Interval-valued hesitant fuzzy linguistic sets and their applications in multi-criteria decision-making problems

Quasirung orthopair fuzzy linguistic sets and their application to multi criteria decision making

Linguistic term fuzzy sets provide an intuitive way to express preferences, enhancing understanding and communication among decision-makers. In this article, we introduce the novel concept of p,q-quasirung orthopair fuzzy linguistic sets (p,q-QOFLSs), which merge the principles of p,q-quasirung orthopair fuzzy sets (p,q-QOFSs) with linguistic fuzzy sets. This new framework offers a more robust approach to handle uncertain and imprecise information in decision-making processes, characterized by linguistic membership and non-membership degrees. We establish several fundamental operational laws, alongside score and accuracy functions, to facilitate the comparison of p,q-quasirung orthopair fuzzy linguistic numbers. Leveraging these operational laws, we propose a series of weighted averaging and geometric operators under p,q-QOFLSs. Furthermore, we formulate a multi-attribute decision-making methodology using these operators. The significance of the proposed method lies in its ability to model complex decision-making scenarios with enhanced precision. A numerical example validates the practicality and adaptability of the methodology, supported by sensitivity analyses and comparative evaluations, highlighting the innovation and efficiency of the approach.

Doctors ranking through heterogeneous information: The new score functions considering patients' emotional intensity

With the popularity of the Internet and the growing complexity of COVID-19, more and more patients tend to consult doctors online. With the difficulty of doctor selection caused by a massive amount of information, this study proposes a hybrid multi-criteria decision-making framework, which can model patients' emotional intensity through heterogeneous information and rank doctors. Firstly, online reviews (ORs) are transformed into probabilistic linguistic term sets through sentiment analysis. Then, new score functions are proposed considering the nonlinear influence of doctors' information and the patients' negative bias toward ORs. Next, a method of weight determination combining the Term Frequency Inverse Document Frequency and the Decision-making Trial and Evaluation Laboratory method is proposed. Finally, the proposed score functions are applied to the Combined Compromise Solution (CoCoSo) method to aggregate information and rank doctors. The proposed method is verified in a case study on haodf.com. The results show that considering the emotional intensity of heterogeneous information will make the recommendations more realistic. Comparative analysis and sensitivity analysis are further performed to illustrate the availability and effectiveness of the proposed method.

A hybrid generalized TODIM based risk prioritization method for failure mode and effect analysis with linguistic Z-numbers

The traditional failure mode and effect analysis (FMEA), as an effective risk analysis technique, has several limitations in the uncertainty modeling and the weights determination of the risk indicators. This paper aims to propose a hybrid risk prioritization method simultaneously considering the characteristics of the reliability associated with the FMEA team members’ evaluation information and their psychological behavior to enhance the performance of the traditional FMEA model. The hybrid risk prioritization method is developed based on the generalized TODIM method and the weighted entropy measure with the linguistic Z-numbers (LZNs). First, the LZNs are adopted to depict the FMEA team members’ cognition information and the reliability of these information. Second, a weighted entropy measure based on the fuzzy entropy and the LZNs is developed to obtain the risk indicators’ weights. Finally, the generalized TODIM method with the LZNs is constructed to obtain the risk priority orders of failure modes, which can effectively simulate the FMEA team members’ psychological character. The applicability and effectiveness of the proposed risk prioritization method is validated through an illustrative example of an integrated steel plant. The results of sensitivity analysis and comparative analysis indicate that the proposed hybrid risk prioritization method is effective and valid, and can get more accurate and practical risk ranking results to help enterprises formulate accurate risk prevention and control plans.

A flexible group decision-making method for green supplier selection integrating MABAC and CRITIC method under the linguistic Z-numbers environment

This paper intends to treat the green supplier selection (GSS) problem as a multi-attribute group decision making (MAGDM) problem, adopt the linguistic Z-number that can more flexibly and accurately express the evaluation information, and expand the traditional multi-attribute boundary approximate area comparison (MABAC) method, combine the CRITIC method of standard importance and consider the risk vector to finally determine the optimal solution. More specifically, the linguistic Z-number is used to describe the fuzzy evaluation information of experts on alternatives under attributes, then the expanded CRITIC method is used to obtain the weight of each given attribute, and finally the MABAC method with added risk vector and expanded is used to obtain the ranking of alternatives and obtain the best solution. Finally, taking green supplier selection as an example, and comparing with other methods, the reliability and effectiveness of the constructed method are verified. The results show that this method can express the evaluation information of experts flexibly and completely, and obtain the ranking results of given schemes through fewer steps, which is reliable and effective.

