Linguistic Scale Functions Research Articles

A Gaussian interval type-2 fuzzy characterization method based on heterogeneous big data and its application in forest ecological assessment

The under-forest economy is a new agricultural and forestry production mode. It can improve the utilization efficiency of forest land and make full use of forest resources, forest space, and forest ecological environment through different forms of industries such as understory planting and breeding. The under-forest economy has important ecological and economic benefits, significant to rural revitalization and industrial structure adjustment. It has been widely discussed by people in recent years. The forest ecological security level is a core factor to be considered in selecting sites for the under-forest economy. In practice, some forest ecological security evaluation indexes usually show heterogeneous forms. To comprehensively evaluate the level of forest ecological security, this study constructs a new multi-indicator fuzzy evaluation method based on heterogeneous big data. Firstly, a new linguistic scale function is defined to realize the consistent conversion of multi-granularity linguistic information. A Gaussian interval type-2 fuzzy aggregation formula for heterogeneous large-scale data is proposed. This formula is used to describe the differences in evaluation information between individuals caused by different knowledge backgrounds of evaluators. Then, the Gaussian interval type-2 fuzzy cross-entropy is defined, and it is verified to satisfy the excellent properties. This cross-entropy is applied to determine the objective weights of evaluation indexes. Considering the risk-averse psychology of experts and combining the prospect theory, the MULTIMOORA method in the Gaussian interval type-2 fuzzy environment is proposed. Finally, the applicability of the constructed Gaussian interval type-2 fuzzy comprehensive evaluation method (GIT2FCE) is verified through a case study conducted on the site selection of the under-forest economic industry.

Fermatean fuzzy Linguistic term set based on linguistic scale function with Dombi aggregation operator and their application to multi criteria group decision –making problem

The selection of an industrial location is a challenging multiple-criteria decision-making (MCDM) problem that depends on taking a variety of locations as well as incompatible and inconsistent criteria. This paper proposed a comprehensive framework for the strategic selection of industrial locations, considering both quantitative and qualitative aspects. Decision-makers (DMs) have to deal with ambiguous information throughout this process due to a complex decision environment or their insufficient knowledge. We present a new Fermatean Fuzzy (FF) Linguistic term set based on the Dombi aggregation operators (AOs). By combining the FF set with Linguistic variables, the FF Linguistic (FFL) set is an effective approach for thoroughly representing uncertain evaluation information. We establish a basic operational principles and certain aggregation operator under FFL information, such as the FF Linguistic Dombi weighted averaging (FFLDWA) operator FF Linguistic Dombi weighted geometric (FFLDWG) operator and some fundamental properties of these operators with appropriated elaboration. Based on these operators, a multi-criteria group decision-making technique is developed. Finally, we used a numerical example to compare the flexibility of the suggested technique with other existing methods. Thus, by knowing priorities industries, the best site can be selected.

Group decision making based on dice similarity measure and 2-dimension linguistic fuzzy weighted arithmetic aggregation operator for 2-dimension linguistic fuzzy variables

In the process of decision-making, it usually applies 2-dimension linguistic fuzzy variable (2DLFV) to describe the uncertainty caused by the decision objects and the decision makers. This proposal aims to design group decision making method based on dice similarity measure (DSM) and 2-dimension linguistic fuzzy weighted arithmetic aggregation (2DLFWAA) operator for 2-dimension linguistic fuzzy framework. Based on the psychological theory and prospect theory, 2-dimension linguistic scale function (2DLSF) about 2DLFV is firstly proposed, and new operational rules of 2DLFV are introduced. Two forms of DSM are proposed to measure the closeness between two 2-dimension linguistic fuzzy sets (2DLFSs). A definition is given for 2DLFWAA operator and some of its properties are studied. Based on the DSM and the 2DLFWAA operator for 2DLFSs, the technique for order of preference by similarity to ideal solution (TOPSIS) method is extended to handle the multiple attribute group decision making (MAGDM) problems under 2-dimension linguistic fuzzy environments. Finally, an illustrative example is provided to show the concrete process of the proposed method. Comparative analysis and sensitivity analysis are conducted to test the rationality and robust of the proposed method. The results suggest that the proposed method offers a flexible and reliable approach in 2-dimension linguistic fuzzy scenarios.

