1 Introduction
Buildings are responsible for an important portion of global energy consumption and carbon emissions. Energy consumption is related to the construction, operation, renovation, and demolition processes of buildings, as well as the production of building materials and various systems (Abass and Muthulingam,
2025). Rapid population growth and migration from rural areas to cities have made the construction sector one of the most energy-intensive and waste-producing sectors (Llantoy
et al.,
2020; Movaffaghi and Yitmen,
2023), making environmental impact management challenging in the construction industry (Tushar
et al.,
2022). Based on the Global Alliance for Buildings and Construction (GABC) 2024/25 global status report, in 2023, buildings accounted for 32% of global energy demand and 34% of CO
2 emissions. It also notes that despite a small reduction in carbon emissions and a slight increase in the use of renewable energy, these gains are insufficient to meet the Paris Agreement targets (GABC,
2025).
With the abandonment of the traditional “take-make-dispose” approach (Attri
et al.,
2025; Wahyu Adi and Wibowo,
2020), the circular economy (CE) perspective, focusing on material circularity, waste reduction, and efficient resource use has also emerged as a strategic framework for the transformation of the construction industry, like other industries (Tan
et al.,
2025; Gupta
et al.,
2025; Jain
et al.,
2025). CE intends to preserve the value of products, materials, and resources throughout their life cycle and to decrease wastes via useful techniques such as reuse, recycling, refurbishment, recovery, and cleaner production (Nayeri
et al.,
2025; Hasheminezhad
et al.,
2024; Salman and Hasar,
2023). In this way, CE aims to maximize the effective and efficient use of production elements, thereby extending their lifespan (Govindan
et al.,
2020). In the construction industry, this could be achieved by using recycled or reusable materials (Melikoglu,
2025; Timm
et al.,
2023), making modular designs (Abdelmageed and Zayed,
2020; Oteng
et al.,
2025), realizing energy-efficient production (Ferreira Junior
et al.,
2025; Ludger Bernsmann and Schleifenbaum,
2025), reducing carbon footprint (Almusaed
et al.,
2024; Iqbal
et al.,
2025), using reverse logistics (Mishra
et al.,
2022), gathering environmental certification systems, and considering life cycle management (Llantoy
et al.,
2020; Manu,
2024).
Sustainability has become a major concern in supply chain management due to increasing environmental pressures, resource scarcity, climate change, and rigourous environmental regulations (Govindan
et al.,
2020). It is evident that supply chains exert a direct influence on various key performance indicators, including energy consumption, waste generation, carbon emissions, transportation activities, and resource efficiency throughout the life cycle of products and materials (Tushar
et al.,
2022). There is an increasing expectation that firms will integrate sustainability considerations into purchasing, logistics, production, and supplier selection processes (Kannan
et al.,
2020). In the construction industry, where material-intensive production and transportation activities create substantial environmental impacts, sustainable supply chain management plays a critical role in reducing waste, improving resource efficiency, lowering carbon emissions, and supporting the circular economy practices (Tushar
et al.,
2022). For this reason, supplier selection decisions are no longer based solely on traditional factors such as cost, quality, and delivery performance, but also increasingly include environmental and circularity-related considerations (Kusi-Sarpong
et al.,
2023; Tramarico
et al.,
2025).
Aerated concrete is frequently preferred in the construction industry for its light weight, satisfactory thermal insulation, and material savings (Gyurkó
et al.,
2019). Collaboration with suppliers who possess those competencies significantly enables aerated concrete companies to support CE. Consequently, supplier selection in the construction supply chain for the aerated concrete industry is crucial for successful CE applications (Tushar
et al.,
2022). Additionally, selecting the right suppliers may reduce costs and increase supply chain efficiency, thereby enhancing the firms’ profitability and ability to meet customer expectations (Ecer
et al.,
2024). Whereas traditional supplier selection processes prioritize factors such as cost, quality, delivery, and financial flexibility (Paul and Pal,
2025), CE-focused supplier selection could consider environmental and social criteria, including waste management, energy efficiency, carbon emissions, environmental compatibility, recyclable raw materials, social responsibility, clean technology, life cycle impacts, etc. (Ulutaş
et al.,
2025; Tramarico
et al.,
2025). Such a broad assessment involves a multi-dimensional decision-making process with inherent uncertainty.
Although there is some research on circular supplier selection in the available literature, many focus on automotive (Govindan
et al.,
2020), electronics (Kannan
et al.,
2020; Menon and Ravi,
2022), manufacturing (Liu
et al.,
2022; Tong
et al.,
2022), textile (Kusi-Sarpong
et al.,
2023; Ecer and Torkayesh,
2022), and chemical (Mina
et al.,
2021; Tramarico
et al.,
2025) industries. However, in the construction sector, supplier selection models that comprehensively incorporate CE principles are limited, and most evaluations are restricted to environmental drivers (Amarasinghe
et al.,
2024; Demirbağ
et al.,
2025). Furthermore, there are a few studies in which CE criteria have been systematically determined in conjunction with expert opinions to cope with uncertainty and actual industry practices. As far as the authors’ knowledge goes, there is no work on supplier selection in the aerated concrete industry. Besides, the existing literature shows that available circular supplier selection works largely focus on developed industrial sectors and global-scale examples. In developing countries, such as Türkiye, applied research on the construction sector and building materials is very scarce. For building materials like aerated concrete, which provides energy efficiency in buildings, has low carbon emissions, and is easy to transport due to its lightness, there is almost no circular supplier evaluation model in the literature. Circular supplier selection also involves managing uncertainty based on expert judgments and evaluations. In the construction industry, where many project-based, simultaneous, or sequential processes are carried out together, it is very difficult to measure supplier performance accurately and objectively. Therefore, decision-makers often rely on judgments based on their experiences or perceptions. In such an environment, supplier selection becomes a decision problem involving intensive uncertainty, and this problem needs to be addressed with reliable and powerful decision support systems. These research gaps stand out as critical for both practical applications and decision-makers for supplier selection in the construction supply chains to achieve sustainable development. This study, therefore, aims to fill those gaps by introducing a supplier selection methodology concerning CE principles. 16 drivers are determined by searching the literature and the opinions of experts. Five large companies operating in the aerated concrete sector in Türkiye are considered alternatives by experts using those drivers. To obtain trustworthy results under uncertainty, a comprehensive fuzzy hyperbolic (HyF) multi-criteria decision-making (MCDM) approach is developed. Criteria weights are decided using the Logarithmic Percentage Change-Driven Objective Weighting (LOPCOW) and Ranking Comparison (RANCOM) methods, balancing objective and subjective information, while alternatives are ranked using the hyperbolic extension of the Deviation-Based Pairwise Assessment Ratio Technique (DEPART) method with hyperbolic fuzzy information. Thus, a cutting-edge decision support system, named HyF-LOPCOW-RANCOM-DEPART, is introduced for the first time.
