A Hesitant Fuzzy Linguistic QFD model for selecting project suppliers

Um modelo baseado em Hesitant Fuzzy Linguistic QFD para seleção de fornecedores de projetos

Abstract

Abstract  Supplier selection in project environments is a complex multicriteria decision-making problem. Uncertainty, qualitative judgments, and limited data availability make the adoption of robust and flexible decision-support approaches essential. In this context, this study proposes a decision model that integrates Hesitant Fuzzy Linguistic Term Sets (HFLTS) with the Quality Function Deployment (QFD) method to support the selection of project suppliers. The model allows decision makers to express hesitant evaluations using comparative linguistic expressions and considers the difficulty of data collection when defining evaluation criteria. A pilot application was conducted in an energy sector company, involving three decision makers and three supplier alternatives evaluated across 11 criteria. The results of the application indicate that delivery capacity and cost were identified as the most heavily weighted criteria. Sensitivity analysis tests suggest the robustness of the supplier ranking. The proposed approach contributes to the literature by integrating hesitation modeling, criteria structuring, and data availability considerations into a unified decision framework.

Keywords:
Project supplier selection; HFLTS-QFD; Multicriteria decision making; Hesitant Fuzzy Linguistic Term Sets

Resumo

Resumo  A seleção de fornecedores em ambientes de projetos é um problema complexo de tomada de decisão multicritério. Incerteza, julgamentos qualitativos e disponibilidade limitada de dados tornam essencial a adoção de abordagens de apoio à decisão robustas e flexíveis. Nesse contexto, este estudo propõe um modelo de decisão que integra os Hesitant Fuzzy Linguistic Term Sets (HFLTS) ao método Quality Function Deployment (QFD) para apoiar a seleção de fornecedores de projetos. O modelo permite que os decisores expressem avaliações hesitantes por meio de expressões linguísticas comparativas e considera a dificuldade de coleta de dados na definição dos critérios de avaliação. Uma aplicação piloto foi conduzida em uma empresa do setor de energia, envolvendo três decisores e três alternativas de fornecedores avaliadas com base em 11 critérios. Os resultados da aplicação indicam que capacidade de entrega e custo foram identificados como os critérios de maior peso. Testes de análise de sensibilidade sugerem a robustez do ranqueamento dos fornecedores. A abordagem proposta contribui para a literatura ao integrar a modelagem da hesitação, a estruturação de critérios e considerações sobre a disponibilidade de dados em um framework unificado de tomada de decisão.

Palavras-chave:
Seleção de fornecedores de projetos; HFLTS-QFD; Tomada de decisão multicritério; Hesitant Fuzzy Linguistic Term Sets

1 Introduction

Several studies recognize that procurement is a strategically important function that helps organizations achieve competitive advantage (Araújo et al., 2017; Hakimi et al., 2024). Project procurement management is crucial for companies responsible for delivering project outcomes. According to the Project Management Institute (PMI, 2017), procurement management for a project includes "the processes necessary to purchase or acquire products, services, or results needed from outside the project team". Project contractors are increasingly focusing on their core activities while attending to their customers, and they may subcontract other activities from external suppliers (Liang et al., 2023a; Resende et al., 2023). Suppliers have a decisive role in project management since they perform activities that can compromise the project's success if they are not carried out appropriately. Therefore, choosing the right supplier for a job is central to guaranteeing a good project outcome (Suprasongsin et al., 2020).

The need to consider several factors contributes to the supplier selection process being dealt with as a multicriteria decision-making (MCDM) problem composed of some interdependent steps (Zimmer et al., 2016; Saputro et al., 2022). Initially, decision makers (DMs) involved in the problem choose a set of evaluation criteria based on the contractor's needs. Next, the relative importance (or weight) of each criterion selected is defined by the judgments made by these DMs. After that, some potential suppliers for the project are assessed by the DMs according to the selected criteria to generate a ranking based on the global performance of each alternative, which should be made using a suitable decision-making method (Araújo et al., 2017; Saputro et al., 2024).

However, the subjectivity of the DMs, the qualitative nature of some of the criteria, and the lack of information about the potential suppliers arise as complicating factors for this decision-making process (Zimmer et al., 2016; Lima-Junior et al., 2023). Several authors highlight the difficulty of evaluating supplier performance using qualitative criteria. It is due to the assessment of these factors by DMs using numerical values that usually leads to inaccuracy of the input data and, consequently, affects the results provided by the model (Liao et al., 2014; Xu & Zhang, 2019).

To address these difficulties, several studies have proposed applying MCDM methods and computational intelligence techniques in an isolated or combined way (Saputro et al., 2022; Lima-Junior et al., 2023). Given the difficulty of modeling subjective judgments, more and more researchers have adopted techniques based on fuzzy logic, which allows the use of linguistic terms such as "high", "medium", or "low", to represent the evaluations of DMs (Suprasongsin et al., 2020; Ortiz-Barrios et al., 2021). Fuzzy logic is applied with other tools, such as QFD (Quality Function Deployment), to meet customer expectations (Finger & Lima-Junior, 2022).

Considering the relevance and the wide variety of quantitative models to support the decision-making process for supplier selection, several literature systematic review studies on the existing approaches have been proposed. Based on the results from review studies proposed by Wetzstein et al. (2016), Zimmer et al. (2016), Araújo et al. (2017), Resende et al. (2021), Saputro et al. (2022), and Lima-Junior et al. (2023); and through the bibliographic research carried out of articles available in databases such as Web of Science, Science Direct, Scopus, and Emerald Insight, we have identified the following research gaps, which motivated the development of the present study:

1. Use of comparative linguistic expressions under hesitation. To date, no MCDM model for project supplier selection supports hesitant evaluations while simultaneously allowing DMs to express their preferences using comparative linguistic expressions (e.g., “between low and medium” or “greater than medium”). Existing models typically allow the DMs to select a single linguistic term, thereby failing to capture the natural hesitation involved in real-world decision-making processes. This limitation may compel DMs to provide precise judgments that do not accurately reflect their true preferences, potentially leading to biased results. Furthermore, constraining evaluations to predefined linguistic terms reduces the expressiveness and naturalness of human judgment. Therefore, addressing this gap is essential to enhance the realism and applicability of supplier selection models in project environments.

2. Consideration of DM’ risk attitudes. Another critical gap is the absence of models that incorporate the risk attitude of the DMs in the evaluation process. Current approaches assume neutral behavior and do not account for situations in which DMs may exhibit pessimistic or optimistic tendencies. As a result, the evaluation process may fail to accurately reflect the preferences of DMs, leading to distorted assessments and potentially suboptimal decisions.

3. Data collection difficulty as a decisive factor in the criteria selection. Finally, existing models overlook the difficulty of collecting reliable information on supplier performance for each criterion. This omission persists despite several studies (Wu & Barnes, 2010; Araújo et al., 2017; Osiro et al., 2018) emphasizing the importance of considering data availability when defining evaluation criteria. In project environments where resources and time are limited, the feasibility of gathering data can play a central role in the choice of evaluation criteria. Furthermore, ignoring the difficulty of data collection may result in the selection of criteria that are impractical to operationalize, increasing time, cost, and uncertainty in the decision process.

The development of a decision model that integrates the QFD (Quality Function Deployment) method with Hesitant Fuzzy Linguistic Term Sets (HFLTSs) has the potential to overcome the limitations identified in the literature. The HFLTS approach, a variation of fuzzy linguistic representation, is designed to capture DMs’ hesitation between linguistic terms (Magalhães & Lima-Junior, 2026). However, it does not provide a structured mechanism to translate project requirements into evaluation criteria. In contrast, QFD offers a systematic framework to link requirements to technical criteria, ensuring alignment with organizational objectives. Therefore, the integration of HFLTS and QFD is complementary: HFLTS improves the representation of uncertainty and hesitation, while QFD structures the decision problem by connecting requirements, criteria, and alternatives (Osiro et al., 2018). This combination enables a more consistent and realistic decision-making process in project supplier selection. Despite these potential benefits of their use, we did not find a decision-making model based on the HFLTS-QFD that supports the supplier selection process.

To address these limitations, this study proposes an MCDM model based on the HFLTS-QFD method to support the selection of criteria and project suppliers. A normative axiomatic quantitative approach based on modeling and simulation was adopted in this study (Bertrand & Fransoo, 2002). A computational model based on the HFLTS-QFD method was implemented using Microsoft Excel software. A pilot application was carried out in an energy company that works on large projects. Additionally, some sensitivity analysis tests involving the variation of input parameters of the proposed model were also performed.

The rest of the paper is organized as follows. Section 2 presents a literature review on project supplier selection. Section 3 explains the fundamentals of HFLTSs and describes the HFLTS-QFD method. Section 4 presents the proposed decision model. Section 5 details the results of the pilot application case. Section 6 discusses the results of the sensitivity analysis tests. Finally, Section 7 compares the model with previous approaches, while Section 8 presents the conclusion and suggestions for further studies.

2 Project supplier selection

Researchers and practitioners have been increasingly paying more attention to the quantitative models for selecting suppliers. According to the definition proposed by the PMBOK guide (Project Management Body of Knowledge) (PMI, 2017), a supplier is an external stakeholder that provides services, products, or results to an organization. From the project and business management perspective, the main objective of contracting suppliers is to achieve better overall performance and better profit margins. Several studies reinforce that suppliers' influence on the success or failure of projects is substantial since their performance affects the outcome of the entire business effort (Liang et al., 2023a).

In general, supplier selection in manufacturing companies presents low risks due to the frequent purchase of routine items, for which suppliers are available in the market. In these cases, the purchase requirements are already well known, and the supplier selection is made from the purchaser's supply base, which usually already has some qualified suppliers for each item through previous experiences (Ortiz-Barrios et al., 2021; Saputro et al., 2022).

In the case of selecting project suppliers, some complicating factors arise, which increase the complexity of the decision-making process. Since the project aims to develop entirely new products or services, in most situations, the purchasing requirements and supplier evaluation criteria are not yet well known, nor is there any previous experience with known suppliers (Zheng et al., 2021). As there are no qualified suppliers for various items to be purchased, managers should adopt the decision-making method that can assist in choosing a set of supplier selection criteria aligned with the project's needs, as well as being able to assess a high number of alternative suppliers (Ortiz-Barrios et al., 2021).

