and strengths of the proposed method.

Three-way group decisions under hesitant fuzzy linguistic environment for green supplier selection

Purpose The purpose of this paper is to propose a three-way group decision-making approach to address the selection of green supplier, by extending decision-theoretic rough set (DTRS) into hesitant fuzzy linguistic (HFL) environment, considering the flexible evaluation expression format of HFL term set (HFLTS) and the idea of minimum expected risk in DTRS. Design/methodology/approach Specifically, the authors first present the calculation method of the conditional probability and discuss the loss functions of DTRS with HFL element (HFLE), along with some associated properties being investigated in detail. Further, three-way group decisions rules can be deduced, followed by the cost of every green supplier candidate. Thus, based on these discussions, a novel green supplier selection DTRS model that combines multi-criteria group decision-making (MCGDM) and HFLTS is designed. Findings A numerical example of green supplier selection, the comparative analysis and associated discussions are conducted to illustrate the applicability and novelty of the presented model. Practical implications The selection of green supplier has played a critically strategic role in sustainable enterprise development due to continuous environmental concerns. This paper offers an insight for companies to select green supplier selection from the perspective of three-way group decisions. Originality/value This paper uses three-way decisions to address green supplier selection in the HFL context, which is considered as a MCGDM issue.

Clustering-based method for large group decision making with hesitant fuzzy linguistic information: Integrating correlation and consensus

Aiming at the large-scale experts and the lower consensus in large group decision making, a novel clustering-based method integrating correlation and consensus of hesitant fuzzy linguistic information is proposed. Firstly, develop a new hesitant degree function for hesitant fuzzy linguistic element considering its scale. Secondly, put forward the correlation measure and consensus measure models combining the hesitant degree. And then present a clustering method integrating the correlation and consensus to divide the large-scale experts into several clusters. The clustering method simultaneously ensures the cohesion of clusters and the gradual increasing of the collective consensus level. After clustering, activate the selection process to update the weights of clusters combining the number of experts in clusters and the consensus level of clusters and use the score function considering the hesitant degree to rank the alternatives. Finally, a case and some comparisons are studied and analyzed to verify the rationality and effectiveness of the method.

CONSENSUS BASED ON MULTIPLICATIVE CONSISTENT DOUBLE HIERARCHY LINGUISTIC PREFERENCES: VENTURE CAPITAL IN REAL ESTATE MARKET

Based on the Computing with Words (CW), double hierarchy hesitant fuzzy linguistic term set (DHHFLTS) can be used to express complex linguistic information accurately with two simple linguistic hierarchies. This paper proposes a group decision making (GDM) model based on multiplicative consistency and consensus with double hierarchy hesitant fuzzy linguistic preference relations (DHHFLPRs). Firstly, a correlation coefficient of DHHFLTSs is defined based on the distance measures of double hierarchy hesitant fuzzy linguistic elements (DHHFLEs). Then, a multiplicative consistency property of DHHFLPRs is investigated, and a consistency checking method and a feedback mechanism-based repairing algorithm are developed to ensure all DHHFLPRs with acceptable multiplicative consistency. Furthermore, a correlation measure for DHHFLPRs based on the correlation coefficient of DHHFLTSs is proposed, and a new consensus reaching method on the basis of the correlation measure is developed, which can be used to fully obtain the consensus degree from both positive and negative angles. Finally, we make some comparative analyses with other existing consistency checking and repairing method as well as the consensus reaching approach to illustrate the effectiveness of the proposed method by a case study concerning the assessment of the venture capital project about real estate market in some cities of China.

Hesitancy degree-based correlation measures for hesitant fuzzy linguistic term sets and their applications in multiple criteria decision making

The hesitant fuzzy linguistic term set (HFLTS) turns out to be useful in representing people's hesitant qualitative information. The aim of this paper is to investigate new correlation measures between HFLTSs and apply them in decision-making process. Firstly, the concepts of mean and hesitancy degree of hesitant fuzzy linguistic elements are introduced. Based on them, we address the drawbacks of the existing correlation measures between HFLTSs. Then, a new correlation coefficient between HFLTSs is established. Additionally, the hesitancy degree of the hesitant fuzzy linguistic correlation coefficient is proposed, which is composed by the upper and lower bounds of the hesitant fuzzy linguistic correlation coefficient. To show the applicability of the proposed correlation measures, a correlation coefficient-based method is developed for multiple criteria decision making in the cases that the weights of criteria are either known or unknown. A practical example concerning the strategic management of Sichuan liquor brands in China is given to validate the proposed method. It is verified that the proposed correlation coefficients between HFLTSs is more convincing than the existing ones and the developed correlation coefficient-based hesitant fuzzy linguistic MCDM with the weights of criteria being either completely known or unknown is applicable.