The research presents significant novelties and contributions in terms of contextual and methodological aspects. It makes significant contributions to the literature on CE-focused supplier selection, specifically in the construction sector. First, addressing supplier selection in the aerated concrete industry within the framework of CE principles fills a notable gap in the literature. The 16 evaluation criteria presented in this study encompass economic, environmental, social, and technological dimensions. These criteria were developed based on both a comprehensive literature review and expert opinions. The research offers an innovative approach by basing the evaluation set not only on theory but also on industry-specific information. The ranking of Türkiye’s leading aerated concrete manufacturers based on expert opinions has enabled the creation of a robust model based on real-world field data. This also increases the applicability of the findings to industry decision-making processes. Furthermore, expanding the CE criteria to include environmental indicators as well as waste management, life cycle assessment, carbon footprint, and technological capabilities enriches the perspective on supplier selection. With all these features, the study integrates theory and practice, producing an innovative approach and providing a significant reference for establishing a circular supply chain in the construction industry. Further, the novel methodological novelties and contributions of this research include:
-
✓ Utilization of a flexible orthopair variant for data interpretation allows decision experts to consider both membership and non-membership grades of a qualitative term, which otherwise is not possible. Moreover, considering a hyperbolic fuzzy set (HyFS) leverages the flexibility in expressing a choice, which is restricted in other variants.
-
✓ Determination of decision experts’ weights (importance) is lacking in extant models, but the proposed framework calculates weights of experts by extending the entropy measure to HyFS and capturing hesitation in the preference distribution for weight calculation.
-
✓ Though criteria weights are calculated, the determination of both subjective and objective weights is usually lacking in the literature. This issue is resolved by this framework, which extends the LOPCOW and RANCOM multi-criteria methods to HyFS, and enables an aggregated weight (importance) for CE criteria.
-
✓ Finally, to rank construction material suppliers, the recently developed DEPART method is extended to HyFS, which determines ranks through relative comparison and duly considers the pairwise values of alternative suppliers, which are lacking in other ranking techniques. Besides, the ranks of suppliers are determined both at the individualistic level and the holistic level by combining the Copeland strategy with DEPART.
The rationale for choosing these decision methods to develop a decision framework is given below:
-
✓ First, rating data from experts is interpreted as HyFS (Dutta and Borah,
2023), which offers two benefits to decision experts, i.e., an orthopair format that enables understanding of both preference and non-preference grades for an option in the decision matrix. Further, the flexibility of choice expression, which is restricted in other orthopair forms, is clarified in the methodology section for readers. These two benefits encouraged authors to utilize HyFS for the interpretation of rating data.
-
✓ Second, criteria selection is performed in order to reduce the complexity of the decision process. For this purpose, the Laplacian score is put forward, which selects criteria in such a manner that the structural semantics of the decision problem remains intact and the complexity is reduced significantly. Rather than reducing the feature (criteria) by transforming the feature set to new spaces, the Laplacian score carefully selects criteria by retaining structural semantics. Later, we deploy an entropy measure for determining the weights of experts, which is not adequately explored in the literature on construction supplier selection.
-
✓ Third, the weights of the criteria are methodically determined, which essentially reduces inaccuracies and subjectivity. As a result, we considered both objective and subjective weighting procedures for obtaining the holistic weights of criteria, both from rating as well as from the ranking of criteria by experts. LOPCOW (Ecer and Pamucar,
2022) was extended in the objective context after considering its merits with respect to nullify the effects of extreme values through a logarithmic function and determining weights with better discriminative abilities, which are otherwise lacking in standard objective methods such as entropy and SAW. In the subjective weight context, we extended the RANCOM (Więckowski
et al.,
2023) method that showcased its superiority in comparison with other subjective weight methods in the study from Więckowski
et al. (
2023).
-
✓ Finally, we ranked alternative suppliers by extending the DEPART method (Keshavarz-Ghorabaee
et al.,
2025) that considers the deviation ratio from ideal and anti-ideal points in order to find the rank order of alternatives. Some notable merits of DEPART that make it more effective than other rank methods are: (i) it determines deviation ratios that enable pairwise alternative comparison rather than distinctive alternative comparison; (ii) decision philosophy of DEPART follows the ideal, anti-ideal, and deviations that can be readily associated with human-driven decision logic and, as a result, the method becomes useful in practical sense and explainable to practitioners during complex decision-making process.