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.

Cross-platform hotel evaluation by aggregating multi-website consumer reviews with probabilistic linguistic term set and Choquet integral

In order to adequately utilize and integrate both ratings and comments from multiple websites, this paper proposes a new hotel evaluation model with probabilistic linguistic information processing. Taking consumers' possible psychological activities when leaving their reviews into consideration, this paper adapts the Weber-Fechner Law with the linguistic scale function and develop a novel unbalanced linguistic scale function. This paper also attempts to develop a method that enables adjusting linguistic-term formations among different websites to make full use of information. Then, we learn the decision criteria and the corresponding weight of hotel evaluation based on analyzing rating rules and consumer comments. Moreover, considering the interrelationships among criteria, this paper extends the Choquet integral to the probabilistic linguistic term set (PLTS) environment and designs some novel fusion operators. Furthermore, considering the fact that different websites mostly focus on heterogeneous hotel criteria, this paper puts forward a weighted averaging linear assignment based ranking method with the aid of PLTS Choquet integral. Finally, a case study of hotel evaluation is given to illustrate the validity and applicability of our proposed approach.

Generalized Fuzzy Linguistic Bicubic B-Spline Surface Model for Uncertain Fuzzy Linguistic Data

A fuzzy linguistic data set that is uncertain is difficult to analyze and describe in the form of a smooth and continuous generic figure. Therefore, the study aims to develop a new model of a B-spline surface using a different approach of a crisp and fuzzy linguistic point relation with three types of linguistic function: low L, medium Mi and high H. These linguistic functions are defined first to introduce the fuzzy linguistic point relation. Then, a new algorithm of the fuzzy linguistic bicubic B-spline surface model is presented to convert fuzzy linguistic data into fuzzy linguistic control points. In addition, a numerical example of fuzzy linguistic data is considered at the end of this study to visualize the suggested model. Thus, the relation between the fuzzy linguistic data points can be analyzed to present another area of knowledge in which symmetry phenomena occur. The symmetry here plays an important role in solving the uncertain fuzzy linguistic data problem by using the suggested model.

A large group hesitant fuzzy linguistic DEMATEL approach for identifying critical success factors in public health emergencies

Purpose

How to identify the critical success factors (CSFs) of public health emergencies (PHEs) is of great practical significance to carry out a scientific and effective risk assessment. The purpose of this paper is to address this issue.

Design/methodology/approach

In this paper, the authors propose a new approach to identify the CSFs by hesitant fuzzy linguistic set and a Decision-Making Trial and Evaluation Laboratory (DEMATEL) approach. First, a larger group of experts are clustered into three groups according to similarity degree. Then, the weight of each cluster is determined by the maximum consensus method, and the overall direct influence matrix is obtained by clustering with hesitant fuzzy linguistic weighted geometric (HFLWG) operators. Finally, the overall direct influence matrix is transformed into the crisp direct impact matrix by the score function, and 11 CSFs of PHEs are identified by using the extended DEMATEL method.

Findings

In addition, an example of PHEs shows that the approach has good identification applicability. The approach can be used to solve the problems of fuzziness and subjectivity in linguistic assessments, and it can be applied to identify the customer service framework with the linguistic assessments process in emergency management.

Originality/value

This paper extends the above DEMATEL method to study in the hesitant fuzzy linguistic context. This proposed hybrid approach has a wider application in the high-risk area where disasters frequently occur.

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.

Sustainable Circular Supplier Selection in the Power Battery Industry Using a Linguistic T-Spherical Fuzzy MAGDM Model Based on the Improved ARAS Method