A group decision-making method for technology selection of petrochemical enterprises

Selecting appropriate energy conservation and emission reduction technologies is essential for the sustainable developments of petrochemical enterprises. It usually involves experienced experts from multi-domain and thus can be regarded as a large-scale group decision-making problem. Existing methods assumed that different experts use the same linguistic term set following the same semantics to express their evaluation values, and derived the ranking of alternatives by an indirectly obtained group preference matrix. Such an approach may induce information loss. To avoid these defects, this study introduces a model based on rank centrality and expert differences to choose appropriate technologies for petrochemical enterprises. First, an attitude parameter is introduced into a linguistic scale function to unify different judgment benchmarks of experts regarding the same linguistic term. Next, a direct weight elicitation method based on rank centrality is developed to deduce the individual rank vector of alternatives. A grey clustering method based on the similarities of individual rank vectors is extended to cluster experts into small groups, and the silhouette coefficient is used to determine clusters weights. Afterwards, the rank vectors of alternatives corresponding to subgroups and the global rank vector are calculated by the weighted averaging operator. Alternatives are ranked by the rank vector of the global group. Finally, four technologies were evaluated by the model, and the preferred technology was identified. The findings indicate that the proposed technology selection model alleviates information loss, elevates group consensus level, and provides a perspective for petrochemical enterprises in search of energy conservation and emission reduction technologies.

New distance measure-driven flexible linguistic consensus model with application to urban flooding risk assessment

As a novel linguistic representation tool, flexible linguistic expression (FLE) has substantial flexibility in expressing ambiguous and uncertain information from experts. However, FLEs pose the following challenges to developing information measurement and consensus mechanisms for FLEs-based multi-attribute group decision-making (MAGDM). (1) The current studies primarily use linguistic distribution approximation or triangular fuzzy numbers to measure the difference between FLEs indirectly without proposing an exact distance measure. (2) Few studies have been conducted on direct accurate consensus models incorporating adaptive consensus feedback mechanisms. To deal with these issues, the flexible linguistic ordinal Deng entropy (FLODE) is firstly proposed to measure the uncertainty of FLEs, and by combining it with linguistic scale functions, a new distance measure for FLEs is constructed, which can accurately measure the level of group consensus and the difference in pairwise FLEs. Subsequently, by integrating the defined FLODE with the classical entropy weight method, a new method for determining the experts’ personalized attribute weights is constructed, fully considering the impact of experts’ personalized attribute weights on decision-making results. Also, a new consensus model incorporating a minimum adjustment feedback mechanism and dynamic personalized attribute weights is developed, in which the feedback adjustment coefficients and personalized attribute weights are dynamically updated during the consensus reaching process (CRP). Lastly, an urban flooding risk assessment is applied to confirm the effectiveness of the proposed consensus model.

Fire safety assessment for alternative cruise ship design based on BWM and DEMATEL by linguistic Z‐number

AbstractThis paper proposes a risk assessment method based on the best‐worst method (BWM) and decision‐making trial and evaluation laboratory (DEMATEL) to evaluate the fire safety level of alternative design schemes for cruise ships relative to the standard‐based options. Firstly, the analytic hierarchy model of fire safety assessment is constructed by analyzing the passive fire protection system, active fire protection system, and evacuation and escape capability of cruise ship large cabins. Then, the linguistic scale functions and Z‐numbers are used to deal with the fuzzy evaluation of fire safety factors by experts, and the maximizing consensus technique is adopted to determine the weight of each expert to enhance group consistency. Considering the influence degree of each factor on fire safety and the correlation between factors, the BWM is combined with DEMATEL to establish the risk source weight calculation model. The fire safety level of alternative cruise ship designs is further determined by the fuzzy comprehensive evaluation approach. Finally, to validate the effectiveness of the proposed method, a fire safety assessment is conducted on the alternative design scheme of a luxury cruise passenger restaurant. The results confirm that the proposed method can effectively evaluate the fire safety of alternative design compared to the standard‐based scheme.

An integrated method for complex heterogeneous multi-attribute group decision-making and application to photovoltaic power station site selection

This paper abstracts the complex heterogeneous multi-attribute group decision-making (CHMAGDM) characterized by two-layer decision-makers (DMs), individual attribute sets, complex relationships among attributes and heterogeneous evaluation information. DMs are composed by internal decision-makers (IDMs) and external decision-makers (EDMs). The evaluation information is represented by linguistic variables (LVs), intervals and real numbers. To handle such CHMAGDM, this paper puts forward an integrated method of prospect theory, DEMATEL (decision-making trial and evaluation laboratory) and QUALIFLEX (qualitative flexible). Firstly, a novel reference point determining approach is proposed based on three special indicators. A linguistic variable inverse prospect value function is designed and introduced to the transformation process from LVs to clouds to reduce the impacts of DMs’ psychological behaviors on decision-making. Secondly, a cloud-based DEMATEL approach is proposed to determine the attribute weights, where LVs are employed to judge the relationships among attributes. A new linguistic scale function is initiated and introduced to another transformation process from clouds to LVs. A representative indicator of cloud is designed for facilitating the normalization of direct relation matrix. Moreover, a linear programming model is built to calculate the attribute weights. Thirdly, an extended QUALIFLEX approach is developed to obtain the optimal ranking and EDM weights, where adoption coefficient is provided by IDMs. Another linear programming model is constructed to calculate the optimal collective concordance/discordance index of each permutation. The optimal ranking is generated by the maximum collective concordance/discordance index. Finally, a photovoltaic power station site selection example validates the proposed method. The advantages are demonstrated with sensitivity and comparison analyses.