It must be noted that hyperbolic fuzzy MCDM is considered a crucial research topic because the HyFS is an emerging orthopair variant that considers both preference (membership) and non-preference (non-membership) grades and has flexible constraints, which allow decision experts to effectively utilize this fuzzy variant for modeling uncertainty during the rating of decision entities. Since the HyFS was recently proposed, its exploration in decision frameworks and solving decision problems has just started, and so it is seen as a promising research topic for researchers to develop decision frameworks under HyFS for rational decision-making. In this paper, we are considering a problem of selecting a suitable supplier in the construction field by focusing on CE principles within the aerated concrete industry. Since the problem has a clear structure of MCDM with different alternative suppliers rated by decision experts on different criteria, we extend this problem into the HyFS-based MCDM construct and attempt to solve the decision problem through a structured methodical framework.
The remaining part of the study is organized as follows. The second section contains a literature review. Within this scope, studies related to CE-focused supplier selection is included. Subsequently, studies employing different methods related to the subject are listed, and research gaps are conveyed. The third section introduces the research methodology. The fourth section presents the application section. The fifth and sixth sections respectively present the discussion, theoretical and practical implications, and conclusions.
3 Research Methodology
The evaluation data obtained based on the expert profiles and business structures defined in this section were used as input in multi-criteria decision-making techniques to solve the circular economy-based supplier selection problem. In our study, we developed a methodological framework based on hyperbolic fuzzy sets to account for the uncertainty arising from the nature of the criteria, the subjective nature of expert opinions, and the uncertainty in the performance of the alternatives. In this context, we explain step by step in the following subsections the hyperbolic fuzzy set structure used in the study, how the criteria and expert weights were determined, and how the alternatives were ranked.
3.1 Preliminaries
We review the hyperbolic fuzzy set and its operations here.
Definition 1 (Yager, 2016).
R is a reference set. q-ROFS
Q on
R is given by,
where
${\mu _{Q}}(r)$ is the degree of preference or membership,
${\upsilon _{Q}}(r)$ is the degree of non-preference or non-membership.
Note that ${\mu _{Q}}(r)$ and ${\upsilon _{Q}}(r)$ are in the unit interval. Also $0\leqslant {\mu _{Q}^{q}}+{\upsilon _{Q}^{q}}\leqslant 1$ with $q\geqslant 1$.
We present the orthopair fuzzy conditions for clarity to readers in Eq. (
2).
Definition 2 (Dutta and Borah, 2023).
R is a reference set. HyFS
B on
R is given by
where
${\mu _{Q}}(r)$ is the degree of preference or membership,
${\upsilon _{Q}}(r)$ is the degree of non-preference or non-membership. Also,
$0\leqslant {\mu _{B}}(r)\boldsymbol{\cdot }{\upsilon _{B}}(r)\leqslant 1$.
Note 1: ${B_{i}}=({\mu _{i}},{\upsilon _{i}})$,
$\forall i=1,2,\dots ,n$ is a hyperbolic fuzzy number (HyFN) and a collection of such numbers constitutes a HyFS.
In the orthopair fuzzy set family, HyFS is a recent inception that is gaining attention from researchers considering its flexibility in choice elicitation, which is restricted or constrained by certain inequalities in the predecessor forms, such as IFS, PFS, FFS, and, in general, q-ROFS. Such inequalities are relaxed in HyFS, and a broader window for choice expression is provided with a two-dimensional representation – both preference and non-preference grades. Driven by the flexibility, we consider HyFN for the study. It must be noted that the earlier fuzzy variants in the orthopair family followed additive constraints, while the HyFS followed multiplicative constraints, and it is based on the concept of a hyperbola as suggested by Dutta and Borah (
2023). Specifically, Dutta and Bahrami (
2025) argued that HyFS incorporates a hyperbolic geometric boundary that facilitates expressiveness and adaptability. Furthermore, it can be noted that in qROFS, there is a need to choose
q a priori, which is a crucial tuning parameter. Choosing a lesser
q blocks several orthopair values (membership and non-membership), while a larger
q requires changing the semantic interpretation of all values simultaneously. As a result, it is more about robustness of representation rather than ranking accuracy when it comes to HyFS versus qROFS. The questions these two sets address are different. In qROFS, the question is ‘what must be the value of
q so that the expert’s choice can be represented?’, whereas in HyFS, the question is ‘what is the expert’s opinion?’ From this, we gain clarity that it is about representational robustness rather than decision accuracy, which motivated authors to choose HyFS for data or rating interpretation. Methodical superiority of the proposed framework can be noticed in Section
1.
Definition 3 (Dutta and Borah, 2023; Divsalar et al., 2023).
Let
${B_{1}}$ and
${B_{2}}$ be two HyFNs. Some operations that can be performed are:
Eqs. (
4)–(
7) refer to operations such as ring sum, scalar multiplication, power function, and ring product, respectively.
Definition 4 (Dutta and Borah, 2023; Divsalar et al., 2023).
Let
${B_{1}}$ and
${B_{2}}$ be any two HyFNs. Then, to compare these two HyFNs, we present the score and accuracy measure, which is given by
here, Eqs. (
8) and (
9) are the score and accuracy measures.
If two HyFNs must be compared, then do the following:
-
• Check the score, if $S({B_{1}})\gt S({B_{2}})$, then ${B_{1}}\gt {B_{2}}$; If $S({B_{1}})=S({B_{2}})$, then go to accuracy measure.
-
• Check the accuracy, if $A({B_{1}})\gt A({B_{2}})$, then ${B_{1}}\lt {B_{2}}$; If $A({B_{1}})=A({B_{2}})$, then ${B_{1}}={B_{2}}$.