In the power battery industry, the selection of an appropriate sustainable recycling supplier (SCS) is a significant topic in circular supply chain management. Evaluating and selecting a SCS for spent power batteries is considered a complex multi-attribute group decision-making (MAGDM) problem closely related to the environment, economy, and society. The linguistic T-spherical fuzzy (Lt-SF) set (Lt-SFS) is a combination of a linguistic term set and a T-spherical fuzzy set (T-SFS), which can accurately describe vague cognition of human and uncertain environments. Therefore, this article proposes a group decision-making methodology for a SCS selection based on the improved additive ratio assessment (ARAS) in the Lt-SFS context. This paper extends the Lt-SF generalized distance measure and defines the Lt-SF similarity measure. The Lt-SF Heronian mean (Lt-SFHM) operator and its weighted form (i.e., Lt-SFWHM) were developed. Subsequently, a new Lt-SF MAGDM model was constructed by integrating the LT-SFWHM operator, generalized distance measure, and ARAS method. In it, the expert weight on the attribute was determined based on the similarity measure, using the generalized distance measure to obtain the objective attribute weight and then the combined attribute weight. Finally, a real case of SCS selection in the power battery industry is presented for demonstration. The effectiveness and practicability of this method were verified through a sensitivity analysis and a comparative study with the existing methods.

Linguistic q-rung orthopair fuzzy multiple-attribute group decision making based on the grey similarity degree and PROMETHEE II method

Linguistic q-rung orthopair fuzzy numbers (Lq-ROFNs) are an effective tool for representing fuzzy linguistic information, and they can obtain a wider expression scope than linguistic intuitionistic fuzzy numbers and linguistic Pythagorean fuzzy numbers by increasing the value of parameter q. In this paper, we propose a new similarity measure called the grey similarity degree between any two Lq-ROFNs based on the concept of the grey correlation degree. Considering the significance of determining unknown weights, we also propose a grey correlation method to determine each expert’s weight under different alternatives and attributes, and we construct an optimization model to determine incompletely known attribute weights. Furthermore, an approach to linguistic q-rung orthopair fuzzy multiple-attribute group decision making is proposed that combines the grey similarity degree with the PROMETHEE II method. Finally, a numerical example is given to illustrate the effectiveness of the proposed method, and a sensitivity analysis and comparison analysis are also performed.

Time-sequential hesitant fuzzy set and its application to multi-attribute decision making

The hesitant fuzzy set has been an important tool to address problems of decision making. There are several various improved hesitant fuzzy sets, such as dual hesitant fuzzy set, hesitant interval-valued fuzzy set, and intuitionistic hesitant fuzzy set, however, no one kind of improved fuzzy sets could reflect attitude characteristics of decision makers on time-sequences. In reality, time-sequence is one important sector to reflect hesitant situations as decision makers might have different knowledges of the same alternative at different moments. To perfect the description of such hesitant situations and obtain more reasonable results of decision making, we define a new kind of hesitant fuzzy set, namely, time-sequential hesitant fuzzy set. Meanwhile, its corresponding basic operators, score function and distance measures are proposed. We also propose the concept of fluctuated hesitant information to describe hesitant degrees of decision makers on time-sequences. By comprehensively utilizing the score function, fluctuated hesitant information and distance measures under time-sequential hesitant fuzzy set, a synthetic decision model is proposed. Two illustrated examples and one real-application are utilized to illustrate the effectiveness and advantage of the synthetic decision model under time-sequential hesitant fuzzy set.

Evaluation of Rural Tourism Landscape Resources in Terms of Carbon Neutrality and Rural Revitalization

Rural tourism landscape resources are important ingredients of rural revitalization and modernization in developing countries and regions. Evaluation methods play a crucial role in the planning, design, transformation, development, and protection of these resources. However, there has been a lack of research on the evaluation of rural tourism landscape resources, especially from the perspective of rural revitalization and carbon neutrality. From the perspective of carbon neutrality and rural revitalization, this article establishes an indicator system to evaluate rural tourism landscape resources based on previous evaluation methods and expert consultations on landscape planning. An evaluation model based on the intuitionistic fuzzy VIKOR method structure matching is also suggested. Some practical suggestions are put forward to promote the values of rural tourism landscape resources through empirical analyses of three regions in Changsha, Hunan, China. Our study shows that the evaluation results could objectively reflect the values and existing problems of rural tourism landscape resources, which could provide practical tools for local government departments to make decisions, and landscape architects to plan and design. Based on this model, further suggestions are provided to improve rural tourism landscape resources.