There is a large variety of criteria that can be adopted to select project suppliers (Hakimi et al., 2024). Watt et al. (2009) examined the literature to identify key factors in contractor selection and tender evaluation for projects and services. They concluded that the most adopted criteria are related to management, expertise, experience, and performance. These authors highlight that results indicate the prevalent use of the so-called ''soft" criteria. In another systematic review study, Araújo et al. (2017) found that the most commonly used criteria for selecting and evaluating project suppliers generally are related to staff features, quality, financial issues, experience, and cost.

The subjectivity of the DMs' opinions regarding criteria importance and supplier scores is a relevant issue that justifies adopting appropriate decision-making methods to deal with imprecise values and uncertain judgments (Resende et al., 2023). The following section discusses some characteristics of these methods.

2.1. Decision models for selecting project suppliers

Literature presents models for selecting project suppliers based on different quantitative techniques, including MCDM methods, artificial intelligence techniques, mathematical programming, and statistical methods. In general, applications of such models are carried out in projects related to construction, highways, product development, information technology, energy, hydro, maintenance, and research and development (Araújo et al., 2017).

An aspect that highly influences the effectiveness of these models is the technique used to assess and select alternative suppliers (Magalhães & Lima-Junior, 2026). Decision techniques present several distinctive aspects, including the nature and number of the criteria adopted, the number of alternatives considered, the ability to support group decision making, and the adequacy to deal with uncertainty (Lima-Junior et al., 2014; Oliveira et al., 2023; Saputro et al., 2024). According to Pelissari et al. (2021), the environment is uncertain when data are challenging to obtain or based on estimates. Uncertainty may also result from the DM in cases where he has some difficulty expressing his knowledge. Thus, selecting an adequate method for selecting project suppliers should consider all these aspects.

Table 1 describes some studies that propose quantitative models to select project suppliers, indicating the decision techniques and context. These studies were collected in the Web of Science, Science Direct, Scopus, and Emerald Insight databases, and using the Google Scholar search tool. AHP (Analytic Hierarchy Process) and Fuzzy AHP stand out among the most frequently applied methods.

Table 1
Decision-making models for selecting project suppliers.

Author(s)	Decision technique(s)	Application context
Safa et al. (2014)	TOPSIS (Technique for Order of Preference by Similarity to Ideal Solution)	General construction
Polat & Eray (2015)	AHP and Evidential Reasoning	Road construction
Gumus et al. (2016)	Fuzzy TOPSIS	Wind power generation
Luzon & El-Sayegh (2016)	AHP and Delphi	Oil and gas industry
Wood (2016)	Fuzzy TOPSIS	Oil industry
Wu et al. (2016)	VIKOR (VlseKriterijumska Optimizcija I Kaompromisno Resenje in Serbian)	Nuclear power plant
Cengiz et al. (2017)	ANP	Construction professionals
Mousakhani et al. (2017)	2-type Fuzzy TOPSIS	Battery manufacturer
Tamosaitiene et al. (2017)	AHP and ARAS (Additive Ratio Assessment)	Construction professionals
Liang & Chong (2019)	HFMD (Hesitant Fuzzy Mark Distance) and Hesitant Fuzzy QUALIFLEX	Bridge construction
Lu et al. (2019)	Fuzzy AHP	Power generation plant
Morkunaite et al. (2019)	PROMETHEE (Preference Ranking Organization Method for Enrichment Evaluation)	Selection of a contractor for the protection and restoration of heritage buildings
Yazdani et al. (2019)	DEMATEL (Decision Making Trial and Evaluation Laboratory) and EDAS (Evaluation based on Distance from Average Solution)	General construction projects in Spain
Liu et al. (2020)	QFD, BWM (Best-worst Method), VIKOR, and DEMATEL.	Blockchain tracing anti-counterfeiting platform project management
Shojaei & Bolvardizadeh (2020)	Rough AHP and Rough TOPSIS	University construction project
Jahangirzadeh et al. (2021)	GRA (Grey Relational Analysis), COPRAS (Complex Proportional Assessment), and multi-objective optimization	Numerical example
RezaHoseini et al. (2021)	Bi-objective linear programming and fuzzy probabilistic approach	Numerical example
Zheng et al. (2021)	Multi-stage mixed-integer stochastic programming	Automobile company
Abdzadeh et al. (2022)	Mixed-integer linear programming	General Construction
Nguyen et al. (2022)	Spherical Fuzzy AHP and WASPAS	Wind energy project
Karabayir & Botsali (2021)	Fuzzy AHP and Fuzzy TOPSIS	General Construction
Rahman et al. (2022)	Multi-objective evolutionary algorithm	Manufacturing projects
Rahman et al. (2022)	Fuzzy Hypersoft Set-based Rough Approximations and Triangular Fuzzy Numbers	General Construction
Tushar et al. (2022)	Fuzzy AHP and PROMETHEE II	Construction industry
Zhu et al. (2022)	AHP and VIKOR	Construction
Asghar et al. (2023)	Complex Picture Fuzzy Soft Set	General Construction
Asadujjaman et al. (2023)	Mixed integer programming model	Numerical example
Chen et al. (2023)	Fuzzy mixed integer linear programming	Numerical example
Dorfeshan et al. (2023)	Interval Type-2 Fuzzy Sets, CODAS (Combinative distance-based assessment), and BWM (Best-Worst Method	General Construction
Deepika et al. (2023)	Fuzzy Delphi, Fuzzy AHP, Fuzzy TOPSIS and DEA	General Construction
Liang et al. (2023a)	Hesitant Fuzzy TOPSIS	Bridge construction
Liang et al. (2023b)	Intuitionistic fuzzy LGDM	Bridge construction
Hakimi et al. (2024)	UTASTAR (Fuzzy Utilities-Additives STAR)	General Construction
Ghafoori & Abdallah (2024)	TOPSIS	General Construction

Although the models presented in Table 1 have contributed to advancing approaches to support project supplier selection, they also present some limitations and difficulties due to the quantitative techniques adopted. Despite the AHP method being widely applied, models based on this technique present limitations regarding the number of criteria and alternatives that can be considered in decision-related problems. Moreover, the AHP presents difficulties in maintaining judgment consistency, making collection judgments longer (Lima-Junior et al., 2014). It is worth mentioning that these limitations are also applicable to models based on the ANP (Cengiz et al., 2017) and Fuzzy AHP (Lu et al., 2019; Karabayir & Botsali, 2021; Tushar et al., 2022; Deepika et al., 2023).

Although the models based on the TOPSIS method (Safa et al., 2014; Ghafoori & Abdallah, 2024) and Fuzzy TOPSIS (Mousakhani et al., 2017; Karabayir & Botsali, 2021) neither limit the number of criteria and alternatives nor require the performance of judgment consistency tests, they present the ranking inversion problem. Apart from the points discussed in this section, some limitations that affect all supplier selection models found in the literature are: 1) absence of a procedure focused on the choice of supplier evaluation criteria that considers not only their weight but also the difficulty of collecting data to evaluate suppliers in each criterion; 2) inability to support decisions in situations in which the DM hesitates when judging; 3) they do not allow DMs to use linguistic expressions to assess criteria weight and alternative performance.

Although adopting the HFLTS-QFD method has the potential to overcome these limitations, it was possible to infer that there are no applications of this technique in the supplier selection process through the bibliographic research carried out in this study. Several systematic review studies on HFLTSs corroborate this finding, including Xu & Zhang (2019), Yu et al. (2022), and Lima-Junior et al. (2023), in which the use of the HFLTS-QFD method for supplier selection was not identified. The following section presents some fundamental definitions for understanding the HFLTS-QFD method.

3 Hesitant Fuzzy Linguistic Term Sets

Fuzzy logic uses everyday linguistic terms rather than crisp values to better capture DMs’ judgments. (Oliveira et al., 2023). However, the DM's hesitation in choosing between linguistic terms to perform an assessment is a frequent problem (Magalhães & Lima-Junior, 2026). To overcome this limitation, Rodríguez et al. (2012) proposed using HFLTS based on Hesitant Fuzzy Sets. The following section presents some fundamental definitions.

3.1. Definition of Hesitant Fuzzy Linguistic Term Set

Let $S$ be a symmetric linguistic term set, as shown in Equation 1 and Figure 1, and $\vartheta$ be a linguistic variable; the HFLTS of $\vartheta$ represented by $H_S\left(\vartheta \right)$ is an ordered finite subset of the consecutive linguistic terms of $S$. Therefore, $H_S\left(\vartheta \right)$ could be subsets as {N, VL and L}, {L} or {M, H, VH and A} (Rodríguez et al., 2012; Finger & Lima-Junior, 2022).

Figure 1
Set of linguistic terms with seven terms.

$S=\left\{s_{-\tau },\cdots ,s_0,\cdots ,s_{\tau }\right\}=\left\{N,VL,L,M,H,VH,A\right\}$ (1)

Everyday, linguistic expressions used to evaluate alternatives can be transformed into HFLTS through context-free grammar for eliciting linguistic information proposed by Rodríguez et al. (2012). This function $e_{G_H}:ll\to H_S$ transforms a linguistic expression $ll$ into HFLTS $(H_S)$. For instance,

$\begin{array}{l}{e}_{G_H}(l{l}_1=greaterthanmedium)=H_S\left\{high,veryhigh,absolute\right\};\\ e_{G_H}\left(l{l}_2=low\right)=H_S\left\{low\right\};\\ e_{G_H}(l{l}_3=betweenverylowandmedium)=H_S\left\{verylow,low,medium\right\};\\ e_{G_H}\left(l{l}_4=atmostlow\right)=H_S\left\{nothing,verylow,low\right\}\end{array}$

and

$$e_{G_H}\left(l{l}_5=atleasthigh\right)=H_S\left\{high,absolute\right\}$$

Thus, DMs can express their hesitation using linguistic expressions instead of choosing just one term from $S$ (Oliveira et al., 2023).

3.2. Distance between collections of HFLTS for multicriteria decision-making

Liao et al. (2014) propose a family of distance and similarity measures between two collections of HFLTSs to be employed in MCDM problems. Each alternative $i$ has a collection of HFS, one for each criterion j. A collection of HFLTS is represented by $H_s^i=\left\{H_s^{i1},H_s^{i2},\dots ,H_s^{im}\right\}$ where each $H_s^{ij}$ is a HFLTS used to evaluate the alternative $i$ based on the criterion $j$. The generalized weighted distance measure between two collections of HFLTS $H_s^1$ and $H_s^2$ is defined by Equation 2.