3.2 Feature Selection
In this section, we present the feature reduction module by considering the Laplacian score. The presented procedure is capable of feature selection with no requirement for class labels. As a result, for decision problems, the Laplacian score is viable. Furthermore, the score retains the local structure or patterns, which mitigates information loss and efficiently reduces complexity or computational overhead.
This score considers alignment with the intrinsic geometry of data. Generally, criteria with low scores are preferred as they retain information about the neighborhood, and so, the top k criteria are selected based on the arrangement of the scores in ascending order. The method performs feature reduction that helps in reducing dimensionality.
The procedure for determining the reduced set of features is:
Input: Experts’ rating criteria – $k\times n$ matrix
Process:
-
• Construct the similarity matrix
-
• Compute the degree matrix and Laplacian matrix
-
• Calculate the mean with respect to the degree matrix for each criterion
-
• Determine the Laplacian score by obtaining variation values
-
• Rank the criteria
End process
Output: A revised criteria set (feature reduced) – $k\times c$ where $c\lt n$.
It must be noted that each criterion is assigned a score, and based on the importance, the top k criteria are chosen. This helps in feature reduction and facilitates local structure intactness.
3.3 Weight Calculation Module
In this section, we present a detailed step-by-step procedure for determining the weights of the criteria and the experts involved in the decision process. It must be noted that the weights or relative importance of a decision entity are not equal, and methodical determination of such values reduces bias and subjectivity (Kao,
2010; Koksalmis and Kabak,
2019). Driven by these studies, we present a methodical setup for determining the weights of the criteria and experts.
In general, weights are determined either with partial a priori information or no such information. The former type incurs a certain level of additional overhead, which in many situations is not practically possible. As a result, the latter type is presented by researchers. In the latter context, objective and subjective weight types exist. Subjective types directly consider ranks or priority to determine the weights (importance), while objective types consider opinions from stakeholders to determine the weights. Since both these types have their own benefits, we consider both types in this study to determine the weights of the criteria. Further, experts’ weights are determined objectively.
LOPCOW and RANCOM methods are extended to HyFS for determining the objective and subjective weights of criteria. LOPCOW follows a logarithmic function that is capable of reducing the scale-size effect, thus making the approach balanced without being affected by value spikes. Also, RANCOM considers ordinal data and pair-wise constructs, enabling careful consideration of each decision entity. Besides, it is intuitive, less impacted by inconsistencies, and computationally feasible. The combination of these two methods yields a holistic criterion weight, which can be further used for rank determination. The entropy approach is extended to HyFS for determining the weights of experts. Entropy determines the uniformity that exists in the construct or entity that is being measured. As a result, a high entropy value indicates high uniformity – less variability. So, there is a tendency for perceived consistency in the rating that would facilitate rational decision-making.
Detailed steps for the calculation are given below:
3.3.1 Objective Weights
Step 1: Consider a $d\times c$ matrix where d experts provide her/his rating on c criteria.
Step 2: Normalize the data by using Eq. (
10). It must be noted that this normalization is irrespective of the criteria type, as the rating is with respect to the level of preference. A normalized
$d\times c$ matrix is obtained.
where
${a_{ij}}$ is the score value,
${a_{\max }}$ and
${a_{\min }}$ are maximum and minimum values.
Step 3: Determine the percentage value for the criterion to form a vector of
$1\times c$. This value indicates the information or discriminatory power of a criterion, and hence, the higher the PV, the higher the importance.
where
$\ln (.)$ is the natural log function and
σ is the standard deviation.
Step 4: Normalize the vector from Eq. (
11) to get the objective weights of the criteria. Apply Eq. (
12) for obtaining the weights.
where
${w_{j}}$ is the weight of the criterion
j.
3.3.2 Subjective Weights
Step 1: Consider the $d\times c$ matrix as before. Determine the rank order based on score values.
Step 2: Determine the matrix of rank comparison (MAC) by using Eq. (
13). This is a square matrix of order
$c\times c$. Specifically, each element in the MAC is determined by a rule provided in Eq. (
13).
Here
${c_{1}}$ and
${c_{2}}$ are any two criteria and
$f(.)$ It is a basic arithmetic function.
Step 3: Determine the net information and normalize the values to get subjective weights of criteria, which is a vector of
$1\times c$ order.
where
${\lambda _{j}}$ is the subjective weight of criterion
j.
Combined weights are determined by taking a linear combination of vectors from Eq. (
12) and Eq. (
14), the objective and subjective weights of criteria. It is also a vector of
$1\times c$ order.
3.3.3 Expert Weight
We put forward an entropy measure for determining the weights of experts. The rationale is discussed above, and the steps for calculation are given below:
Step 1: Obtain the decision matrices from each expert.
Step 2: Determine the entropy of criteria with respect to each expert using Shanon entropy.
Step 3: Calculate the net entropy associated with expert rating.
Step 4: Normalize the values to obtain the weights of experts.
3.4 Ranking Method
In this section, we present a HyFS extension of the DEPART method (Keshavarz-Ghorabaee
et al.,
2025), which is a recently developed ranking approach for determining the priority of alternatives. The method follows relational pairwise comparison, which sets it apart from other popular methods in the decision-making field. Most extant methods follow distance measure or uni-directed utility measure, which lack careful consideration of the decision entities.
DEPART, in contrast, considers a pairwise approach and hence, every entity in the set is given due consideration. The main philosophy of DEPART is to calculate deviation from best and worst and determine ratios that are finally aggregated to form scores. As a result, DEPART is fully relative, unlike other rank methods that are either partially relative or non-relative.
