Fuzzy Linguistic Environment Research Articles

A PSO-algorithm-based dual consensus method for large-scale group decision making and its application in medical imaging equipment purchasing

The increasing complexity of social activities requires an expanding number of people to be involved in decision-making, so that the large-scale multi-attribute group decision-making problems have gained widespread attention. After overviewing the researches of large-scale multi-attribute group decision-making methods, we have found that: The existing methods only consider consensus based on evaluation information of alternatives, while ignoring the consensus on importance of attributes. Thus, in order to tackle the issues and describe the hesitancy of decision makers in the decision-making process, this paper proposes a novel dual consensus method in large-scale multi-attribute group decision making under hesitant fuzzy linguistic environment. In the consensus reaching process, the method considers not only the consensus on the evaluation information of alternatives, but also the consensus on the importance of attributes, where both consensus reaching processes are implemented by the particle swarm optimization algorithm. The subjective weights of attributes are derived from the consensus reaching process of preference matrices, and the objective weights of attributes are obtained from the consensus reaching process of decision matrices, so as to acquire the comprehensive weights. After that, the overall ranking of alternatives can be obtained by TODIM. Finally, the proposed method is applied to a case study of medical imaging equipment purchasing decision-making, and the comprehensive analysis is provided to clarify advantages of the proposed method.

CODAS method for Pythagorean 2-tuple linguistic multiple attribute group decision making

The evaluation of the financial performance of universities is conducive to the sustainable development of universities. Based on this, we extend the traditional CODAS (COmbinative Distance-based ASsessment) method to the Pythagorean 2-tuple linguistic fuzzy environment and propose a P2TL-CODAS model to evaluate the financial management performance of universities. Firstly, we briefly describe the definition, the score function, accuracy function, operational laws and the distance calculating method of P2TLSs. Next, two aggregation operators of P2TL including Pythagorean 2-tuple linguistic weighted averaging (P2TLWA) operator and Pythagorean 2-tuple linguistic weighted geometric (P2TLWG) operator are also introduced to fuse overall Pythagorean 2-tuple linguistic evaluation information. Then the steps of CODAS method are depicted briefly. Moreover, we use linguistic Pythagorean 2-tuple linguistic fuzzy numbers to extend the CODAS method. The P2TL-CODAS model is established and all computing steps are simply presented. Furthermore, we apply the proposed method to evaluate the financial management performance about five universities. Finally, a comparison between P2TL-CODAS method and P2TL-TODIM method is made to demonstrate the stability of the new method. The results show that the proposed method has unique advantages.

Three-way group decisions using evidence theory under hesitant fuzzy linguistic environment

In the actual decision-making process, there will be situations where decision-makers with hesitant attitudes have difficulties in evaluating alternatives numerically, and hesitant fuzzy linguistic term sets can provide decision-makers with an effective way to describe hesitancy in linguistic terms. In multi-attribute group decision-making, each decision maker typically holds different preferences. If the variation in decision makers’ assessment weights across evaluations of each attribute for every alternative is not adequately accounted for, it can result in a problem of coarse-grained calculations, leading to information loss. Additionally, the three-way decision model faces significant challenges in information fusion within the context of the hesitant fuzzy linguistic environment. Therefore, we propose a new three-way decision-making model under the hesitant fuzzy linguistic environment. The model obtains the confidence of different decision makers in attribute evaluations through the fusion of D-S evidence theory, and can perform more fine-grained fusion calculations on the evaluation information of different decision makers. In addition, the model considers the cost function of each alternative in different decision-making actions under hesitant fuzzy linguistic environment, calculates the two thresholds of each alternative in the three-way decision model, and derives the decision rules. The effectiveness of the model is verified through a numerical example and two comparative experiments, therefore, the model can be applied in intelligent classification or recommendation systems of hesitant fuzzy linguistic information systems.