Hesitant fuzzy linguistic portfolio model with variable risk appetite and its application in the investment ratio calculation

Qualitative evaluation information is important for financial decision-making and investment when quantitative data are unavailable. Although an alternative ranking is available, specific portfolio and optimal investment ratios cannot be obtained by using the qualitative decision-making methods. To address this issue, this paper proposes a hesitant fuzzy linguistic portfolio model based on the max-score rule and the hesitant fuzzy linguistic element with variable risk appetite (HFLE-RA). The HFLE-RA is able to express qualitative evaluation information by using the hesitant fuzzy linguistic term set and describe the variable investor risk appetites by introducing the asymmetric sigmoid semantics. Thus, different investors can be distinguished by the risk appetite parameters according to the asymmetric sigmoid semantics, and the optimal investment ratios can be obtained by applying the proposed portfolio model. Moreover, the investment opportunities and efficient frontiers of the hesitant fuzzy linguistic portfolio model are investigated. Also, a value-at-risk fitting approach is introduced to calculate the risk appetite parameters. Based on these works, a qualitative investment ratio calculation process is provided in the HFLE-RA environment. Lastly, a real example of calculating the optimal investment ratios for four newly listed stocks in the Growth Enterprises Market board of the Shenzhen Stock Exchange is provided to demonstrate the proposed approaches.

An integrated method for cognitive complex multiple experts multiple criteria decision making based on ELECTRE III with weighted Borda rule

The ELECTRE (ELimination Et Choix Traduisant la REalité, in French) is an effective multiple criteria decision making method based on comparative analysis. Among the family of the ELECTRE methods and their extensions, the ELECTRE III is widely used since it can tackle uncertain and imprecise information. The hesitant fuzzy linguistic term set can represent people's perceptions more comprehensively and flexibly than exact numbers especially in cognitive complex decision-making process. In this paper, we develop an integrated method based on the ELECTRE III to handle the cognitive complex multiple experts multiple criteria decision making problems in which the cognitive complex information is represented by hesitant fuzzy linguistic term sets and the outranking relations between alternatives are calculated by a novel score-function-based distance measure between hesitant fuzzy linguistic elements. A combinative weight-determining method involving both subjective and objective opinions of experts is introduced to derive the weights of criteria. After obtaining the ranking of alternatives from each experts’ decision matrix by the distillation algorithm, the weighted Borda rule is implemented to aggregate the rankings of alternatives regarding different experts. Some ordinal consensus measures are introduced to identify the reliability of the final ranking result. An application of hospital ranking in China is provided to validate the efficiency of the proposed method.

Double Hierarchy Hesitant Fuzzy Linguistic LINMAP Method for Multiple Attribute Group Decision Making

Compared with hesitant fuzzy linguistic term set (HFLTS), double hierarchy hesitant fuzzy linguistic term set (DHHFLTS) has a second hierarchy linguistic term set, which is a detailed supplementary of each linguistic term included in the first hierarchy linguistic term set. Thus, DHHFLTS can express more complex and sufficient evaluation information than HFLTS. To solve multiple attribute group decision making (MAGDM) problems in which the assessment values of alternatives and the preference relations between alternatives are denoted by double hierarchy hesitant fuzzy linguistic elements, this paper extends the traditional LINMAP method under double hierarchy hesitant fuzzy linguistic environment. A practical example is provided to demonstrate the applicability of the proposed method.