A fuzzy decision support model for online review-driven hotel selection by considering risk attitudes of customers

Online hotel reviews provide a vital information source for customers to select an optimal hotel, but a large amount of vague and unstructured information increases the difficulty of decision-making. From the perspective of customers’ risk attitudes, this paper proposes a novel fuzzy decision support model for hotel selection based on online reviews. Firstly, the useful information from online reviews is extracted by attribute extraction and sentiment analysis, and then this information is aggregated into the Probabilistic Linguistic Term Set (PLTS) by considering the weight of each review. Secondly, the improved linguistic scale functions are constructed from the perspective of customers’ risk attitude to convert PLTS into quantitative information. Thirdly, an integrated attribute weighting method is presented based on objective weights of the statistical measure and subjective weights of the Analytic Hierarchy Process (AHP) technique. Fourthly, an extended Combinative Distance-based Assessment (CODAS) method is developed to evaluate the performances of hotels. The effectiveness of the proposed model is verified by the practical case from TripAdvisor.com and the comparative analysis with the existing methods.

Two-rank multi-attribute group decision-making with linguistic distribution assessments: An optimization-based integrated approach

In real life, two-rank multi-attribute decision-making (MADM), in which all alternatives are divided into two preference-ordered categories, is common. In this paper, we investigate two-rank multi-attribute group decision-making (MAGDM) with linguistic distribution assessments (LDAs). A challenge when tackling such two-rank problems is establishing an LDAs-based two-rank model that maintains a balance between classification accuracy and computational complexity. When neither the threshold nor the number of alternatives within each category is specified in advance, determining individual two-rank results and subsequently aggregating the two-rank results for each decision-maker to resolve conflicts within the group is another challenge. Given these, we aim to propose a novel approach for two-rank MAGDM with LDAs. The main innovations and contributions of this paper are as follows. (a) From the perspective of linguistic scale function (LSF)-based cumulative expectations, we present a new LDAs-based distance measure that exhibits several desirable properties. A new score function for comparing LDAs is subsequently proposed using the new distance and the idea of the Technique for Order Preference by Similarity to Ideal Solution (TOPSIS). (b) Using the minimum intensity of reversed rankings combined with the misclassification ratio of alternatives as an integrated objective function, we construct two 0-1 integer programming models incorporating constraints associated with the centers and priorities of categories to determine the optimal individual and group two-rank results of alternatives, respectively. (c) We apply our method to two-rank MAGDM associated with short video placement platforms. Comparing the proposed approach with other two-rank MAGDM approaches further demonstrates its effectiveness and rationality.

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.

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

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

A Multi-attribute Two-Sided Matching Decision Method Based on Multi-granularity Probabilistic Linguistic MARCOS

With the complexity of the matching environment, individual differences in matching objects and the uncertainty of evaluation information should be considered. The probabilistic linguistic term set (PLTS) is a useful tool to describe the uncertainty and limited cognition of matching objects. Thus, this paper proposes a multi-attribute two-sided matching method based on multi-granularity probabilistic linguistic MARCOS. First, we use a probabilistic linguistic term set with different granularities to express the evaluation information of different matching objects. Then, a conversion function is used to unify different granularity probabilistic linguistic terms. Second, a linguistic scale function is introduced to improve the expectation function, deviation degree, and distance of PLTS. The processed probabilistic linguistic evaluation information is transformed into accurate utility values through the transformation function. The evaluation attribute weights are determined by PLTS distance entropy. Based on this, this paper proposes a multi-granularity probabilistic linguistic MARCOS method to obtain the two-sided satisfaction degree. Finally, an optimization model which aims to maximize the overall satisfaction degree of matching objects by considering the stable matching condition is then established and solved to determine the matching between matching objects. The multi-objective two-sided matching model is constructed with the objective of maximizing the two-sided satisfaction degree. A case study of the service outsourcing matching is presented to validate the proposed method. The comparative analyses and discussions are also provided to demonstrate its effectiveness and scientific character.