New approach for quality function deployment based on social network analysis and interval 2-tuple Pythagorean fuzzy linguistic information

Quality function deployment (QFD) is a useful quality management tool for the transformation of customer requirements (CRs) into engineering characteristics (ECs) in product development. In the literature, a lot of QFD approaches have been proposed to overcome the deficiencies and enhance the performance of the traditional QFD method. However, there are several issues deserving further investigation for improving QFD: majority of the existing methods describe experts’ opinions with single linguistic terms directly, which may produce the loss of information; most of the improved QFD methods cannot take the consensus levels among experts into account. In this study, we develop a new integrated QFD approach based on the interval 2-tuple Pythagorean fuzzy linguistic sets (I2PFLSs), the social network consensus reaching (SNCR) model, and an extended combined compromise solution (CoCoSo) method. There are three main contributions of the presented study: First, the correlation assessments between CRs and ECs given by experts are handled with the I2PFLSs. Second, the SNCR with minimum adjustment distance is employed to coordinate experts’ conflict correlation assessments by considering their trust relationships. Third, an extended CoCoSo method is employed to determine the importance ranking of ECs within the interval 2-tuple Pythagorean fuzzy linguistic environment. Finally, we present an electric vehicle product development case to demonstrate the effectiveness and superiority of the proposed QFD approach. The results show that the new QFD can express experts’ fuzzy and uncertain linguistic assessment information flexibly, deal with experts’ consensus in correlation assessment process, and yield more precise importance ranking of ECs for product improvement.

The Shapley value based on hesitant fuzzy linguistic comprehensive entropy and its application in noncooperative-cooperative biform game

Profit allocation is a decision-making process, and noncooperative-cooperative biform game can effectively depict the real competitive-cooperative relationship. This paper aims to construct an effective Shapley function of biform game in hesitant fuzzy linguistic environment, which can reasonably analyze the formation and the distribution of profits by taking into account the individual hesitation and information fuzziness. Firstly, we propose a new construction method of an entropy for hesitant fuzzy linguistic term sets (HFLTSs). This entropy measure can describe the linguistic information from the aspects of fuzziness and hesitation, which improves the flaws of the existing entropy for HFLTSs. After that, a function for calculating confidence level is defined based on comprehensive entropy. Then in order to study the profit allocation in a competitive-cooperative environment, we define hesitant fuzzy linguistic biform game and its characteristic function, and the effectiveness of the proposed Shapley value function according to an axiomatic system is proved. Finally, the feasibility of this approach is indicated by an example of profit allocation of cooperation in watershed management considering information asymmetry.

A global optimization feedback model with PSO for large scale group decision making in hesitant fuzzy linguistic environments

In an increasingly complex and uncertain decision-making environment, large-scale group decision-making (LSGDM) can offer a more efficient method, allowing a large number of decision-makers (DMs) to truly participate in the decision-making process. The consensus-reaching process (CRP) is an effective method for resolving conflicting opinions among large-scale DMs. However, in the existing CRP of LSGDM, the new consensus state and the adjustment cost borne by inconsistent DMs after implementing feedback suggestions are not taken into consideration. To address this issue, this paper proposes a global optimization feedback model with particle swarm optimization (PSO) for LSGDM in hesitant fuzzy linguistic environments. An improved density-based spatial clustering of applications with noise (DBSCAN) on hesitant fuzzy linguistic term sets (HFLTSs) is introduced to classify large-scale DMs into several clusters, and a weight determination method that combines cluster size and intra-cluster tightness is also presented. The consensus degree of clusters is calculated at two levels: intra-consensus and inter-consensus. To improve the global consensus level with minimum cost, a global optimization feedback model is established to generate recommendation advice for inconsistent DMs, and the model is solved by PSO. A numerical example related to “COVID-19” and some comparisons are provided to verify the feasibility and advantages of the proposed method.