Driven by these merit points, in this work, we extend DEPART to HyFS for ranking. The steps involved in the ranking are clarified below:
Step 1: Consider
d experts who rate
a alternatives over
c criteria. The decision matrices are formed with qualitative ratings, and the entries are transformed to HyFN, and the score is determined by using Eq. (
8).
Step 2: Form positive and negative deviation matrices by using Eqs. (
15)–(
16). These are matrices of order
$a\times c$.
where
${a_{ij}}$ is the score value.
Here, ${a_{j}^{+}}=\max ({a_{ij}})$ for benefit and $\min ({a_{ij}})$ for cost. It is the opposite for ${a_{j}^{-}}$.
Step 3: Form a pairwise positive and negative ratio of deviation by using Eqs. (
17)–(
18). These are square matrices of order
$a\times a$.
where
f and
g are any two alternatives.
Here, $P=\max ({p_{ij}})$ and $N=\max ({n_{ij}})$.
Step 4: Determine the net pairwise deviation by using Eq. (
19). Determine the score and arrange alternatives in descending order of score.
Arrange the score in descending order of values. A higher score is highly preferred, and so on.
From Eq. (
20),
d vectors of
$1\times a$ order are obtained. These are rank orders of alternatives based on data from each expert. To combine the ordering and obtain a net rank vector, the Copeland procedure is presented. Steps are given below:
-
• Consider a $a\times d$ matrix and $1\times d$ vector as input;
-
• Obtain the weighted decision matrix of order $a\times d$ by multiplying the weights of the expert by every value in the decision matrix;
-
• Calculate the net score alternatively to obtain a vector of $1\times a$;
-
• Identify the maximum value from the vector and subtract each value from the maximum to obtain a rank vector, which must be arranged in descending order to obtain the net rank of alternatives.
By applying the procedure mentioned above, a combined rank order is obtained that yields a vector of $1\times a$ order. A single aggregated rank vector is obtained by considering rank vectors from d experts’ rating data.
4 Application
The proposed HyF-LOPCOW-RANCOM-DEPART model is applied to address the CE-focused supplier selection problem in the aerated concrete industry. In this context, researchers designed a multi-layered research process to comprehensively solve the problem, as shown in Fig.
1.

Fig. 1
Detailed flowchart of the proposed HyF-LOPCOW-RANCOM-DEPART methodology, organized into three stages: data collection, mathematical processing, and validation.
The preparation process for this study was carried out in 3 stages. In the first step, a pool of criteria containing 22 main criteria was created through face-to-face interviews with relevant literature and experts. The experts consulted on the construction industry’s circular economy-focused supplier selection was building construction, concrete manufacturing, and building market parts sales managers. These individuals were also involved in the data collection process in the third stage. Furthermore, the positions and experience of the industry experts were, respectively: building construction company owner (7 years), building materials store company owner (8 years), building materials store, and building construction company owner (25 years), building materials store marketing-sales manager (11 years), and construction materials supplier marketing-sales manager (11 years). Despite the fact that three of the participating experts are company owners or senior decision-makers, the study aimed to reduce potential individual bias by including experts from a variety of professional backgrounds, including purchasing, accounting, operations, and management. Furthermore, the entropy-based expert weighting approach was utilized to minimize the dominance of highly uniform evaluations by considering the consistency and variation of expert judgments. Given that supplier selection decisions in the construction materials sector are influenced by both operational and financial considerations, it was considered important to include company owners in order to reflect real-world decision-making dynamics.
In the second stage, experts from academia and industry checked the suitability of the criteria pool for the study. These experts were also among the practitioners mentioned earlier.
Specifically, the suitability of the 22-criterion pool was assessed through a structured voting exercise: each candidate’s criterion was put to the panel, and the experts voted on its relevance and appropriateness for circular-economy-based supplier selection in the aerated concrete industry. Criteria that did not attain the agreed majority support, chiefly those judged redundant with a retained criterion, not specific to the aerated concrete supply chain, or of limited practical measurability, were removed. As a result, six criteria were eliminated, and the remaining 16 criteria (Table
2) were carried forward to the data-collection survey in the next stage.
The criteria used in the study, along with their definitions and references, are shown in Table
2. The research data were collected in the third stage between October and November, 2025, from five experts (EXT1-EXT5). The participants consisted of company owners and managers in purchasing and marketing departments who were directly involved in the decision-making processes regarding supplier selection. Participants had between 7 and 25 years of experience, ensuring that supplier evaluations were based on both industry knowledge and field experience. Participants had at least a university degree, typically in business administration or accounting. Their age range was 30–45. Considering their industry experience and age, it is clear that they were directly involved in field work after their education. For evaluations in a multi-dimensional and in-depth field like the circular economy, this panel is considered a suitable data source.
Table 2
Criteria set used in the study.