A Novel Approach for Multiplicative Linguistic Group Decision Making Based on Symmetrical Linguistic Chi-Square Deviation and VIKOR Method

Most linguistic-based approaches to multi-attribute group decision making (MAGDM) use symmetric, uniformly distributed sets of additive linguistic terms to express the opinions of decision makers. However, in reality, there are also some problems that require the use of asymmetric, uneven, i.e., non-equilibrium, multiplicative linguistic term sets to express the evaluation. The purpose of this paper is to propose a new approach to MAGDM under multiplicative linguistic information. The aggregation of linguistic data is an important component in MAGDM. To solve this problem, we define a chi-square for measuring the difference between multiplicative linguistic term sets. Furthermore, the linguistic generalized weighted logarithm multiple averaging (LGWLMA) operator and linguistic generalized ordered weighted logarithm multiple averaging (LGOWLMA) operator are proposed based on chi-square deviation. On the basis of the proposed two operators, we develop a novel approach to GDM with multiplicative linguistic term sets. Finally, the evaluation of transport logistics enterprises is developed to illustrate the validity and practicality of the proposed approach.

Evaluate the locations for smart waste bins using BWM and WASPAS methods under a probabilistic linguistic environment

 The decreasing resources of the earth and the deterioration of the environment are offering new challenges for handling waste management practices. The establishment of the smart waste bins plays an important role in promoting the development of waste classification and treatment fundamentally. We developed the evaluation system for the location selection problem of smart waste bins. Considering the uncertainty in the location selection of smart waste bins, the probabilistic linguistic term sets (PLTSs) are selected to express the evaluation information. Because of the excellent performance in weight-determing, the best worst method (BWM) is chosen to get the weight of criteria. While the weighted aggregated sum product assessment (WASPAS) method could handle both the qualitative and quantitative information, which are considered to derive the final ranking of the alternatives. This paper proposed a new group multi-criteria decision making approach integrating the BWM and the WASPAS with probabilistic linguistic information. Finally, in the empirical example, a sensitivity analysis shows that the proposed method is stable, a comparison analysis with PL-TOPSIS, PL-VIKOR, and PL-TODIM reflects its effectiveness and rationality, and the managerial implication verifies its usefulness and practicability, which also give guide to the company, government and resident.

The operational properties of linguistic interval valued q-Rung orthopair fuzzy information and its VIKOR model for multi-attribute group decision making

As a generalization of linguistic q-rung orthopair fuzzy set (Lq-ROFS), linguistic interval valued q-Rung orthopair fuzzy set (LIVq-ROFS) is a new concept to deal with complex and uncertain decision making problems which Lq-ROFS cannot handle. Due to the lack of information in decision making process, decision makers mostly prefer to give their preferences in interval form rather than a crisp number. In this situations, LIVq-ROFS appears up as a useful tool. In this work, we define operational laws of LIVq-ROFS and prove some properties. Furthermore, we propose the conception of the LIVq-ROF weighted averaging operator and give its formula by mathematical induction. To compare two or more linguistic interval valued q-Rung orthopair fuzzy numbers (LIVq-ROFNs), the improved form of score function is also given. Considering the powerfulness of LIVq-ROFSs handling ambiguity and complex uncertainty in practical problems, the key innovation of this paper is to develop the linguistic interval-valued q-rung orthopair fuzzy VIKOR model that is significantly different from the existing VIKOR methodology. The computing steps of this newly created model are briefly presented. Finally, the effectiveness of model is verified by an example and through comparative analysis, the superiority of VIKOR method is further illustrated.

Multiple attribute group decision-making based on interval-valued q-rung orthopair uncertain linguistic power Muirhead mean operators and linguistic scale functions

Fuzzy set theory and its extended form have been widely used in multiple-attribute group decision-making (MAGDM) problems, among which the interval-valued q-rung orthopair fuzzy sets (IVq-ROFSs) got a lot of attention for its ability of capturing information denoted by interval values. Based on the previous studies, to find a better solution for fusing qualitative quantization information with fuzzy numbers, we propose a novel definition of interval-valued q-rung orthopair uncertain linguistic sets (IVq-ROULSs) based on the linguistic scale functions, as well as its corresponding properties, such as operational rules and the comparison method. Furthermore, we utilize the power Muirhead mean operators to construct the information fusion method, and provide a variety of aggregation operators based on the proposed information description environment. A model framework is constructed for solving the MAGDM problem utilizing the proposed method. Finally, we illustrate the performance of the new method and investigate its advantages and superiorities through comparative analysis.