$d_{gwd}\left(H_s^1,H_s^2\right)={\left({{\displaystyle \sum }}_{j=1}^m\frac{w_j}{L}{{\displaystyle \sum }}_{l=1}^L{\left(\frac{\left|{\delta }_l^{1j}-{\delta }_l^{2j}\right|}{2\tau +1}\right)}^{\lambda }\right)}^{\frac{1}{\lambda }}$ (2)

where $W={\left(w_1,w_2,\cdots ,w_m\right)}^t$ is the weighting vector that satisfied two conditions: $0\le w_j\le 1$ and ${{\displaystyle \sum }}_{j=1}^m{w}_j=1$; $L$ is the number of linguistic terms in $H_s^{ij}$; ${\delta }_l^{1j}$ is $lth$ term of $H_S^{1j}$ and ${\delta }_l^{2j}$ is $lth$ term of $H_S^{2j}$; $2\tau +1$ is the number of linguistic terms in $S$; and $\lambda$ is a parameter to determine different distance measures. This work uses Euclidean distance ($\lambda =2$). In an MCDM problem, the DMs should evaluate alternatives $X=\left\{x_i|i=\mathrm{1,}\cdots ,n\right\}$ based on multiple criteria $C=\left\{c_j|j=\mathrm{1,}\cdots ,m\right\}$. The judgment matrix using HFLTS, with entries of alternatives in the rows and criteria in the columns, is represented by Equation 3 (Liao et al., 2014; Osiro et al., 2018).

${ℍ}_S=\left[\begin{array}{cc}\begin{array}{cc}{H}_S^{11}& H_S^{12}\\ H_S^{21}& H_S^{22}\end{array}& \begin{array}{cc}\cdots & H_S^{1m}\\ \cdots & H_S^{2m}\end{array}\\ \begin{array}{cc}⋮& ⋮\\ H_S^{n1}& H_S^{n2}\end{array}& \begin{array}{cc}\ddots & ⋮\\ \cdots & H_S^{nm}\end{array}\end{array}\right]$ (3)

where $H_S^{ij}$ is a HFLTS obtained from the linguistic expression used to evaluate the $ith$ alternative with respect to the $jth$ criterion. For each $H_S^{ij}$ there is the upper bound $H_S^{ij+}=max\left\{s_{ij}|s_{ij}\in H_S^{ij}\right\}$ and the lower bound $H_S^{ij-}=min\left\{s_{ij}|s_{ij}\in H_S^{ij}\right\}$. Then, the definitions of the positive ideal solution $S{I}^{+}$ and the negative ideal solution $S{I}^{-}$ are respectively presented by Equations 4 and 5 (Finger & Lima-Junior, 2022):

$S{I}^{+}=\left\{H_S^{j+}|j=\mathrm{1,}\cdots ,m\right\}$ (4)

$S{I}^{-}=\left\{H_S^{j-}|j=\mathrm{1,}\cdots ,m\right\}$ (5)

where:

$\begin{array}{l}{H}_S^{j+}=\{max\left\{s_{ij}|i=\mathrm{1,}\cdots ,n\right\}forbenefitcriterion{c}_j,\\ min\left\{s_{ij}|i=\mathrm{1,}\cdots ,n\right\}forcostcriterion{c}_j\}\end{array}$ (6)

$\begin{array}{l}{H}_S^{j-}=\{min\left\{s_{ij}|i=\mathrm{1,}\cdots ,n\right\}forbenefitcriterion{c}_j,\\ max\left\{s_{ij}|i=\mathrm{1,}\cdots ,n\right\}forcostcriterion{c}_j\}\end{array}$ (7)

The distances between each alternative xi and the ideal solutions determine the overall performance ranking of each alternative. Liao et al. (2014) proposed a distance measure that is called satisfaction degree $\eta$ of an alternative $x_i$, which is shown in Equation 8. In this equation, $\theta$ is a risk parameter which represents the level of risk accepted by the DMs, $\theta \in \left[\mathrm{0,1}\right]$. While $\theta >0.5$ implies a pessimistic point of view of the DM, $\theta <0.5$ implies an optimistic view.

$\eta \left(x_i\right)=\frac{\left(1-\theta \right)d\left(x_i,x^{-}\right)}{\theta d\left(x_i,x^{+}\right)+\left(1-\theta \right)d\left(x_i,x^{-}\right)}$ (8)

3.3 The HFLTS-QFD approach

The QFD method has expanded its use to different processes, such as supplier selection, teamwork management, and costs (Lima-Junior & Carpinetti, 2016). In addition, many authors have proposed improvements in the QFD to address the subjectivity and imprecision of the data used in the quality matrix. These proposals are based on different techniques, such as DEMATEL (Yazdani et al., 2020), fuzzy numbers (Juan et al., 2009), interval type-2 fuzzy (Efe et al., 2020), and interval-valued intuitionistic fuzzy sets (Yu et al., 2018). Regarding Hesitant Fuzzy Set Theory, two proposals were found in the literature: Önar et al. (2016) and Osiro et al. (2018).

Önar et al. (2016) use HFLTS to deal with DMs' judgments in their Hesitant Fuzzy QFD approach. They applied AHP with TOPSIS in the computational steps, so HFLTS were used to construct pairwise comparison matrices. In contrast, Osiro et al. (2018) developed a HFLTS-QFD approach based on combining HFLTS and the distance measurements proposed by Liao et al. (2014) to weigh requirements and rank performance indicators. This approach eliminates pairwise comparison matrices, requires less time to gather the DMs' evaluations, and presents less computational effort. Therefore, this work uses the HFLTS-QFD approach developed by Osiro et al. (2018), which has the following four stages to select a set of metrics to assess supply chain sustainability:

1. The DMs select a set of requirements and assess the importance of each one according to the specific strategy of their organization, using HFLTS. The relative weight of each requirement is calculated based on the distances of each requirement from the positive ideal solution and the negative ideal solution of the set of requirements;

2. The DMs select a set of metrics related to the requirements from the previous stage. The relationship between each metric and each requirement is assessed using HFLTS-QFD. The distances of each metric from the positive ideal solution and the negative ideal solution of the set of metrics are used to determine the weight of each metric;

3. The degree of difficulty in collecting data to assess each metric is determined in the same way as in the previous stages, considering information availability, human resources, time required, and other resources;

4. The categorization and final selection of metrics for assessing supply chain sustainability is based on a two-dimensional model. The horizontal axis represents the difficulty of data collection for each metric, and the vertical axis represents the relative importance of each metric.

The following section presents the proposed model for selecting criteria and suppliers based on this method.

4 The proposed decision model for project supplier selection

Figure 2 presents the proposed decision model to support the project supplier selection process, which is composed of four stages. The first three stages are based on the studies developed by Lima-Junior & Carpinetti (2016), PMI (2017), Osiro et al. (2018), and Liang et al. (2023a), while the fourth stage is based on Juan et al. (2009) and Oliveira et al. (2023). Although the model is analytically sophisticated, DMs interact with it through simple and intuitive linguistic evaluations.

Figure 2
The proposed decision model for project supplier selection.

Stage 1 is based on the “What matrix” of the QFD method, which is applied for listing and weighting the requirements of the purchasing company. This stage begins with defining the experts who will act as DMs in the supplier selection process. It is important to consider the involvement of experts from different functional areas. Thus, the project scope should serve as a guide to define the areas of origin of the DMs, such as logistics, quality, finance, purchasing, and products. The model can also be applied in the presence of a single DM. In such cases, the aggregation step becomes unnecessary. However, this may reduce the robustness of the results, as the evaluation of criteria and suppliers relies on a single perspective, potentially increasing subjectivity and bias.

After defining the DMs, they should choose a set of requirements related to the project's performance objectives. Based on the Project Management Institute (PMI, 2017), the knowledge areas defined in the PMBOK (Project Management Body of Knowledge) guide were adopted to represent the project’s performance priorities, as presented in Table 2. The 2017 edition was selected due to its structured and detailed organization of knowledge areas, which can be directly operationalized within the QFD framework. In contrast, more recent versions (e.g., PMBOK 2021) adopt a principle-based approach, offering greater flexibility but less granularity for defining explicit and measurable project requirements. Such granularity is essential for the systematic construction of the proposed model.

Table 2
A list of requirements is suggested for selecting project suppliers.

Requirements
1	Project integration management
2	Project scope management
3	Project schedule management
4	Project cost management
5	Project quality management
6	Project resource management
7	Project communications management
8	Project risk management
9	Project procurement management
10	Project stakeholder management

Then, using the linguistic terms shown in Figure 1, DMs assess each requirement's importance level, considering the project's priorities. These judgments may be represented as linguistic expressions, as shown in Table 3. One or more linguistic terms may be chosen for each requirement assessed, or even a linguistic expression. Table 3 details the transformation functions used to convert linguistic expressions into HFLTS. At the end of the first stage, the weight of each requirement, also called the degree of satisfaction $\eta \left(R_k\right)$, is calculated using Equations 2, 6, 7 and 8. These values should be normalized using Equation 9, which assures that the sum of the weights of the requirements is equal to one.

Table 3
Linguistic expressions to evaluate requirements, criteria, and suppliers.

Expressions	Transformation function $e_{G_H}$ (Rodríguez et al., 2012)	Example of use (based on Figure 1)	Activated linguistic terms
“At most...”	$e_{G_H}\left(atmost{s}_i\right)$=$\{s_j|s_j\in sand{s}_j\le s_i$}	At most low	[N, VL, L]
“Lower than...”	$e_{G_H}\left(lowerthan{s}_i\right)$=$\{s_j|s_j\in sand{s}_j<s_i$}	Lower than low	[N, VL]
“At least...”	$e_{G_H}\left(atleast{s}_i\right)$=$\{s_j|s_j\in sand{s}_j\ge s_i$}	At least high	[H, VH, A]
“Greater than...”	$e_{G_H}\left(greaterthan{s}_i\right)$=$\{s_j\left|s_j\in sand{s}_j\right.〉s_i$}	Greater than high	[VH, A]
“Between ... and ...”	$e_{G_H}\left(between{s}_{i}and{s}_j\right)$=$\{s_k|s_k\in sand{s}_i\le s_k\le s_j$}	Between low and high	[L, H]

$v_i\left(R_k\right)=\eta \left(R_k\right)/\sum \eta \left(R_k\right)$ (9)

Stage 2 is based on the "How matrix" of the QFD method, whose objective is to establish the weight of the criteria by assessing the interrelationships between these criteria and the requirements defined in the previous stage. The DMs should define an initial set of supplier evaluation criteria, considering the project's performance objectives and the requirements selected in the previous stage. These criteria may be defined based on literature studies on decision making for project supplier selection (Table 1). The construction of this list considered the inclusion of criteria related to economic performance, environmental and social issues, and other relevant factors within project management. However, this list is not exhaustive. The DMs may include additional criteria to take into account all the needs of the project.