| Criteria |
Criteria name |
Definition |
References |
| CRT1 |
Customer expectations |
The product’s level of meeting customer needs in terms of performance, durability, and delivery. |
Expert opinion |
| CRT2 |
Quality |
Product quality is quality consistency, quality management systems (ISO 9001, etc.). |
(Alavi et al., 2021; Feng and Gong, 2020; Govindan et al., 2020; Kannan et al., 2020; Khalili Nasr et al., 2021; Liu et al., 2022; Masoomi et al., 2022; Menon and Ravi, 2022; Mina et al., 2021; Perçin, 2022; Tong et al., 2022; Tushar et al., 2022) |
| CRT3 |
Cost |
It includes topics such as product unit cost, production and logistics costs, and price competitiveness. |
(Paul and Pal, 2025; Alavi et al., 2021; Feng and Gong, 2020; Kannan et al., 2020; Liu et al., 2022; Masoomi et al., 2022; Menon and Ravi, 2022; Perçin, 2022; Tong et al., 2022; Tushar et al., 2022) |
| CRT4 |
Constraints on the deferred payment option |
Financial flexibility in sales terms refers to payment facilities. |
Expert opinion |
| CRT5 |
Energy consumption inefficiency |
The use of energy-saving technologies in production processes. |
(Paul and Pal, 2025; Feng and Gong, 2020; Haleem et al., 2021; Masoomi et al., 2022; Menon and Ravi, 2022) |
| CRT6 |
Inefficiency in the use of recycled material use |
The percentage of recycled content in raw material sourcing and production. |
(Alavi et al., 2021; Kannan et al., 2020; Khalili Nasr et al., 2021; Mina et al., 2021; Perçin, 2022; Tushar et al., 2022) |
| CRT7 |
Inefficiency in waste management and recovery |
It refers to the reuse or recycling of production waste. |
(Alavi et al., 2021; Haleem et al., 2021; Luthra et al., 2017) |
| CRT8 |
Carbon footprint |
The level of reduction in greenhouse gas emissions arising from production and transportation. |
(Paul and Pal, 2025; Feng and Gong, 2020; Tong et al., 2022) |
| CRT9 |
Non-compliance with environmental certification |
It includes obtaining environmental management certifications such as CE, ISO 14001, LEED, etc. |
(Feng and Gong, 2020; Haleem et al., 2021; Khalili Nasr et al., 2021; Tushar et al., 2022) |
| CRT10 |
Gaps in green supply chain/logistics |
It includes topics such as local supply advantages, emission reduction in transportation, and logistics efficiency. |
(Kusi-Sarpong et al., 2023) |
| CRT11 |
Technological capability limitation |
It includes dimensions such as Rand D capacity, the level of innovation in production technologies, and digitalization. |
(Alavi et al., 2021; Feng and Gong, 2020; Haleem et al., 2021; Khalili Nasr et al., 2021; Liu et al., 2022; Luthra et al., 2017; Mina et al., 2021; Perçin, 2022; Tushar et al., 2022) |
| CRT12 |
Product life-cycle management |
The product’s lifespan is the management of its reuse and recycling potential. |
| CRT13 |
Occupational health and safety |
Worker safety and the prevention of workplace accidents in production facilities. |
(Kannan et al., 2020; Liu et al., 2022; Luthra et al., 2017; Menon and Ravi, 2022; Perçin, 2022) |
| CRT14 |
Social responsibility and ethics |
Employee rights, transparency, contribution to society, and ethical trade principles. |
(Alavi et al., 2021; Kannan et al., 2020; Khalili Nasr et al., 2021; Liu et al., 2022; Menon and Ravi, 2022; Perçin, 2022) |
| CRT15 |
Corporate reputation vulnerability |
The company’s reputation in the industry, past performance, and references. |
(Alavi et al., 2021; Haleem et al., 2021; Khalili Nasr et al., 2021; Tushar et al., 2022) |
| CRT16 |
Insufficiency in managerial compliance and top management support |
It includes administrative support for circular economy policies and sustainability strategies. |
(Haleem et al., 2021; Kusi-Sarpong et al., 2023) |
Decision-makers evaluated five major firms that play an important role in the aerated concrete industry using the suggested framework in this research. In line with the principles of confidentiality and impartiality, the names of the companies included in the study are not explicitly stated; companies are referred to by codes AL1–AL5. Firms of varying scales and organizational structures operating in Türkiye’s construction industry are involved in the production and distribution of aerated concrete. They include those with nationwide recognition as well as those active in specific regional markets. The circular supplier selection process is not based on a single profile but rather reflects the industry’s overall structure.
The assessments obtained from the experts and businesses defined in this section were directly used in the application of the circular economy-based supplier selection model developed in the study. These data, based on expert opinions, were analysed within the framework of hyperbolic fuzzy sets to determine the criterion weights and alternative rankings. The steps followed during the application process are presented below.
The steps for determining the values of decision entities are given below:
Step 1: Collect data from five experts (EXT) on 16 criteria. Each expert rates the criteria to form a 5×16 weight calculation matrix (Table
3).
Step 2: Considering the dimension of the data, the feature reduction algorithm is applied from Section
3.2 for determining the Laplacian score. From the algorithm, it is clear that a criterion with a low score gets a high preference, meaning that the criterion has greater representation ability compared to others.
Table 3
Expert rating on criteria.
| CW |
EXT1 |
EXT2 |
EXT3 |
EXT4 |
EXT5 |
| CRT1 |
6 |
6 |
4 |
6 |
6 |
| CRT2 |
6 |
6 |
4 |
6 |
6 |
| CRT3 |
5 |
7 |
5 |
6 |
7 |
| CRT4 |
5 |
7 |
2 |
5 |
7 |
| CRT5 |
6 |
6 |
4 |
3 |
7 |
| CRT6 |
4 |
4 |
3 |
2 |
4 |
| CRT7 |
4 |
4 |
3 |
2 |
4 |
| CRT8 |
4 |
5 |
3 |
2 |
4 |
| CRT9 |
6 |
6 |
3 |
3 |
4 |
| CRT10 |
6 |
6 |
4 |
4 |
4 |
| CRT11 |
6 |
6 |
4 |
5 |
7 |
| CRT12 |
7 |
5 |
4 |
6 |
4 |
| CRT13 |
6 |
7 |
4 |
6 |
5 |
| CRT14 |
6 |
6 |
4 |
6 |
6 |
| CRT15 |
6 |
7 |
4 |
6 |
7 |
| CRT16 |
6 |
7 |
4 |
4 |
5 |
Table 4
Similarity matrix of criteria.