Route intelligent recommendation model and algorithm under the Pythagorean hesitant fuzzy linguistic environment

Route intelligent recommendation model and algorithm under the Pythagorean hesitant fuzzy linguistic environment

Vector Similarity Measures of Dual Hesitant Fuzzy Linguistic Term Sets and Their Applications

The dual hesitant fuzzy linguistic term set (DHFLTS) is defined by two functions that express the grade of membership and the grade of non-membership using a set of linguistic terms. In the present work, we first quote an example to point out that the existing complement operation of DHFLTS is on the wrong track. Meanwhile, we redefine this operation to fill the holes in the existing ones. Next, the notion of information energy under a dual hesitant fuzzy linguistic background is provided in order to build the criteria weight determination model. To further facilitate the theory of DHFLTS, we propose two vector similarity measures, i.e., Jaccard and Dice similarity measures, and their weighted forms for DHFLTS. In addition, we pioneer some generalized similarity measures of DHFLTSs and indicate that the Dice similarity measures are particular instances of the generalized similarity measures for some parameter values. Afterward, the similarity measures-based model with unknown weight information under the background of dual hesitant fuzzy linguistic environment is constructed. Lastly, an illustrated example is included to validate the method’s application, along with sensitivity analysis and comparative analysis, demonstrating the practicality and validity of its results.

Q-rung orthopair triangular fuzzy linguistic Frank aggregation operators and their application

The aim of this paper is to introduce a Frank operator in the q-rung orthopair triangular fuzzy linguistic environment on the basis of the notion of the Frank operator and the q-rung orthopair fuzzy set. Firstly, the concept of a q-rung orthopair triangular fuzzy linguistic set (q-ROTrFLS) is proposed, then several basic operations, score, and accuracy functions to compare the q-ROTrFLS values are defined. Secondly, a series of q-rung orthopair triangular fuzzy linguistic Frank aggregation operators are developed, such as q-rung orthopair triangular fuzzy linguistic Frank weighted average (q-ROTrFLWA)operator,q-rung orthopair triangular fuzzy linguistic Frank weighted geometric (q-ROTrFLWG) operator, and we introduce several relevant properties of these operators and prove their validity, and show the relevant relationship between some operators. Thirdly, two different decision-making approaches are constructed in the q-rung orthopair triangular fuzzy linguistic environment. Furthermore, a practical example is given to explain the developed methods. Finally, a comparative study is conducted, and the relevant sensitivity analysis is also discussed, and the outcome shows the prominence and the effectiveness of the developed methods compared to previous studies.

Sustainable evaluation of energy storage technologies for wind power generation: A multistage decision support framework under multi-granular unbalanced hesitant fuzzy linguistic environment

Energy storage technology (EST) plays a foundational role for dealing with the intermittency of wind power and accelerating the structural revolution of renewable energy systems. Generally, EST selection is treated as a multiple-criteria group decision-making problem. However, stakeholders are not allowed to express multiple preferences via personalized linguistic distribution assessment and their risk appetites have received less attention in the existing approaches. This study aims at prioritizing ESTs by developing a novel multistage support framework where multi-granular unbalanced hesitant fuzzy linguistic term sets (UHFLTSs) are adopted to depict and quantify stakeholders’ opinions based on personalized semantics and granularities. A sustainable index system is devised in four dimensions (economic, technical, environmental and social) and the extended best-worst method (BWM) under multi-granular UHFLTSs environment is combined with maximum deviation method to determine the hybrid weights of criteria. A novel approach linking multi-granular UHFLTSs with double parameters TOPSIS method integrating risk appetite and optimism preference of stakeholders is further proposed by constructing optimization model, which can simultaneously yield the credible experts’ weights and prioritize the most desirable technology. The application of the proposed framework is demonstrated through an empirical case. Eventually, sensitivity analysis and comparative analysis are implemented to verify the effectiveness and validity of our proposal.

Hesitant 2-tuple fuzzy linguistic multi-criteria decision-making method based on correlation measures.