After the initial criteria selection, the DMs should assess the relationship intensity between each criterion and requirement using linguistic terms or expressions, as shown in Figure 1 and Table 3. Like stage 1, the degree of satisfaction for each criterion ($\eta \left(C_j\right)$) is calculated using Equations 2, 6, 7 and 8. The normalized weights ($w\left(C_j\right)$) are obtained according to Equation 10. Sigmoid normalization was adopted in this step because it provides well-balanced and evenly distributed output values. Additionally, this normalization approach aligns with the methodological foundations of the HFLTS-QFD method, as employed by Osiro et al. (2018).

$w\left(C_j\right)=\frac{1}{1+e^{-\frac{\eta \left(C_j\right)-\overline{\eta \left(C\right)}}{{\sigma }_{\eta \left(C_j\right)}}}}$ (10)

Like the technically feasible assessment proposed by the QFD method, Stage 3 focuses on assessing the difficulty of collecting data necessary to evaluate supplier performance against the criteria defined in the previous stage. It aims to categorize the criteria defined in stage 2, considering their weights and the degree of difficulty of data collection to assess supplier performance on such criteria. Based on Lima-Junior & Carpinetti (2016), the evaluation of the difficulty of data collection by DMs considers the following factors:

1. Availability of information: this factor considers the information available, the existence of historical records or tacit knowledge by part of the DMs that may be applied to assess supplier performance in each criterion;

2. Human resources and time needed: it considers the number of people involved in the process and the time needed to assess alternative suppliers;

3. Additional resources: it considers any other necessary resources, such as contracting services from third parties.

Again, assessing these factors is qualitative and requires judgment by the DMs. This judgment takes place similarly to the previous stages, guided by a scale containing five linguistic terms in Figure 3 and linguistic expressions in Table 3.

Figure 3
A basic set of linguistic terms to evaluate the difficulty of data collection.

To calculate the score for each criterion in stage 3, it is considered that the “availability of information” is a cost factor because the difficulty of collecting data decreases with increased availability of information. Thus, in applying the HFLTS-QFD method, calculations of the criteria scores in “availability of information” use the lower limit to define their positive ideal solution (Equation 6) and the upper limit to determine the negative ideal solution (Equation 7). On the other hand, “human resources and time needed” and “additional resources” are considered as benefit criteria. Therefore, calculations of the criteria scores in these factors consider the upper limit to represent their positive ideal solution and the lower limit to define their ideal negative solution. The score of each criterion concerning the difficulty of data collection is determined by Equation 8 and normalized through Equation 10.

Subsequently, the criteria should be grouped in the categorization matrix proposed by Lima-Junior & Carpinetti (2016). This matrix subdivides the criteria into four groups:

1. Priority criteria: this group includes the criteria most related to the priority requirements, being the preferred ones as they present relatively low difficulty of data collection;

2. Critical criteria: criteria in this group are also highly related to the priority requirements. Thus, it is important to consider them in the supplier selection process. The DMs should choose only the vital ones;

3. Complementary criteria: the criteria of this group are not preferred, as they have relatively low importance. However, as they have relatively low difficulty in data collection, some may be included in the supplier selection process, depending on the number of priority and complementary criteria already selected;

4. Costly criteria: the criteria of this group should not be chosen, as they are the least important and require a relatively high effort to collect supplier performance data.

Finally, stage 4 aims to evaluate potential suppliers and choose one or more among them. The DMs should initially point out which potential suppliers will be considered in the assessment process. Then, they evaluate the performance of each alternative supplier, considering the criteria chosen in stage 3. Equations 2, 6, 7 and 8 are applied to obtain the supplier's global score values, which are then normalized using Equation 9. The normalized values are used to rank suppliers in decreasing order. Thus, the supplier(s) with the highest score should be chosen.

In this study, the DMs’ risk attitudes are incorporated through a parameter $\theta$ in the satisfaction degree function used to evaluate requirements, criteria, and alternatives (Equation 8). This parameter allows modeling different behavioral perspectives, ranging from pessimistic ($\theta >0.5)$ to optimistic ($\theta <0.5)$, influencing how distances to ideal solutions are interpreted. As a result, the model provides greater flexibility and realism by allowing DMs to adjust the evaluation according to their risk tolerance. The following section details the pilot application of the proposed model.

5 Pilot application in an energy sector company

A pilot application case was carried out at a Brazilian electric energy company. The company operates in the generation, transmission, distribution, and sale of electricity, according to concessions granted by ANEEL (National Electric Energy Agency). It provides access to the electricity grid for the population as a whole, for large companies, and for small rural properties located in the most remote regions. Most of the company's significant investment projects refer to the construction of hydroelectric plants, wind farms, substations, and transmission lines in Brazilian territory. These works are performed by third parties. The company's technical staff oversees the project's planning, which involves supplier selection and monitoring.

To manage its projects, the company makes use of a methodology based on the PMBOK guide, not limited to the simple management of resources, costs, and deadlines, but also the management of relationships that the project has within the business environment in which it is inserted. As a mixed capital company, the company is subject to the constitutional principles of public administration, according to Federal Law 13,303 (Brasil, 2016). It also complies with other applicable rules that regulate supplier qualification, which implies hiring through bids, except for cases of dismissal and unenforceable bidding. Each contract must have its particularities analyzed by experts who consider both the need to comply with applicable legal regulations and their experience in analyzing potential suppliers. Thus, the pilot application was made aiming at the selection of a supplier among three already qualified by the company, for the construction of a transmission line with the following basic characteristics: nominal voltage of 230 kV, connection with two substations in simple circuit, and an approximate length of 30 kilometers.

Three experts participated in the decision-making process. The experts were selected based on their professional experience, area of expertise, and direct involvement in similar projects within the company. DM1 contributes technical expertise in civil engineering aspects, DM2 brings experience in project scheduling and planning activities, and DM3 provides a strategic perspective on project management and decision-making processes. All participants have at least ten years of professional experience in the energy sector and have been actively involved in projects related to the construction of transmission infrastructure, ensuring both expertise and representativeness.

5.1 Stage 1: Definition and weighting of requirements

Considering the project’s main objective, which is the conclusion of the works and the start of operations within the deadline stipulated by the regulatory agency, the DMs chose four requirements from those listed in Table 2. This choice occurred in a meeting with the DMs’ group that involved the presentation of the proposed model and the explanation of how the DMs would express their judgments. In this meeting, each DM provided a brief account of his or her experience in previous works, whose scope was similar to the pilot application project. This discussion contributed to attaining a consensual definition of the requirements to be considered in the model application. Using the set of linguistic terms defined in Figure 1 and the expressions in Table 3, the DMs assessed the level of relative importance of the four selected requirements, as indicated in Table 4. Table 5 shows the results of converting these judgments into the HFLTS format, according to the definitions presented in Section 3.1 and Table 3.

Table 4
Requirements assessment using linguistic terms and expressions (“What matrix”).

Requirements		DM1	DM2	DM3
R1	Project scope management	At least high	Between medium and high	Between low and medium
R2	Project schedule management	At least very high	Between high and very high	At least very high
R3	Project cost management	Absolute	Between medium and very high	At least high
R4	Project risk management	At least very high	Between medium and high	At least very high

Table 5
Conversion results of the requirements assessment into HFLTS.

	DM1	DM2	DM3
R1	[H, VH, A]	[M, H]	[L, M]
R2	[VH, A]	[H, VH]	[VH, A]
R3	[A]	[M, H, VH]	[H, VH, A]
R4	[VH, A]	[M, H]	[VH, A]

Still in stage 1, a sequence of calculations was performed to obtain the weight of the requirements. First, the ideal positive solution ($S{I}^{+}$) was identified using Equation 6, which resulted in $S{I}^{+}$= {[A], [VH], [A]}. The same procedure was adopted for the ideal negative solution ($S{I}^{-}$) using Equation 7, resulting in $S{I}^{-}$ = {[H], [M], [L]}. Then, where the DMs have the same level of experience, the weights assigned to the opinions of the three DMs were equal (1/3). The distance from the ideal positive solution for each alternative ($d\left(H_s^{kt},H_S^{t+}\right)$) was determined by Equation 2. Similarly, the distance from the ideal negative solution and the scores of each alternative ($d\left(H_s^{kt},H_S^{t-}\right)$) were obtained. After that, the application of Equation 8 produced the weights of the requirements ($\eta \left(R_k\right)$) based on the values of $d\left(H_s^{kt},H_S^{t-}\right)$ and $d\left(H_s^{kt},H_S^{t+}\right)$. Finally, the requirements weights were normalized ($v\left(R_k\right))$ using Equation 9, which are shown in Table 6.

Table 6
Results of the calculations of the requirements weights.

	$d\left(H_s^{kt},H_S^{t+}\right)$	$d\left(H_s^{kt},H_S^{t-}\right)$	$\eta \left(R_k\right)$	$v\left(R_k\right)$	Rank
R2	0.101	0.345	0.774	0.320	1
R3	0.151	0.323	0.682	0.282	2
R4	0.154	0.325	0.678	0.280	3
R1	0.337	0.135	0.286	0.118	4

The results shown in Table 6 pointed out that the project schedule management requirement (R₂) is the most important, followed by the project cost management requirement (R₃). According to the DMs, the higher importance of these requirements is related to the fact that the company operates in a tightly regulated market, where the delay in starting the operation of the transmission line results in the non-receipt of the values stipulated in contract and the payment of a fine to ANEEL. Another observation made by the DMs is that the project risk management (R₄) had a weight very close to that attributed to cost management, also because it could directly impact on the date scheduled for the start of operations in the contract. Project scope management (R₁), on the other hand, had less significance due to the difficulty of its modification, given the technical characteristics of this type of project and the current legal regulation.