| Similarity |
0 |
1 |
2 |
3 |
4 |
| 0 |
0 |
0.571 |
0.324 |
0.373 |
0.378 |
| 1 |
0.571 |
0 |
0 |
0.136 |
0.523 |
| 2 |
0.324 |
0 |
0 |
0.514 |
0.283 |
| 3 |
0.373 |
0.136 |
0.514 |
0 |
0.339 |
| 4 |
0.378 |
0.523 |
0.283 |
0.339 |
0 |
| Degree |
0 |
1 |
2 |
3 |
4 |
| 0 |
1.647 |
0 |
0 |
0 |
0 |
| 1 |
0 |
1.229 |
0 |
0 |
0 |
| 2 |
0 |
0 |
1.122 |
0 |
0 |
| 3 |
0 |
0 |
0 |
1.362 |
0 |
| 4 |
0 |
0 |
0 |
0 |
1.523 |
Table
4 gives the similarity matrix and degree vector values that are calculated by using the Laplacian algorithm. The values 0 to 4 denote EXT1 to EXT5. A Laplacian matrix is determined by using these two results, and that is shown in Table
5. Finally, the score vector of each criterion is determined, and based on the ascending order of scores, the criteria are arranged. From the list, the best
K criteria are chosen.
Table 5
Laplacian matrix of criteria.
| Laplacian matrix |
0 |
1 |
2 |
3 |
4 |
| 0 |
1.647 |
−0.571 |
−0.324 |
−0.373 |
−0.378 |
| 1 |
−0.571 |
1.229 |
0 |
−0.136 |
−0.523 |
| 2 |
−0.324 |
0 |
1.122 |
−0.514 |
−0.283 |
| 3 |
−0.373 |
−0.136 |
−0.514 |
1.362 |
−0.339 |
| 4 |
−0.378 |
−0.523 |
−0.283 |
−0.339 |
1.523 |
The score value for each criterion is determined as CRT1: 1.183, CRT2: 1.183, CRT3: 1.139, CRT4: 0.99, CRT5: 1.019, CRT6: 1.018, CRT7: 1.018, CRT8: 0.923, CRT9: 0.94, CRT10: 1.034, CRT11: 1.047, CRT12: 1.297, CRT13: 1.133, CRT14: 1.183, CRT15: 1.012, and CRT16: 0.885 based on the values in Table
5. By arranging these values in ascending order, the top 10 criteria chosen are CRT4, CRT5, CRT6, CRT7, CRT8, CRT9, CRT10, CRT11, CRT15, and CRT16.
These ten criteria constitute the reduced set used for the subsequent criteria weighting and supplier ranking; the remaining six are retained in the validated framework but excluded from the computational evaluation in order to reduce dimensionality. Hence, the framework validates 16 criteria, of which 10 are used in the final evaluation. It is noted that the Laplacian score is applied to the 16 expert-validated criteria (not the original 22-criterion pool): the 22 to 16 reduction is the prior Stage-2 expert-voting step, whereas the Laplacian score performs this data-driven 16 to 10 reduction while preserving the local structure of the rating data. Figure
2 reports the Laplacian score of each of the 16 criteria and the top-10 (lowest-score) criteria that are retained.
Step 3: Collect data about alternatives from the experts. Five alternatives are rated based on 10 criteria (feature reduced) by five experts. So, five matrices of
$5\times 10$ are obtained (Table
6).

Fig. 2
Laplacian scores of the 16 criteria in ascending order. The top-10 criteria with the lowest scores (CRT16, CRT8, CRT9, CRT4, CRT15, CRT6, CRT7, CRT5, CRT10, CRT11) are retained; the six with the highest scores are eliminated.
Step 4: Use the data from Step 3 (Table
6) and the procedure in Section
3.3 for determining the weights of experts. A vector of
$1\times 5$ is obtained (Table
7).
Table 6
Decision matrix from experts.