A novel picture fuzzy linguistic Muirhead Mean aggregation operators and their application to multiple attribute decision making

The Picture fuzzy linguistic set (PFLS) is an extension of the intuitionistic fuzzy set (IFS) and linguistic variables (LVs), which has been applied successfully in the process of decision making. Considering the lack of closeness of extant PFLS operations and the interrelationship among input attributes do not consider. In this paper, for the sake of addressing those limitations, we firstly redefine some novel operational laws for PFLS by introducing linguistic scale functions and the related properties are studied. Then, a novel score function and accuracy function are also defined to compare PFLSs. Subsequently, in consideration of the superiority of the Muirhead Mean (MM) operator in capturing the interaction relationship between the input parameters, we extend the MM operator to the Picture fuzzy linguistic context and then propose Picture fuzzy linguistic weighted MM operator and its dual form in a new light. After that, these operators have adopted to build two novel models to solve multiple attribute decision-making (MADM) problems. Finally, a practical example for the selection of the innovative “Mobike” sharing bike design is provided to illustrate the practicality and effectiveness of proposed approaches.

A Hybrid Approach of VIKOR and Bi-Objective Decision Model for Emergency Shelter Location–Allocation to Respond to Earthquakes

Earthquakes have catastrophic effects on the affected population, especially in undeveloped countries or regions. Minimizing the impact and consequences of earthquakes involves many decisions and disaster relief operations that should be optimized. A critical disaster management problem is to construct shelters with reasonable capacity in the right locations, allocate evacuees, and provide relief materials to them within a reasonable period. This study proposes a bi-objective hierarchical model with two stages, namely, the temporary shelter stage and the short-term shelter stage. The proposed objectives at different stages are to minimize the evacuation time, maximize the suitability based on qualitative factors, and minimize the number of sites while considering the demand, capacity, utilization, and budget constraints. The performance evaluation of the emergency shelter was carried out by fuzzy-VIKOR, and the most ideal location of the shelter was determined through multiple standards. Emergency management organizations can benefit from the collective expertise of multiple decision-makers because the proposed method uses their knowledge to automate the location and allocation process of shelters. In the case of Chengdu, Sichuan Province, China, the results of using this hybrid approach provide the government with a range of options. This method can realize the trade-off between efficiency and cost in the emergency shelter location and material distribution, and realize reliable solutions in disaster emergencies.

A Decision-Making Approach Based on New Aggregation Operators under Fermatean Fuzzy Linguistic Information Environment

Fermatean fuzzy linguistic (FFL) set theory provides an efficient tool for modeling a higher level of uncertain and imprecise information, which cannot be represented using intuitionistic fuzzy linguistic (IFL)/Pythagorean fuzzy linguistic (PFL) sets. On the other hand, the linguistic scale function (LSF) is the better way to consider the semantics of the linguistic terms during the evaluation process. It is worth noting that the existing operational laws and aggregation operators (AOs) for Fermatean fuzzy linguistic numbers (FFLNs) are not valid in many situations, which can generate errors in real-life applications. The present study aims to define new robust operational laws and AOs under Fermatean fuzzy linguistic environment. To do so, first, we define some new modified operational laws for FFLNs based on LSF and prove some important mathematical properties of them. Next, the work defines several new AOs, namely, the FFL-weighted averaging (FFLWA) operator, the FFL-weighted geometric (FFLWG) operator, the FFL-ordered weighted averaging (FFLOWA) operator, the FFL-ordered weighted geometric (FFLOWG) operator, the FFL-hybrid averaging (FFLHA) operator and the FFL-hybrid geometric (FFLHG) operator under Fermatean fuzzy linguistic environment. Several properties of these AOs are investigated in detail. Further, based on the proposed AOs, a new decision-making approach with Fermatean fuzzy linguistic information is developed to solve group decision-making problems with multiple attributes. Finally, to illustrate the effectiveness of the present approach, a real-life supplier selection problem is presented where the evaluation information of the alternatives is given in terms of FFLNs. Compared to the existing methods, the salient features of the developed approach are (1) it can solve decision-making problems with qualitative information data using FFLNs; (2) It can consider the attitudinal character of the decision-makers during the solution process; (3) It has a solid ability to distinguish the optimal alternative.