5.2 Stage 2: Criteria definition and weighting

Considering the scope and requirements of the project, the DMs selected 12 criteria. This selection was based on criteria employed in previous studies (Table 1) and it took place by means of a discussion and consensus in a meeting that lasted approximately 3 hours. After this selection, also by consensus, the DMs judged the intensity of the relationship between these criteria and the requirements defined in stage 1 using the terms shown in Figure 1 and the expressions in Table 3. Table 7 presents these judgments. Due to page limitations, the converted expressions into HFLTS are not reported in the manuscript.

Table 7
Evaluation of the relationship intensity between criteria and requirements (“How matrix”).

	Criteria	R1	R2	R3	R4
C1	Delivery capacity	At least VH	At least VH	Between M and VH	Between H and VH
C2	Project management competence	At least VH	VH	At least VH	Between H and VH
C3	Financial condition	VH	Between M and H	Between M and H	Between M and H
C4	Reliability	At least H	Between H and VH	Between H and VH	At least VH
C5	Technical knowledge	At least VH	At least VH	Between H and VH	At least VH
C6	Cost	Between H and VH	Between M and H	At least VH	At least VH
C7	Supplier profile	Between M and H	Between M and VH	Between M and VH	Between H and VH
C8	Financial power	Between M and H	Between M and H	VH	At least VH
C9	Environmental policies	Between M and H	Between M and VH	Between M and VH	Between H and VH
C10	Safety programs	Between L and M	Between L and M	Between M and VH	Between H and VH
C11	Delivery lead time	Between H and VH	At least VH	H	Between M and H
C12	Speed of problem resolution	Between H and VH	At least VH	Between H and VH	At least VH

At the end of stage 2, $S{I}^{+}$was calculated using Equation 6 and $S{I}^{-}$ using Equation 7. The results obtained were $S{I}^{+}$ = {[A], [A],[ A], [A]} and $S{I}^{-}$ = {[L], [L], [M], [M]}. The distances from the ideal solutions, ($d\left(H_s^{jk},H_S^{k+}\right)$) and ($d\left(H_s^{jk},H_S^{k-}\right)$), was calculated using Equation 2. Then, Equation 8 calculated the satisfaction degree of each criterion ($\eta \left(C_j\right)$) based on $d\left(H_s^{jk},H_S^{k+}\right)$, and negative $d\left(H_s^{jk},H_S^{k-}\right)$. The values of ($\eta \left(C_j\right)$) were normalized according to Equation 10 to obtain the criteria weights ($w\left(C_j\right)$). Results of these calculations are presented in Table 8.

Table 8
Results of the criteria weight calculations.

	Criterion	$d\left(H_s^{jk},H_S^{k+}\right)$	$d\left(H_s^{jk},H_S^{k-}\right)$	$\eta \left(C_j\right)$	$w\left(C_j\right)$	Rank
C5	Technical knowledge	0.147	0.404	0.733	0.7852	1
C2	Project management competence	0.158	0.375	0.704	0.7474	2
C12	Speed of problem resolution	0.163	0.386	0.703	0.7465	3
C4	Reliability	0.194	0.342	0.639	0.6478	4
C1	Delivery capacity	0.214	0.368	0.633	0.6383	5
C6	Cost	0.233	0.326	0.584	0.5522	6
C11	Delivery lead time	0.264	0.325	0.552	0.4953	7
C8	Financial power	0.258	0.287	0.527	0.4484	8
C7	Supplier profile	0.295	0.246	0.454	0.3239	9
C9	Environmental policies	0.295	0.246	0.454	0.3239	10
C3	Financial condition	0.346	0.209	0.377	0.2146	11
C10	Safety programs	0.391	0.168	0.301	0.1357	12

The results shown in Table 8 have pointed out technical knowledge (C₅) as the criterion with the most significant importance, followed by project management competence (C₂), speed of problem resolution (C₁₂), reliability (C₄), and delivery capacity (C₁). According to the DMs, the ordering indicated by the criteria classification reflects what is expected for this type of project considering the long execution period (usually between 18 and 36 months), and the fact that the work covers facilities across several municipalities in distinct states favors unpredictability due to different legal regulations, climatic variations, and different stakeholders.

5.3 Stage 3: Evaluation of the difficulty of data collection and criteria selection

In stage 3 of the proposed model application, the difficulty of collecting supplier performance data concerning the criteria evaluated in stage 2 was analyzed. As discussed in Section 4, the DMs' assessment of the difficulty of data collection considers three factors: information availability, human resources, time, and the additional resources needed to obtain this data. The DMs made this assessment using linguistic terms and expressions shown in Figure 3 and Table 3, respectively. The result of this consensual evaluation is presented in Table 9.

Table 9
Evaluation of the difficulty of data collection using linguistic expressions.

	Information availability (F1)	Human resources and time (F2)	Additional resource required (F3)
C1	At least medium	Between low and medium	At most low
C2	Between low and medium	Between medium and high	At most low
C3	Between medium and high	Between low and medium	At most low
C4	Between medium and high	Between medium and high	Between low and medium
C5	Between medium and high	Between medium and high	Between low and medium
C6	At least high	Between low and medium	Between low and medium
C7	Between low and high	Between medium and high	Between medium and high
C8	Between low and medium	Between low and medium	At most low
C9	Between medium and high	Between low and medium	Between low and medium
C10	Between medium and high	Between low and medium	Between low and medium
C11	Between medium and high	Between low and medium	At most low
C12	Between low and medium	Between medium and high	Between medium and high

The "availability of information" factor was modeled as a cost criterion, as the difficulty of collecting data decreases as the availability of information increases. On the other hand, "human resources and necessary time" and "additional resources" were considered benefit criteria. With these considerations, the results obtained were $S{I}^{+}$ = [L, H, H] and $S{I}^{-}$ = [VH, L, VL]. As presented in Table 10, the distances were determined using Equation 2, and the degree of satisfaction ($\eta \left(C_j\right)$) for each criterion was calculated according to Equation 8. These values were also normalized using Equation 10 to generate the difficulty of data collection ($\text{z}\left({\text{C}}_{\text{j}}\right)$) values.

Table 10
Calculations of the difficulty of data collection for each criterion.

	Criterion	$d\left(H_s^{ju},H_S^{u+}\right)$	$d\left(H_s^{ju},H_S^{u-}\right)$	$\eta \left(C_j\right)$	$z\left(C_j\right)$	Rank
C12	Speed of problem resolution	0.245	0.787	0.763	0.880	1
C7	Supplier profile	0.327	0.739	0.694	0.817	2
C4	Reliability	0.469	0.548	0.539	0.594	3
C5	Technical knowledge	0.469	0.548	0.539	0.594	4
C2	Project management competence	0.548	0.616	0.530	0.578	5
C8	Financial power	0.616	0.548	0.470	0.472	6
C10	Safety programs	0.548	0.469	0.461	0.456	7
C9	Environmental policies	0.548	0.469	0.461	0.456	8
C11	Delivery lead time	0.678	0.374	0.356	0.281	9
C3	Financial condition	0.678	0.374	0.356	0.281	10
C6	Cost	0.678	0.374	0.356	0.281	11
C1	Delivery capacity	0.739	0.327	0.306	0.215	12

After calculating the difficulty of data collection, the criteria were grouped into the categorization matrix shown in Figure 4. Since delivery capacity (C₁) and cost (C₆) present high weight and low difficulty of data collection, they were classified as priority. Adopting these criteria may contribute to making the supplier selection process more effective and agile.

Figure 4
Result of the criteria categorization.

The project management competence (C₂), technical knowledge (C₅), reliability (C₄), and speed of problem resolution (C₁₂) criteria were classified as critical. Analyzing these results, the DMs observed that among the five criteria with the highest weight, only the delivery capacity criterion did not remain among the five with the most significant difficulty in data collection. Despite the high effort required for data collection, they decided to select all the critical criteria.

Classified as complementary, the financial condition (C₃), financial power (C₈), environmental policies (C₉), safety programs (C₁₀), and delivery lead time (C₁₁) criteria were considered as having relatively low importance. Nonetheless, the DMs preferred to consider all the complementary criteria in the supplier evaluation process, since they present low difficulty in data collection and can enable a more accurate supplier selection assessment. Finally, the supplier profile criterion (C₇) was classified as costly, which led to its elimination as it is less important and requires a relatively high effort in data collection. Therefore, from the results obtained in stage 3, C₁, C₂, C₃, C₄, C₅, C₆, C₈, C₉, C₁₀, C₁₁, and C₁₂ criteria were chosen.

5.4 Stage 4: Supplier assessment and selection

In the last model application stage, the DMs pointed out three alternatives to be assessed concerning the criteria selected in stage 3. These alternatives have been part of the company's supplier base for more than 5 years and have worked on other transmission line construction projects developed by the company. Again, the assessment was made by the DMs in a consensual way using linguistic terms and expressions shown in Figure 1 and Table 4, respectively. The DMs’ judgments regarding supplier performance on each criterion are presented in Table 11.

Table 11
Assessment of supplier alternatives regarding criteria using linguistic terms and expressions.

	A1	A2	A3
C1	Between medium and high	Between medium and high	Between low and high
C2	Between medium and VH	Between medium and high	Between low and medium
C3	Between medium and high	Between medium and VH	Medium
C4	High	Between high and VH	Between medium and high
C5	High	Between medium and VH	Between medium and high
C6	Between medium and high	Between medium and high	Medium
C8	At least medium	At least high	Between medium and high
C9	High	Between medium and VH	Between medium and high
C10	High	Between medium and high	Between medium and high
C11	Between medium and high	Between medium and VH	At least medium
C12	Between medium and high	Between low and medium	Between low and high

Most of the criteria were modeled as benefit criteria. Thus, the upper limit was adopted as the positive ideal solution and the lower limit as the negative ideal solution. The exceptions were the cost (C₆) and delivery time lead (C₁₁) criteria, which were modeled as cost criteria, since the lower the score achieved by the suppliers in these criteria, the better the final classification. Under these conditions, the results were $S{I}^{+}$= {[H], [VH], [VH], [VH], [VH], [M], [A], [VH], [H], [M], [H]} and $S{I}^{-}$ = {[L], [L], [M], [M], [M], [H], [M] , [M], [M], [A], [L]}. Based on these values, $d\left(H_s^{ij},H_S^{j+}\right)$ and $d\left(H_s^{ij},H_S^{j-}\right)$ were calculated for each alternative according to Equation 2. The application of Equation 8 determined the satisfaction degree of the alternatives ($\eta \left(A_i\right)$) using these distances. The values obtained for $\eta \left(A_i\right)$ were normalized according to Equation 9 to define the global score of each supplier ($g\left(A_i\right)$). The results of these calculations are presented in Table 12 as a result of the application of the model.