Correlation is considered the most important factor in analyzing the data in statistics. It is used to measure the movement of two different variables linearly. The concept of correlation is well-known and used in different fields to measure the association between two variables. The hesitant 2-tuple fuzzy linguistic set (H2FLS) comes out to be valuable in addressing people’s reluctant subjective data. The purpose of this paper is to analyze new correlation measures between H2FLSs and apply them in the decision-making process. First and foremost, the ideas of mean and variance of hesitant 2-tuple fuzzy linguistic elements (H2FLEs) are introduced. Then, a new correlation coefficient between H2FLSs is established. In addition, considering that different H2FLEs may have different criteria weights, the weighted correlation coefficient and ordered weighted correlation coefficient are further investigated. A practical example concerning the detailed procedure of solving problems is exemplified to feature the reasonableness and attainability of the proposed technique in situations where the criteria weights are either known or unknown. When the weight vector is unknown, the best-worst method (BWM) is used to acquire the criteria weights in the context of a hesitant 2-tuple fuzzy linguistic environment. Furthermore, a comparative study is undertaken with current techniques to provide a vision into the design decision-making process. Finally, it is verified that the proposed correlation coefficient between H2FLSs is more satisfactory than the extant ones, and the correlation coefficient with the weights of criteria being either known or unknown is applicable.

Multi-criteria evaluation of smart product-service design concept under hesitant fuzzy linguistic environment: A novel cloud envelopment analysis approach

Design concept evaluation is an essential but challenging task in smart product service system (SPSS) design. It is critical to select the design concept with better smart experience to ensure the success of SPSS design. Meanwhile, SPSS design concept evaluation is an expert knowledge-based decision process with scant data and a short time window under a hesitant, ambiguous, and subjective environment, which would lead to low decision-making efficiency and inaccurate evaluation results. Hence, this paper proposes a novel cloud envelopment analysis method to evaluate SPSS design concept with respect to smart experience criteria. The proposed method integrates hesitant fuzzy linguistic terms (HFLTs), cloud model and data envelopment analysis (DEA) method to accurately evaluate SPSS design concepts with handling the hesitancy, fuzziness and randomness in qualitative and subjective information. A hybrid model of normal cloud and trapezium cloud is used to quantify hybrid-length HFLT variables to avoid decision information loss and distortion. A novel cloud non-linear programming model is constructed to extend the classical DEA into cloud environment. Finally, a case study and some comparison analyses illustrate the effectiveness and advantages of proposed method.

Promoting the physician–patient consensus with a hesitant fuzzy linguistic consensus method based on betweenness relation

As the relationship between physicians and patients faces increasing challenges, physician–patient relation has gradually become the common concern of the whole society. To relieve this kind of pressure, the mechanism that reaches a consensus between physicians and patients on treatment choices needs to be discussed. Considering that there always exist uncertainties during the medical treatment process, this paper aims to develop a decision-making method to address the consensus issues under a hesitant fuzzy linguistic environment. Since patients and physicians possess different backgrounds and multiple specialties, they are allowed to evaluate alternatives under the individual set of criteria. Then, a Simos–Roy–Figueira method is proposed to derive the weights of criteria with hesitant fuzzy linguistic information. The ELECTRE III method is introduced to obtain the ranking of alternatives from each decision maker’s opinions. Further, a novel consensus method based on betweenness relation is developed to address the obtained rankings. Finally, the process to determine the treatment plan for a hepatocellular carcinoma patient is solved by the proposed method. The obtained result is considered reasonable by experts involved in the consultation, which illustrates the effectiveness of the method. Then, some simulation experiments are designed to show the features of the method. The short running time of the proposed method shows its high efficiency.

Optimization of Cold Chain Logistics with Fuzzy MCDM Model

Vaccines are biological products containing a weakened, inactivated part of bacteria or viruses that are not harmful to the human body. Vaccine manufacturers and distributors should always store vaccines at the right temperature. To do this task, manufacturers and distributors need to manage cold supply chains to the required standards. Cold chain management helps manufacturers control and keep vaccines at the right temperature while ensuring quality and extending their expiration date. That will help businesses in the medical industry reduce economic losses, avoid waste, and bring more significant benefits to patients. The selection and evaluation process for logistics suppliers, especially those who deal with low-temperature storage, considers many factors to reduce the potential waste of products from poor storage strategies. The author introduces an integrated approach to solve such a fuzzy multiple criteria decision-making (MCDM) problem based on the Fuzzy Analytical Hierarchy Process (FAHP) model and an Interactive and Multi-criteria Decision-Making in Portuguese Model (TODIM) model methods under the fuzzy linguistic environment. In this work, the SF-AHP method derives criteria weights in the first stage, and then a TODIM method is presented to identify the ranking of logistics providers. Finally, the authors present a case study on the evaluation and selection of cold chain logistics suppliers to demonstrate the applicability of the proposed fuzzy MCDM model.