An extended TDM method under probabilistic interval-valued hesitant fuzzy environment for stock selection

Generally, in real decision-making, all the pieces of information are used to find the optimal alternatives. However, in many cases, the decision-makers (DMs) only want “how good/bad a thing can become.” One possibility is to classify the alternatives based on minimum (tail) information instead of using all the data to select the optimal options. By considering the opportunity, we first introduce the value at risk (VaR), which is used in the financial field, and the probabilistic interval-valued hesitant fuzzy set (PIVHFS), which is the generalization of the probabilistic hesitant fuzzy set (PHFS). Second, deemed value at risk (DVaR) and reckoned value at risk (RVaR) are proposed to measure the tail information under the probabilistic interval-valued hesitant fuzzy (PIVHF) environment. We proved that RVaR is more suitable than DVaR to differentiate the PIVHFEs with example. After that, a novel complete group decision-making model with PIVHFS is put forward. This study aims to determine the most appropriate alternative using only tail information under the PIVHF environment. Finally, the proposed methods’ practicality and effectiveness are tested using a stock selection example by selecting the ideal stock for four recently enrolled stocks in China. By using the novel group decision-making model under the environment of PIVHFS, we see that the best stock is E₄ when the distributors focus on the criteria against 10% certainty degree and E₁ is the best against the degree of 20%, 30%, 40% and 50% using the DVaR method. On the other hand when RVaR method is used then the best alternative is E₄ and the worst is E₂ against the different certainty degrees. Furthermore, a comparative analysis with the existing process is presented under the PHF environment to illustrate the effectiveness of the presented approaches.

Fulfilling External Stakeholders’ Demands—Enhancement Workplace Safety Using Fuzzy MCDM

Sustainable development and project stakeholder management indicate a business practice where an organization strives to fulfil the demands of the important stakeholders for the project’s success. If one company relies on subassembly parts from its supplier, then it might be considered that it has high interest for enhancing the business continuity of the supplier. This issue has become more complex during 2020 due to turbulent business conditions where the problem of the safety and health of workers during daily work has become one of main reasons for business vulnerability. Besides the above-mentioned, project stakeholders may have different demands. The implementation of the management actions that lead to the fulfilment of stakeholder demands (SDs), such as addressing ongoing issues, are almost always limited by the available budget. The contribution of this research is providing the input for determining the actions which should address the most important SDs. Those activities may be seen as part of the strategy for external stakeholder management and successful long-term relationship. The determination of the priorities of SDs is based on a fuzzy multicriteria optimization model with type-2 fuzzy sets.

Multi-attribute decision-making method based on a novel distance measure of linguistic intuitionistic fuzzy sets

Linguistic intuitionistic fuzzy sets can qualitatively rather than quantitatively express data in the form of membership degree. But quantitative tools are required to handle qualitative information. Therefore, an improved linguistic scale function, which can more accurately manifest the subjective feelings of decision-makers, is employed to deal with linguistic intuitionistic information. Subsequently, due to some commonly used distance measures do not comprehensively evaluate the information of linguistic intuitionistic fuzzy sets, an improved distance measure of linguistic intuitionistic fuzzy sets is designed. It considers the cross-evaluation information to get more realistic reasoning results. In addition, a new similarity measure defined by nonlinear Gaussian diffusion model is proposed, which can provide different response scales for different information between various schemes. The properties of these measures are also studied in detail. On this basis, a method in linguistic intuitionistic fuzzy environment is developed to handle multi-attribute decision-making problems. Finally, an illustrative example is given to demonstrate the effectiveness of the proposed method and the influence of the parameters is analyzed.

Extended VIKOR-QUALIFLEX Method Based on Trapezoidal Fuzzy Two-Dimensional Linguistic Information for Multiple Attribute Decision-Making with Unknown Attribute Weight

Considering the advantages of trapezoid fuzzy two-dimensional linguistic variables (TrF2DLVs), which can not only accurately describe the qualitative evaluation but also use qualitative linguistic variables (LVs) to describe the confidence level of this evaluation in the second dimension, this paper proposes a novel method based on trapezoidal fuzzy two-dimensional linguistic information to solve multiple attribute decision-making (MADM) problems with unknown attribute weight. First, a combination weight model is constructed, which covers a subjective weight determination model based on the proposed trapezoidal fuzzy two-dimensional linguistic best-worst method (TrF2DL-BWM) and an objective weight determination model based on the proposed CRITIC method. Then, in order to accurately rank the alternatives, an extended VIKOR-QUALIFLEX method is proposed, which can measure the concordance index of each ranking combination by means of group utility and individual maximum regret value of each evaluation alternative. Finally, a practical problem of lean management assessment for industrial residential projects is solved by the proposed method, and the effectiveness and advantages of the method are demonstrated by comparative analysis and discussion.