Table 12
Calculation results of supplier scores and ranking.

Supplier	$d\left(H_s^{ij},H_S^{j+}\right)$	$d\left(H_s^{ij},H_S^{j-}\right)$	$\eta \left(A_i\right)$	$g\left(A_i\right)$	Rank
Alternative 1	0.359	0.535	0.598	0.394	1
Alternative 2	0.417	0.503	0.547	0.360	2
Alternative 3	0.591	0.354	0.374	0.246	3

Observing the results shown in Table 12, the DMs were surprised by the final classification. According to them, at first, the most natural choice would be alternative 2, with which they had worked more often. Asked what would lead them to make this choice, they were unanimous in citing the larger supplier size regarding the number of employees and the scope of the works already carried out with the company. After checking the assessments made, the team observed that the judgments were very similar regarding the performance of alternatives 1 and 2 for the priority criteria. However, the judgments regarding performance against the critical criteria favored alternative 1, which justified the result endorsed by the DMs.

6 Sensitivity analysis

Sensitivity analysis is a technique that allows to measure the effect of changing input parameter values in a decision model. Its application is quite frequent in studies involving the proposal of MCDM models since the sensitivity analysis helps to map what a model does (Magalhães & Lima-Junior, 2026). In the present study, some tests involving sensitivity analysis were conducted to verify how the variation of the values of θ (Equation 8) may affect the criteria categorization results. As described in Section 5, the pilot application used parameter θ as 0.5 to capture a balanced view of the DMs. To assess the result of the choice of criteria considering optimistic and pessimistic views, based on variations of θ, the following scenarios were tested:

1. Optimistic scenario: the value of parameter θ was defined as 0.1 to calculate the criteria weight (stage 2). To calculate the difficulty of data collection (stage 3), θ = 0.9 was used. This inversion in the values of θ for calculating the difficulty of data collection was made since a high score in this dimension negatively impacts the evaluated criterion;

2. Pessimistic scenario: In this case, the value of θ was defined as 0.9 for calculating the criteria weights. To calculate the difficulty of data collection, the θ value was considered as 0.1.

In both scenarios, only the values of θ were changed in relation to the application case. The DMs' judgments were not modified, nor were the values of θ for calculating the weight of the requirements. We selected the values 0.1 and 0.9 (rather than the boundary values 0 and 1) because using the extreme values leads either to identical scores or to a division by zero, rendering the results invalid or uninformative. The new scores obtained for the criteria under the two scenarios are plotted in Figure 5, allowing a comparison of the changes in the criteria categorization results.

Figure 5
The criteria categorization results for the pessimistic, application, and optimistic scenarios.

In Figure 5, the categorization results for different scenarios are represented as follows:

1. Circle: represents the criteria categorization results obtained in the application;

2. Rectangle: indicates the criteria categorization results in the pessimistic scenario;

3. Triangle: illustrates the categorization results in the optimistic scenario;

4. Highlighted elements (in blue): identify group criteria that changed about the categorization attained in the application case.

Analyzing the results shown in Figure 5, it is observed that in a scenario with pessimistic DMs, the cost criterion (C₆) leaves the priority condition to be included in the complementary criteria group. The only priority criterion in the pessimistic scenario is the delivery capacity (C₁). In addition, financial power (C₈), environmental policies (C₉), and security programs (C₁₀) changed their criteria classification from complementary to costly, as the difficulty of data collection scores increased in the pessimistic scenario. In the optimistic scenario, there was a change in the classification of the financial power (C₈) and delivery lead time (C₁₁) criteria, which are no longer complementary to assuming priority status. Variations in the values of the parameter θ did not lead to any changes in the relative order of the criteria.

These results were consistent since, in the pessimistic scenario, four criteria were moved to groups of lesser importance. In contrast, the classification of two criteria improved in the optimistic scenario. In calculating criteria weights and assessing data collection difficulty, the two highest-ranked criteria in the optimistic scenario showed increased scores compared to the application case. At the same time, those in intermediate positions experienced slight reductions in their weights. The opposite effect was observed in the pessimistic scenario.

Additional tests were conducted to assess the impact of varying risk preferences on supplier ranking. Under the optimistic scenario, $\text{g}\left({\text{A}}_1\right)$ = 3460, $\text{g}\left({\text{A}}_2\right)$ = 0.3405, and $\text{g}\left({\text{A}}_3\right)$ improved to 0.3136. In the pessimistic scenario, $\text{g}\left({\text{A}}_1\right)$ increased to 0.4399, $\text{g}\left({\text{A}}_2\right)$ reached 0.3669, and $\text{g}\left({\text{A}}_3\right)$ dropped to 0.1933. The optimistic scenario led to an overall score improvement for the alternative ranked last, while the pessimistic scenario significantly reduced only the score of this same alternative. Despite changes in performance scores, the ranking of the alternatives remained consistent across all scenarios.

These results indicate that the proposed model is sensitive to variations in θ while maintaining stable supplier rankings, thereby demonstrating robustness and reliability under different decision-making conditions.

7 Comparison with previous studies

A comparative analysis was conducted to highlight the advantages of the proposed model in relation to previous studies in the literature (shown in Table 1). With regard to models for project supplier selection, the proposed approach offers the following key contributions:

1. It considers the opinions of several DMs to select requirements, criteria, and suppliers. Using Equation 2, the proposed model enables the consideration of different weights for the DMs' judgments, according to their level of technical knowledge and experience. Moreover, unlike the previous models presented in Table 1, it is possible to incorporate a pessimistic and optimistic view in the decision-making process by setting the values of parameter θ;

2. This is especially useful in decision-making processes under uncertainty and hesitation, in which the DMs cannot easily choose a single linguistic term to express their preferences. Thus, in contrast to the models presented in Table 1, as well as those proposed by Lima-Junior et al. (2016) and Calache et al. (2019) for supplier selection and evaluation based on fuzzy logic, the proposed approach enables DMs to express their preferences using multiple linguistic terms or expressions, thereby providing greater flexibility in the assessment of requirements, criteria, and suppliers. It is important to emphasize that the models proposed by Liang & Chong (2019) and Liang et al. (2023a) have also been developed to deal with environments of uncertainty and hesitation, but they do not allow the attribution of linguistic expressions by DMs;

3. It does not present limitations on the number of criteria or alternatives that can be evaluated, as occurs in models that are based on comparative methods, such as AHP and ANP;

4. Unlike the models shown in Table 1, it supports criteria weighting and selection based on their relationship with the contractor's requirements. In addition, it considers the difficulty of evaluating supplier performance on each criterion as a decisive factor in the choice of criteria, which contributes to adopting criteria that are more important and easier to implement.

8 Conclusion

This study proposed a new model based on the HFLTS-QFD method to support the decision-making process for project supplier selection. The model allows the choice of criteria and suppliers in different types of projects where external parties need to be contracted to fulfill the scope. A pilot application was made in an energy company involving three DMs. The delivery capacity (C₁) and cost (C₆) criteria were categorized as priorities, as they presented high importance and low difficulty in data collection. Other criteria classified as critical or complementary were also selected. Then, based on the assessment of three suppliers using the previously chosen criteria, it was possible to point out the most suitable alternative for contracting. Moreover, sensitivity analysis tests showed that incorporating a pessimistic or optimistic view in the decision model may consistently change the categorization results of the criteria.

Regarding the study's limitations, although the proposed model supports the DMs in choosing criteria and selecting suppliers, it does not monitor supplier performance after contracting. Another limitation of the HFLTS-QFD method arises during the aggregation of DMs’ judgments. The resulting HFLTS does not distinguish between linguistic terms that appear in multiple individual assessments and those that occur in only a single judgment, which may lead to information loss in specific situations. In this regard, future studies could address this limitation by employing Possibility Distribution Hesitant Fuzzy Linguistic Sets in combination with the QFD method for project supplier selection. Additionally, implementing the proposed model as software with a graphical user interface could help assess its suitability for continuous use in real-world decision-making contexts. Finally, future research may explore the integration of the proposed framework with other multi-criteria decision-making techniques or machine learning approaches to enhance its robustness and adaptability in complex project environments.

Acknowledgements

The authors would like to thank the COPEL experts who participated in the pilot application of the proposed model and contributed with their evaluations.

• Financial support:
  This work was supported by the National Council for Scientific and Technological Development (CNPq), Brazil, under Grant No. 313556/2023-7.
• How to cite:
  Lima-Junior, F. R., Siqueira Júnior, J. A., Osiro, L., & Resende, C. H. L. (2026). A Hesitant Fuzzy Linguistic QFD model for selecting project suppliers. Gestão & Produção, 33, e0526. https://doi.org/10.1590/1806-9649-2026v33e0526

Statement on Data Availability

The data supporting the findings of this study are contained within the article. No additional datasets were generated or analyzed during the current study.