Selection of renewable energy sources: a novel VIKOR approach in an intuitionistic fuzzy linguistic environment

Selection of renewable energy sources: a novel VIKOR approach in an intuitionistic fuzzy linguistic environment

ELECTRE II method based on the cosine similarity to evaluate the performance of financial logistics enterprises under double hierarchy hesitant fuzzy linguistic environment

ELECTRE II method based on the cosine similarity to evaluate the performance of financial logistics enterprises under double hierarchy hesitant fuzzy linguistic environment

Tranquility and Anxiety in Multi-Attribute Decision Making Under Hesitant Fuzzy Linguistic Environment with Interactive Attributes: A Set-Valued Fuzzy Rough Set Approach

Tranquility and Anxiety in Multi-Attribute Decision Making Under Hesitant Fuzzy Linguistic Environment with Interactive Attributes: A Set-Valued Fuzzy Rough Set Approach

Statistical and analytical approach of multi-criteria group decision-making based on the correlation coefficient under intuitionistic 2-tuple fuzzy linguistic environment

The correlation between two different variables possesses an important place in the field of statistics. Correlation is used to estimate the change in one variable associated with another variable. The concept of correlation is well known but it is not used within intuitionistic 2-tuple fuzzy linguistic (I2TFL) information. To investigate the best alternative among different alternatives in multi-criteria group decision-making (MCGDM) problems, our aim is to propose a formula for the correlation coefficient based on I2TFL information. A new type of information energy for I2TFL element is defined first and then the correlation coefficient between I2TFL information are discussed based on this information energy. In addition, considering that different I2TFL elements may have different criteria weights, the weighted correlation coefficients are further investigated. Some of the properties of the proposed correlation coefficient are also mentioned and verified. Furthermore, best-worst method (BWM) is expanded to uncertain situations like I2TFL BWM, where the data is expressed in I2TFL form. Utilizing the idea of BWM, linearly constrained optimization problems are framed to acquire weights of criteria in the context of I2TFL environment. Two numerical illustrations are described to confirm the effectiveness of the proposed work in the cases where the criteria weights are either known or unknown. Finally, comparative discussions between the proposed approach and existing practices are taken to reveal the importance of our work.

Some q-rung orthopair trapezoidal fuzzy linguistic hamacher aggregation operators and their applications

A Hamacher operator in a q-rung orthopair trapezoidal fuzzy linguistic environment is studied based on the definition of the q-rung orthopair fuzzy set and the Hamacher aggregation operator. First, we define a new fuzzy variable called q-rung orthopair trapezoidal fuzzy linguistic sets, and the operational laws, score function, accuracy function, comparison rules, and distance measures of the IVPFLVS are defined. Second, based on the Hamacher operator and the q-rung orthopair trapezoidal fuzzy linguistic sets, we propose several q-rung trapezoidal fuzzy linguistic Hamacher operator information aggregation operators, such as the generalized q-rung orthopair trapezoidal fuzzy linguistic Hamacher weighted averaging (q-GROTrFLHWA) operator, and the generalized q-rung orthopair trapezoidal fuzzy linguistic Hamacher weighted geometric (q-GROTrFLHWG) operator. Third, some desirable properties of the correlation operators, such as idempotency, boundedness, and monotonicity are discussed. Finally, there are two group decision schemes based on q-rung orthopair trapezoidal fuzzy information with known attribute weights. The decision-making scheme is applied to the evaluation of school teaching quality, and the practicability and effectiveness of the scheme are demonstrated by different methods.

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.