Applications of Hesitant Interval Neutrosophic Linguistic Schweizer-Sklar Power Aggregation Operators to MADM

Hesitant interval neutrosophic linguistic sets (HINLSs) are one of the core generalization of various sets, such as neutrosophic set (NS), interval neutrosophic set (INS), and interval neutrosophic linguistic set (INLS). HINLS can represent the uncertainty, inconsistency, and reluctance of assessment specialists by expressing qualitative and quantitative information. The goal of this article is to introduce a novel MADM technique that can account for changes in the semantic environment as well as negative consequences of experts’ excessive evaluation values. First, several innovative operational rules based on Schweizer-Sklar (SS) t -norm and t -conorm and a novel comparison procedure for HINLS are established by integrating different linguistic scale functions. This allows for varied semantic settings to be handled. Then, various innovative HINL Schweizer-Sklar power aggregation operators (AOs) are suggested, containing hesitant interval neutrosophic SS power average (HINLSSPA) operator, weighted hesitant interval neutrosophic SS power average (WHINLSSPA) operator, hesitant interval neutrosophic SS power geometric average (HINLSSPGA) operator, weighted hesitant interval neutrosophic SS power geometric average (WHINLSSPGA) operator, some core properties, and various special cases of these AOs are examined. Additionally, based on the initiated AOs, a multiple attribute decision making (MADM) technique with HINL information is anticipated. Finally, a numerical example is illustrated to show the effectiveness and practicality of the anticipated MADM method. A comparison with existing approaches are also discussed.

A Novel Interval-Valued q-Rung Dual Hesitant Linguistic Multi-Attribute Decision-Making Method Based on Linguistic Scale Functions and Power Hamy Mean.

The interval-valued q-rung dual hesitant linguistic (IVq-RDHL) sets are widely used to express the evaluation information of decision makers (DMs) in the process of multi-attribute decision-making (MADM). However, the existing MADM method based on IVq-RDHL sets has obvious shortcomings, i.e., the operational rules of IVq-RDHL values have some weaknesses and the existing IVq-RDHL aggregation operators are incapable of dealing with some special decision-making situations. In this paper, by analyzing these drawbacks, we then propose the operations for IVq-RDHL values based on a linguistic scale function. After it, we present novel aggregation operators for IVq-RDHL values based on the power Hamy mean and introduce the IVq-RDHL power Hamy mean operator and IVq-RDHL power weighted Hamy mean operator. Properties of these new aggregation operators are also studied. Based on these foundations, we further put forward a MADM method, which is more reasonable and rational than the existing one. Our proposed method not only provides a series of more reasonable operational laws but also offers a more powerful manner to fuse attribute values. Finally, we apply the new MADM method to solve the practical problem of patient admission evaluation. The performance and advantages of our method are illustrated in the comparative analysis with other methods.

Pythagorean Fuzzy Linguistic Power Generalized Maclaurin Symmetric Mean Operators and Their Application in Multiple Attribute Group Decision-Making

As an extension of Pythagorean fuzzy sets and linguistic term sets, Pythagorean fuzzy linguistic sets (PFSs) are powerful to describe decision-making information quantificational and qualitatively, which have received much scholars’ attention. The purpose of this paper is to propose a new multiple attribute group decision-making (MAGDM) approach with Pythagorean fuzzy linguistic (PFL) information. To this end, we firstly analyze the drawbacks of existing operations of PFL numbers and propose new operational rules based on linguistic scale function. The power average (PA) operator is famous for its capacity of reducing the negative influence of unreasonable evaluation values provided by prejudiced decision makers on the decision results. The generalized Maclaurin symmetric mean (GMSM) can not only capture the interrelationship among multiple inputs but also manipulate the effect of related properties by adjusting the parameters. When considering aggregation operators of PFL numbers, we combine PA with GMSM and propose the PFL power generalized Maclaurin symmetric and the PFL power generalized weighted Maclaurin symmetric operators. We also study important properties and special cases of these operators. We continue to investigate MAGDM problems with PFL decision information and propose a novel method to determine the optimal alternative. Finally, we conduct numerical examples to demonstrate the effectiveness of our proposed method. We also attempt to illustrate the advantages and superiorities of the proposed method via comparative analysis.

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.

An asymmetric trapezoidal cloud-based linguistic group decision-making method under unbalanced linguistic distribution assessments

Linguistic group decision-making issues occur very frequently in practical decision situations. As a kind of information representation, unbalanced linguistic distribution assessments (ULDAs) are commonly utilized in the linguistic group decision-making process. To thoroughly well describe linguistic information, a numerical concept is developed, namely asymmetric trapezoidal cloud (ATC) models. These models overcome the inherent limitation of cloud models, and they are followed by a series of related contents involving a comparison method, distance measure and operational rule. Then, a rational conversion method is proposed to establish a bridge between ULDAs and ATCs. To meet our research requirements, extended linguistic scale functions (LSFs) are introduced to create a map from linguistic terms to numerical values; the map is based on numerical scale (NS) models. Subsequently, two types of decision support models are presented to solve multicriteria group decision-making issues: ATC power average (ATCPA)-based and TODIM-PROMETHEE Ⅱ-based decision support models. An illustrative case study involving the evaluation of industrial sewage discharge is utilized to validate the feasibility of our decision support models, and it is followed by an analytical comparison and discussion. The findings demonstrate that our work has an excellent performance and some practical implications.

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.