References

• Abdzadeh, B., Noori, S., & Ghannadpour, S. F. (2022). Simultaneous scheduling of multiple construction projects considering supplier selection and material transportation routing. Automation in Construction, 140, 104336. https://doi.org/10.1016/j.autcon.2022.104336
  » https://doi.org/10.1016/j.autcon.2022.104336
• Araújo, M. C., Alencar, L. H., & Mota, C. M. (2017). Project procurement management: a structured literature review. International Journal of Project Management, 35(3), 353-377. https://doi.org/10.1016/j.ijproman.2017.01.008
  » https://doi.org/10.1016/j.ijproman.2017.01.008
• Asadujjaman, M., Rahman, H. F., Chakrabortty, R. K., & Ryan, M. J. (2023). An integrated multi-project scheduling, materials ordering and suppliers selection problem. Procedia Computer Science, 219, 1609-1616. https://doi.org/10.1016/j.procs.2023.01.453
  » https://doi.org/10.1016/j.procs.2023.01.453
• Asghar, A., Khan, K. A., Albahar, M. A., & Alammari, A. (2023). An optimized multi-attribute decision-making approach to construction supply chain management by using complex picture fuzzy soft set. PeerJ. Computer Science, 9, e1540. https://doi.org/10.7717/peerj-cs.1540 PMid:37705663.
  » https://doi.org/10.7717/peerj-cs.1540
• Bertrand, J. W. M., & Fransoo, J. (2002). Operations management research methodologies using quantitative modeling. International Journal of Operations & Production Management, 22(2), 241-264. https://doi.org/10.1108/01443570210414338
  » https://doi.org/10.1108/01443570210414338
• Brasil. (2016, 1 de julho). Dispõe sobre o estatuto jurídico da empresa pública, da sociedade de economia mista e de suas subsidiárias, no âmbito da União, dos Estados, do Distrito Federal e dos Municípios (Lei nº 13.303, de 30 de junho de 2016). Brasília, DF: Diário Oficial da República Federativa do Brasil.
• Calache, L. D. R., Pedroso, C. B., Lima, F. R. Jr, & Carpinetti, L. C. R. (2019). Proposta de um modelo de avaliação e de seleção de fornecedores de manutenção industrial utilizando Fuzzy-TOPSIS. Gestão & Produção, 26(2), e3565. https://doi.org/10.1590/0104-530x-3565-19
  » https://doi.org/10.1590/0104-530x-3565-19
• Cengiz, A. E., Aytekin, O., Ozdemir, H., Kusan, H., & Cabuk, A. (2017). A multi-criteria decision model for construction material supplier selection. Procedia Engineering, 196, 294-301. https://doi.org/10.1016/j.proeng.2017.07.202
  » https://doi.org/10.1016/j.proeng.2017.07.202
• Chen, Z., Hammad, A. W. A., Waller, S. T., & Haddad, A. N. (2023). Modelling supplier selection and material purchasing for the construction supply chain in a fuzzy scenario-based environment. Automation in Construction, 150, 104847. https://doi.org/10.1016/j.autcon.2023.104847
  » https://doi.org/10.1016/j.autcon.2023.104847
• Deepika, S., Anandakumar, S., Bhuvanesh Kumar, M., & Baskar, C. (2023). Performance appraisement of supplier selection in construction company with fuzzy AHP, fuzzy TOPSIS, and DEA. Journal of Intelligent & Fuzzy Systems, 45(6), 10515-10528. https://doi.org/10.3233/JIFS-231790
  » https://doi.org/10.3233/JIFS-231790
• Dorfeshan, Y., Jolai, F., & Mousavi, S. M. (2023). A multi-criteria decision-making model for analyzing a project-driven supply chain under interval type-2 fuzzy sets. Applied Soft Computing, 148, 110902. https://doi.org/10.1016/j.asoc.2023.110902
  » https://doi.org/10.1016/j.asoc.2023.110902
• Efe, B., Yerlikaya, M. A., & Efe, Ö. F. (2020). Mobile phone selection based on a novel quality function deployment approach. Soft Computing, 24(20), 15447-15461. https://doi.org/10.1007/s00500-020-04876-x
  » https://doi.org/10.1007/s00500-020-04876-x
• Finger, G. S. W., & Lima-Junior, F. R. (2022). A Hesitant Fuzzy Linguistic QFD approach for formulating sustainable supplier development programs. International Journal of Production Economics, 247, 108428. https://doi.org/10.1016/j.ijpe.2022.108428
  » https://doi.org/10.1016/j.ijpe.2022.108428
• Ghafoori, M., & Abdallah, M. (2024). Multi-criteria decision support model for material and supplier selection in the construction industry. International Journal of Construction Management, 25(41), 1-10.
• Gumus, S., Kucukvar, M., & Tatari, O. (2016). Intuitionistic fuzzy multi-criteria decision-making framework based on life cycle environmental, economic and social impacts: the case of U.S. wind energy. Sustainable Production and Consumption, 8, 78-92. https://doi.org/10.1016/j.spc.2016.06.006
  » https://doi.org/10.1016/j.spc.2016.06.006
• Hakimi, M., Daneshvar, A., Ehsanifar, M., & Nouri, I. (2024). Applying fuzzy utilities additives STAR for sustainable supplier selection in Iran’s construction industry. International Journal of Engineering, 37(10), 2008-2020. https://doi.org/10.5829/IJE.2024.37.10A.12
  » https://doi.org/10.5829/IJE.2024.37.10A.12
• Jahangirzadeh, A., Mousavi, S. M., & Dorfeshan, Y. (2021). A new decision model for weighting of experts and selecting the best sustainable supplier in project procurement problems under a grey environment. Journal of Industrial and Systems Engineering, 13, 87-101.
• Juan, Y. K., Perng, Y. P., Castro-Lacouture, D., & Lu, K. S. (2009). Housing refurbishment contractors selection based on a hybrid fuzzy-QFD approach. Automation in Construction, 18(1), 139-144. https://doi.org/10.1016/j.autcon.2008.06.001
  » https://doi.org/10.1016/j.autcon.2008.06.001
• Karabayir, A. N., & Botsali, A. R. (2021). Supplier selection among different scale construction companies using fuzzy AHP and fuzzy TOPSIS. El-Cezeri Fen ve Mühendislik Dergisi, 9(1), 35-48. https://doi.org/10.31202/ecjse.933617
  » https://doi.org/10.31202/ecjse.933617
• Liang, R., & Chong, H. (2019). A hybrid group decision model for green supplier selection: a case study of megaprojects. Engineering, Construction, and Architectural Management, 26(8), 1712-1734. https://doi.org/10.1108/ECAM-10-2018-0462
  » https://doi.org/10.1108/ECAM-10-2018-0462
• Liang, R., Li, R., Yan, X., Xue, Z., & Wei, X. (2023a). Evaluating and selecting the supplier in prefabricated megaprojects using extended fuzzy TOPSIS under hesitant environment. Engineering, Construction, and Architectural Management, 30(5), 1902-1931. https://doi.org/10.1108/ECAM-09-2021-0793
  » https://doi.org/10.1108/ECAM-09-2021-0793
• Liang, R., Li, R., & Chong, H.-Y. (2023b). Sustainable supplier selection for prefabricated megaprojects during COVID-19. Building Research and Information, 51(5), 533-554. https://doi.org/10.1080/09613218.2023.2165474
  » https://doi.org/10.1080/09613218.2023.2165474
• Liao, H., Xu, Z., & Zeng, X.-J. (2014). Distance and similarity measures for hesitant fuzzy linguistic term sets and their application in multi-criteria decision making. Information Sciences, 271, 125-142. https://doi.org/10.1016/j.ins.2014.02.125
  » https://doi.org/10.1016/j.ins.2014.02.125
• Lima-Junior, F. R., Osiro, L., & Carpinetti, L. C. R. (2014). A comparison between fuzzy AHP and fuzzy TOPSIS methods for supplier selection. Applied Soft Computing, 21, 194-209. https://doi.org/10.1016/j.asoc.2014.03.014
  » https://doi.org/10.1016/j.asoc.2014.03.014
• Lima-Junior, F. R., & Carpinetti, L. C. R. (2016). A multi-criteria approach based on fuzzy QFD for choosing criteria for supplier selection. Computers & Industrial Engineering, 101, 269-285. https://doi.org/10.1016/j.cie.2016.09.014
  » https://doi.org/10.1016/j.cie.2016.09.014
• Lima-Junior, F. R., Carvalho, G. M. R., & Carpinetti, L. C. R. (2016). A methodology based on fuzzy inference and SCOR model for supplier performance evaluation. Gestão & Produção, 23(3), 515-534.
• Lima-Junior, F. R., Oliveira, M. E. B., & Resende, C. H. L. (2023). An overview of applications of hesitant fuzzy linguistic term sets in supply chain management: the state of the art and future directions. Mathematics, 11(13), 2814. https://doi.org/10.3390/math11132814
  » https://doi.org/10.3390/math11132814
• Liu, A., Liu, T., Mou, J., & Wang, R. (2020). A supplier evaluation model based on customer demand in blockchain tracing anti-counterfeiting platform project management. Journal of Management Science and Engineering, 5(3), 172-194. https://doi.org/10.1016/j.jmse.2020.06.001
  » https://doi.org/10.1016/j.jmse.2020.06.001
• Lu, Z., Sun, X., Wang, Y., & Xu, C. (2019). Green supplier selection in straw biomass industry based on cloud model and possibility degree. Journal of Cleaner Production, 219, 995-1005. https://doi.org/10.1016/j.jclepro.2018.10.130
  » https://doi.org/10.1016/j.jclepro.2018.10.130
• Luzon, B., & El-Sayegh, S. M. (2016). Evaluating supplier selection criteria for oil and gas projects in the UAE using AHP and Delphi. International Journal of Construction Management, 16(2), 175-183. https://doi.org/10.1080/15623599.2016.1146112
  » https://doi.org/10.1080/15623599.2016.1146112
• Magalhães, W. R., & Lima-Junior, F. R. (2026). Risk prioritization in manufacturing processes under hesitation. Benchmarking: An International Journal, 33(5), 1507-1536. https://doi.org/10.1108/BIJ-06-2024-0510.
• Morkunaite, Z., Podvezko, V., Zavadskas, E. K., & Bausys, R. (2019). Contractor selection for renovation of cultural heritage buildings by PROMETHEE method. Archives of Civil and Mechanical Engineering, 19(4), 1056-1071. https://doi.org/10.1016/j.acme.2019.05.008
  » https://doi.org/10.1016/j.acme.2019.05.008