Hesitant Fuzzy Linguistic Analytic Hierarchical Process With Prioritization, Consistency Checking, and Inconsistency Repairing

Analytic hierarchy process (AHP), as one of the most important methods to tackle multiple criteria decision-making problems, has achieved much success over the past several decades. Given that linguistic expressions are much closer than numerical values or single linguistic terms to a human way of thinking and cognition, this paper investigates the AHP with comparative linguistic expressions. After providing the snapshot of classical AHP and its fuzzy extensions, we propose the framework of hesitant fuzzy linguistic AHP, which shows how to yield a decision for qualitative decision-making problems with complex linguistic expressions. First, the comparative linguistic expressions over criteria or alternatives are transformed into hesitant fuzzy linguistic elements and then the hesitant fuzzy linguistic preference relations (HFLPRs) are constructed. Considering that HFLPRs may be inconsistent, we conduct consistency checking and improving processes after obtaining priorities from the HFLPRs based on a linear programming method. Regarding the consistency-improving process, we develop a new way to establish a perfectly consistent HFLPR. The procedure of the hesitant fuzzy linguistic AHP is given in stepwise. Finally, a numerical example concerning the used-car management in a lemon market is given to illustrate the efficiency of the proposed hesitant fuzzy linguistic AHP method.

Hesitant Fuzzy Linguistic Possibility Degree-Based Linear Assignment Method for Multiple Criteria Decision-Making

Hesitant fuzzy linguistic term set (HFLTS), as a flexible tool to represent people’s uncertain cognition, has attracted lots of scholars’ research interests, and a series of methodologies have been proposed to deal with a variety of decision-making problems. In this paper, we develop a hesitant fuzzy linguistic possibility degree-based linear assignment (HFL-PDLA) method to tackle the multiple criteria decision-making (MCDM) problems under hesitant fuzzy linguistic environment. Firstly, we define the possibility degree of hesitant fuzzy linguistic element (HFLE). Additionally, some relevant concepts related to the HFL-PDLA method are proposed, such as the relative difference matrix, the rank contribution matrix, the optimal permutation matrix, etc. Furthermore, the algorithm of the HFL-PDLA method is given to deal with hesitant fuzzy linguistic MCDM problems. Moreover, we apply the HFL-PDLA method to deal with a practical case which is to select the optimal treatment technology for disposing the outspent or old medical apparatuses and instruments in West China Hospital (WCH). Finally, we show the advantages of the HFL-PDLA method by making some comparative analyses with the TOPSIS method, the VIKOR method the PROMETHEE method and the LINMAP method.

A New Hesitant Fuzzy Linguistic ORESTE Method for Hybrid Multicriteria Decision Making

The hesitant fuzzy linguistic term set (HFLTS) is an effective tool to express the experts’ subjective evaluations in the processes of decision making. To solve the problem with both qualitative and quantitative criteria in the context of HFLTSs and the crisp weights of criteria being unknown, this paper proposes a new multicriteria decision making method. First, formulas are developed to convert the quantitative data into the hesitant fuzzy linguistic elements. Then, motivated by the ORESTE method, we develop a new global preference score function to aggregate the criterion weights and criterion values, both of which are expressed as hesitant fuzzy linguistic elements. To get the real relation between alternatives, three preference intensity formulas are proposed and a hesitant fuzzy linguistic indifference threshold is introduced. We establish a conflict test framework after detailed research on the threshold values. On these bases, a new hesitant fuzzy linguistic ORESTE method is developed and the calculation process of this method is described. A case study on supplier selection is then presented to illustrate the method. Finally, some comparative analyses with other methods are conducted to show the practicability and reliability of the proposed method.

Multiple criteria decision making based on distance and similarity measures under double hierarchy hesitant fuzzy linguistic environment

The hesitant fuzzy linguistic term set (HFLTS) has been studied from different research directions. To describe the complicated linguistic information more accurately and reasonably, the double hierarchy linguistic term set (double hierarchy LTS) and double hierarchy hesitant fuzzy linguistic term set (double hierarchy HFLTS) were defined. Considering that the distance and similarity measures are the basis of decision making with double hierarchy hesitant fuzzy linguistic information, this paper proposes some distance and similarity measures of double hierarchy hesitant fuzzy linguistic elements (DHFLEs) and double hierarchy HFLTSs from different angles. We develop a decision-making method to deal with multiple criteria decision making (MCDM) problems on the basis of these distance and similarity measures. Finally, we apply this method to deal with a practical MCDM problem about Sichuan liquor brand assessment.