Probabilistic Hesitant Intuitionistic Fuzzy Linguistic Term Sets and Their Application in Multiple Attribute Group Decision Making

Multi-attribute group decision-making (MAGDM) is widely applied to various areas for solving real-life problems, including technology selection, credit assessment, strategic planning evaluation, supplier selection, etc. To describe the complex and imprecise cognition, it is more convenient to provide the decision-making information in linguistic terms rather than concrete numerical values. Thus, several linguistic models, such as the fuzzy linguistic approach (FLA), hesitant fuzzy linguistic term sets (HFLTSs), hesitant intuitionistic fuzzy linguistic term sets (HIFLTSs), and probabilistic linguistic term sets (PLTS) have been proposed successively. Due to the flexibility and comprehensiveness of PLTS, it has aroused growing concern. However, it also has a big limitation of requiring the membership degree to be 1 by default, and it does not consider the degree of non-membership and hesitancy of a linguistic variable. Therefore, the probabilistic hesitant intuitionistic fuzzy linguistic term sets (PHIFLTSs) have been presented to extend the PLTS by combining the membership and non-membership in symmetry to depict the evaluation of the experts. To overcome the existing shortcomings and enrich the methodology framework of PHIFLTSs, some novel operational laws are defined to extend the applicability and methodology of the PHIFLTSs in MAGDM. Furthermore, the distance and correlation measures for the PHIFLTSs are improved to make up the shortage of the current distance measures. In addition, the unbalanced linguistic terms are taken into account to represent the cognitive complex information of experts. At last, a MAGDM model based on the multiplicative multi-objective optimization by ratio analysis (MULTIMOORA) approach with the use of the developed novel operational laws and correlation measures is presented, which results in more accuracy and effectiveness. A real-word application example is presented to demonstrate the working of the proposed methodology. Moreover, a thorough comparison is done with related existing works in order to show the validity of this methodology.

Interval probability hesitant fuzzy linguistic analytic hierarchy process and its application in talent selection

Hesitant fuzzy linguistic term set (HFLTS) can handle the qualitative and hesitant information in multiple attribute decision making (MADM) problems which are widely used in various fields. However, the experts’ evaluation of information is not completely reliable in the situation where their own knowledge background is insufficient. In order to deal with deviations due to incomplete reliability of the evaluation, this paper first proposes the interval probability hesitant fuzzy linguistic variable (IPHFLV), which takes the HFLTS as the evaluation part and adds a novel element-reliability of evaluation, thus can describe the different credibility of information evaluation due to the familiarity of experts with schemes and the differences in knowledge cognition. The operation rules and comparison methods are also illustrated. Particularly, under the inspiration of probability theory, we propose the possibility degree of the IPHFLVs. Then we propose IPHFL-AHP based on the AHP and interval probability hesitant fuzzy linguistic variable. Especially, the general geometric consistency index (G-GCI) based on the unbiased estimator of the variance is presented to measure the consistency and the iterative algorithm is constructed to improve the consistency. We use the possibility degree to calculate the priority vector to acquire the total ranking and introduce the process of IPHFL-AHP. Finally, case study of talent selection is given to illustrate the effectiveness and feasibility of the proposed method.

A Stochastic Dominance-Based Approach for Hotel Selection under Probabilistic Linguistic Environment

Online reviews of hotels reflect tourist perception and evaluation, which are becoming an important perspective of studying hotel selection. In this paper, we prefer to use a probabilistic linguistic term set (PLTS) to fully reveal evaluation grades and the corresponding probability distribution in the online reviews of hotels. In this way, we propose a novel stochastic dominance-based approach based on stochastic dominance degrees of PLTSs and a stochastic multi-criteria acceptability analysis (SMAA) method that tolerates missing information. Among them, first-, second-, and third-order stochastic dominance degrees of PLTSs are calculated on the premise that the dominance relationships between PLTSs can be defined based on first-, second-, and third-order stochastic dominance rules of PLTSs. Based on these basic researches, five hotels are selected as alternatives in our case study to verify the validity and feasibility of the proposed approach. In the end, data analysis illustrates the influence of parameter and linguistic scale functions and how to choose appropriate parameter values. Furthermore, comparative analysis with other methods shows the stability of the proposed approach.