• Mousakhani, S., Nazari-Shirkouhi, S., & Bozorgi-Amiri, A. (2017). A novel interval type-2 fuzzy evaluation model based group decision analysis for green supplier selection problems. Journal of Cleaner Production, 168, 205-218. https://doi.org/10.1016/j.jclepro.2017.08.154
  » https://doi.org/10.1016/j.jclepro.2017.08.154
• Nguyen, V. T., Hai, N. H., & Lan, N. T. K. (2022). Spherical fuzzy multicriteria decision-making model for wind turbine supplier selection. Energies, 15(3), 713. https://doi.org/10.3390/en15030713
  » https://doi.org/10.3390/en15030713
• Oliveira, M. E. B., Lima-Junior, F. R., & Galo, N. (2023). A comparison of hesitant fuzzy VIKOR methods for supplier selection. Applied Soft Computing, 149, 110920. https://doi.org/10.1016/j.asoc.2023.110920
  » https://doi.org/10.1016/j.asoc.2023.110920
• Önar, S. Ç., Büyüközkan, G., Öztaysi, B., & Kahraman, C. (2016). A new hesitant fuzzy QFD approach: an application to computer workstation selection. Applied Soft Computing, 46, 1-16. https://doi.org/10.1016/j.asoc.2016.04.023
  » https://doi.org/10.1016/j.asoc.2016.04.023
• Ortiz-Barrios, M., Cabarcas-Reyes, J., Ishizaka, A., Barbati, M., Jaramillo-Rueda, N., & de Jesús Carrascal-Zambrano, G. (2021). A hybrid fuzzy multi-criteria decision-making model for selecting a sustainable supplier of forklift filters. Annals of Operations Research, 307(1-2), 443-481. https://doi.org/10.1007/s10479-020-03737-y
  » https://doi.org/10.1007/s10479-020-03737-y
• Osiro, L., Lima-Junior, F. R., & Carpinetti, L. C. R. (2018). A group decision model based on quality function deployment and hesitant fuzzy for selecting supply chain sustainability metrics. Journal of Cleaner Production, 183, 964-978. https://doi.org/10.1016/j.jclepro.2018.02.197
  » https://doi.org/10.1016/j.jclepro.2018.02.197
• Pelissari, R., Oliveira, M. C., Abackerli, A. J., Ben-Amor, S., & Assumpção, M. R. P. (2021). Techniques to model uncertain input data of multi-criteria decision-making problems: a literature review. International Transactions in Operational Research, 28(2), 523-559. https://doi.org/10.1111/itor.12598
  » https://doi.org/10.1111/itor.12598
• Polat, G., & Eray, E. (2015). An integrated approach using AHP-ER to supplier selection in railway projects. Procedia Engineering, 123, 415-422. https://doi.org/10.1016/j.proeng.2015.10.068
  » https://doi.org/10.1016/j.proeng.2015.10.068
• Project Management Institute – PMI. (2017). A guide to the Project Management Body of Knowledge (PMBOK® Guide). Newtown Square.
• Rahman, H. F., Chakrabortty, R. K., Elsawah, S., & Ryan, M. J. (2022). Energy-efficient project scheduling with supplier selection in manufacturing projects. Expert Systems with Applications, 193, 116446. https://doi.org/10.1016/j.eswa.2021.116446
  » https://doi.org/10.1016/j.eswa.2021.116446
• Resende, C. H. L., Geraldes, C. A. S., Lima-Junior, F. R., & Lima, F. R. (2021). Decision models for supplier selection in Industry 4.0 era: a systematic literature review. Procedia Manufacturing, 55, 492-499. https://doi.org/10.1016/j.promfg.2021.10.067
  » https://doi.org/10.1016/j.promfg.2021.10.067
• Resende, C. H. L., Lima-Junior, F. R., & Carpinetti, L. C. R. (2023). Decision-making models for formulating and evaluating supplier development programs. Transportation Research Part E, Logistics and Transportation Review, 180, 103340. https://doi.org/10.1016/j.tre.2023.103340
  » https://doi.org/10.1016/j.tre.2023.103340
• Rezahoseini, A., Noori, S., & Ghannadpour, S. F. (2021). Integrated scheduling of suppliers and multi-project activities for green construction supply chains under uncertainty. Automation in Construction, 122, 103485. https://doi.org/10.1016/j.autcon.2020.103485
  » https://doi.org/10.1016/j.autcon.2020.103485
• Rodríguez, R. M., Martinez, L., & Herrera, F. (2012). Hesitant fuzzy linguistic term sets for decision making. IEEE Transactions on Fuzzy Systems, 20(1), 109-119. https://doi.org/10.1109/TFUZZ.2011.2170076
  » https://doi.org/10.1109/TFUZZ.2011.2170076
• Safa, M., Shahi, A., Haas, C. T., & Hipel, K. W. (2014). Supplier selection process in an integrated construction materials management model. Automation in Construction, 48, 64-73. https://doi.org/10.1016/j.autcon.2014.08.008
  » https://doi.org/10.1016/j.autcon.2014.08.008
• Saputro, T. E., Figueira, G., & Almada-Lobo, B. (2022). Supplier selection under different purchasing strategies. Computers & Industrial Engineering, 167, 108010. https://doi.org/10.1016/j.cie.2022.108010
  » https://doi.org/10.1016/j.cie.2022.108010
• Saputro, T. E., Rosiani, T. Y., Mubin, A., Dewi, S. K., & Baroto, T. (2024). Green supplier selection under supply risks. Journal of Cleaner Production, 449, 141788. https://doi.org/10.1016/j.jclepro.2024.141788
  » https://doi.org/10.1016/j.jclepro.2024.141788
• Shojaei, P., & bolvardizadeh, A. (2020). Rough MCDM model for green supplier selection in Iran. Built Environment Project and Asset Management, 10(3), 437-452. https://doi.org/10.1108/BEPAM-11-2019-0117
  » https://doi.org/10.1108/BEPAM-11-2019-0117
• Suprasongsin, S., Yenradee, P., & Huynh, V. N. (2020). A weight-consistent model for fuzzy supplier selection and order allocation problem. Annals of Operations Research, 293(2), 587-605. https://doi.org/10.1007/s10479-019-03354-4
  » https://doi.org/10.1007/s10479-019-03354-4
• Tamosaitiene, J., Zavadskas, E. K., Šileikaitė, I., & Turskis, Z. (2017). A novel hybrid MCDM approach for complicated supply chain management problems in construction. Procedia Engineering, 172, 1137-1145. https://doi.org/10.1016/j.proeng.2017.02.168
  » https://doi.org/10.1016/j.proeng.2017.02.168
• Tushar, Z. N., Bari, A. B. M. M., & Khan, M. A. (2022). Circular supplier selection in the construction industry. Sustainable Manufacturing and Service Economics, 1, 100005. https://doi.org/10.1016/j.smse.2022.100005
  » https://doi.org/10.1016/j.smse.2022.100005
• Watt, D. J., Kayis, B., & Willey, K. (2009). Identifying key factors in the evaluation of tenders for projects and services. International Journal of Project Management, 27(3), 250-260. https://doi.org/10.1016/j.ijproman.2008.03.002
  » https://doi.org/10.1016/j.ijproman.2008.03.002
• Wetzstein, A., Hartmann, E., Benton, W. C., Jr., & Hohenstein, N.-O. (2016). A systematic assessment of supplier selection literature. International Journal of Production Economics, 182, 304-323. https://doi.org/10.1016/j.ijpe.2016.06.022
  » https://doi.org/10.1016/j.ijpe.2016.06.022
• Wood, D. (2016). Supplier selection for development of petroleum industry facilities applying fuzzy and intuitionistic fuzzy TOPSIS. Journal of Natural Gas Science and Engineering, 28, 594-612. https://doi.org/10.1016/j.jngse.2015.12.021
  » https://doi.org/10.1016/j.jngse.2015.12.021
• Wu, C., & Barnes, D. (2010). Partner selection in agile supply chains. International Journal of Production Economics, 125, 284-293. https://doi.org/10.1016/j.ijpe.2010.02.010
  » https://doi.org/10.1016/j.ijpe.2010.02.010
• Wu, Y., Chen, K., Zeng, B., Xu, H., & Yang, Y. (2016). Supplier selection in nuclear power industry with extended VIKOR method under linguistic information. Applied Soft Computing, 48, 444-457. https://doi.org/10.1016/j.asoc.2016.07.023
  » https://doi.org/10.1016/j.asoc.2016.07.023
• Xu, Z., & Zhang, S. (2019). An overview on the applications of the hesitant fuzzy sets in group decision-making. Frontiers of Engineering Management, 6(2), 163-182. https://doi.org/10.1007/s42524-019-0017-4
  » https://doi.org/10.1007/s42524-019-0017-4
• Yazdani, M., Chatterjee, P., Pamucar, D., & Abad, M. D. (2019). A risk-based integrated decision-making model for green supplier selection. Kybernetes, 49(4), 1229-1252. https://doi.org/10.1108/K-09-2018-0509
  » https://doi.org/10.1108/K-09-2018-0509
• Yazdani, M., Wang, Z. X., & Chan, F. T. S. (2020). A decision support model based on DEMATEL, QFD and fuzzy values. Soft Computing, 24, 12449-12468. https://doi.org/10.1007/s00500-020-04685-2
  » https://doi.org/10.1007/s00500-020-04685-2
• Yu, L., Wang, L., & Bao, Y. (2018). Technical attributes ratings in fuzzy QFD. Soft Computing, 22(6), 2015-2024. https://doi.org/10.1007/s00500-016-2464-8
  » https://doi.org/10.1007/s00500-016-2464-8
• Yu, D., Sheng, L., & Xu, Z. (2022). Knowledge diffusion trajectories in the hesitant fuzzy domain. International Journal of Fuzzy Systems, 24(5), 2382-2396. https://doi.org/10.1007/s40815-022-01287-y
  » https://doi.org/10.1007/s40815-022-01287-y
• Zheng, M., Zhou, H., Jiang, P., Pan, E., Zhao, S., & Wu, K. (2021). Supplier selection problem for multiple projects with uncertain demand and project life cycles. Computers & Operations Research, 132, 105312. https://doi.org/10.1016/j.cor.2021.105312
  » https://doi.org/10.1016/j.cor.2021.105312
• Zhu, Z., Xin, Y., & Jing, Y. (2022). Analysis on AHP-VIKOR-based supplier selection for large equipment maintenance of construction enterprises. Journal of Engineering Science and Technology Review, 15(6), 42-48.
• Zimmer, K., Fröhling, M., & Schultmann, F. (2016). Sustainable supplier management: A review of models supporting sustainable supplier selection, monitoring and development. International Journal of Production Research, 54(5), 1412-1442. https://doi.org/10.1080/00207543.2015.1079340
  » https://doi.org/10.1080/00207543.2015.1079340

• Editor-in-Chief
  Pedro Munari

Publication Dates

• Publication in this collection
  10 Aug 2026
• Date of issue
  2026

History

• Received
  19 Feb 2026
• Reviewed
  01 Apr 2026
• Accepted
  15 May 2026