| Criterion–Expert |
AL1 |
AL2 |
AL3 |
AL4 |
AL5 |
| CRT4–EXT1 |
4 |
4 |
4 |
4 |
4 |
| CRT4–EXT2 |
7 |
5 |
6 |
7 |
7 |
| CRT4–EXT3 |
3 |
2 |
3 |
3 |
4 |
| CRT4–EXT4 |
4 |
4 |
5 |
4 |
5 |
| CRT4–EXT5 |
4 |
4 |
4 |
4 |
4 |
| CRT5–EXT1 |
6 |
4 |
4 |
4 |
6 |
| CRT5–EXT2 |
5 |
5 |
4 |
5 |
5 |
| CRT5–EXT3 |
4 |
5 |
4 |
6 |
3 |
| CRT5–EXT4 |
7 |
7 |
5 |
5 |
7 |
| CRT5–EXT5 |
4 |
4 |
5 |
4 |
4 |
| CRT6–EXT1 |
4 |
4 |
4 |
4 |
4 |
| CRT6–EXT2 |
4 |
4 |
4 |
4 |
5 |
| CRT6–EXT3 |
3 |
6 |
4 |
5 |
2 |
| CRT6–EXT4 |
7 |
7 |
5 |
4 |
6 |
| CRT6–EXT5 |
5 |
6 |
5 |
5 |
4 |
| CRT7–EXT1 |
4 |
4 |
4 |
4 |
4 |
| CRT7–EXT2 |
6 |
7 |
6 |
5 |
6 |
| CRT7–EXT3 |
3 |
7 |
5 |
5 |
1 |
| CRT7–EXT4 |
6 |
6 |
4 |
4 |
6 |
| CRT7–EXT5 |
5 |
6 |
4 |
5 |
5 |
| CRT8–EXT1 |
4 |
4 |
4 |
4 |
4 |
| CRT8–EXT2 |
7 |
7 |
6 |
6 |
7 |
| CRT8–EXT3 |
3 |
6 |
3 |
4 |
2 |
| CRT8–EXT4 |
6 |
6 |
5 |
5 |
5 |
| CRT8–EXT5 |
4 |
6 |
5 |
5 |
5 |
| CRT9–EXT1 |
5 |
4 |
4 |
4 |
5 |
| CRT9–EXT2 |
7 |
7 |
7 |
7 |
7 |
| CRT9–EXT3 |
5 |
6 |
4 |
5 |
3 |
| CRT9–EXT4 |
6 |
7 |
5 |
4 |
6 |
| CRT9–EXT5 |
4 |
6 |
4 |
5 |
5 |
| CRT10–EXT1 |
5 |
4 |
4 |
4 |
5 |
| CRT10–EXT2 |
6 |
7 |
5 |
5 |
7 |
| CRT10–EXT3 |
5 |
6 |
4 |
5 |
3 |
| CRT10–EXT4 |
4 |
6 |
4 |
5 |
6 |
| CRT10–EXT5 |
5 |
6 |
4 |
4 |
5 |
| CRT11–EXT1 |
5 |
4 |
4 |
4 |
5 |
| CRT11–EXT2 |
6 |
7 |
6 |
6 |
6 |
| CRT11–EXT3 |
5 |
7 |
5 |
6 |
4 |
| CRT11–EXT4 |
6 |
7 |
4 |
4 |
6 |
| CRT11–EXT5 |
5 |
7 |
4 |
6 |
6 |
| CRT15–EXT1 |
6 |
4 |
4 |
4 |
6 |
| CRT15–EXT2 |
7 |
7 |
7 |
7 |
7 |
| CRT15–EXT3 |
5 |
7 |
3 |
4 |
5 |
| CRT15–EXT4 |
5 |
7 |
5 |
4 |
4 |
| CRT15–EXT5 |
6 |
6 |
6 |
6 |
6 |
| CRT16–EXT1 |
6 |
4 |
4 |
4 |
6 |
| CRT16–EXT2 |
7 |
5 |
6 |
7 |
7 |
| CRT16–EXT3 |
3 |
6 |
4 |
5 |
4 |
| CRT16–EXT4 |
6 |
7 |
4 |
4 |
5 |
| CRT16–EXT5 |
7 |
7 |
5 |
5 |
5 |
Table 7
Entropy values of experts.
| ENT EXT1 |
ENT EXT2 |
ENT EXT3 |
ENT EXT4 |
ENT EXT5 |
| 1.609438 |
1.578417 |
1.554161 |
1.579711 |
1.609438 |
| 1.468365 |
1.488357 |
1.457769 |
1.553098 |
1.586629 |
| 1.609438 |
1.652961 |
1.366196 |
1.520871 |
1.547699 |
| 1.609438 |
1.556763 |
1.486519 |
1.501412 |
1.547699 |
| 1.609438 |
1.399258 |
1.29921 |
1.565377 |
1.547699 |
| 1.579711 |
1.650291 |
1.481371 |
1.527846 |
1.522251 |
| 1.579711 |
1.715194 |
1.481371 |
1.500698 |
1.522251 |
| 1.579711 |
1.747302 |
1.517754 |
1.490963 |
1.527846 |
| 1.468365 |
1.837625 |
1.450043 |
1.492798 |
1.609438 |
| 1.468365 |
1.779347 |
1.457769 |
1.48296 |
1.541284 |
Use the procedure in the expert weight calculation section to determine the entropy (Table
7) associated with each expert rating, and by normalization, we get weights as: 0.201, 0.198, 0.188, 0.212, and 0.202, respectively.
Step 5: Consider the rating of 10 criteria by five experts to form a weight matrix of
$5\times 10$ order. By applying the criteria weight procedures from Section
3.3, the objective and subjective weights of the criteria are determined. Each weight yields a vector of
$1\times 10$. They are combined to form a single weight vector of
$1\times 10$.
Table 8
Feature-reduced criteria set from Laplacian score.
| Criteria |
EXT1 |
EXT2 |
EXT3 |
EXT4 |
EXT5 |
| CRT4 |
5 |
7 |
2 |
5 |
7 |
| CRT5 |
6 |
6 |
4 |
3 |
7 |
| CRT6 |
4 |
4 |
3 |
2 |
4 |
| CRT7 |
4 |
4 |
3 |
2 |
4 |
| CRT8 |
4 |
5 |
3 |
2 |
4 |
| CRT9 |
6 |
6 |
3 |
3 |
4 |
| CRT10 |
6 |
6 |
4 |
4 |
4 |
| CRT11 |
6 |
6 |
4 |
5 |
7 |
| CRT15 |
6 |
7 |
4 |
6 |
7 |
| CRT16 |
6 |
7 |
4 |
4 |
5 |
Table
8 provides ratings from experts on the criteria that are considered for the study after feature reduction. Laplacian score supported the feature-reduction and facilitated dimensionality reduction, which, from the managerial context, corresponds to reduced complexity and computational overhead. Eqs. (
10)–(
12) corresponds to the determination of criteria weights by LOPCOW. Data in Table
8 is transformed to its corresponding HyFSs, and scores are determined. Eq. (
11) determines the percentage value, which maps to a logarithmic scale for nullifying the spikes in value due to extreme value rating and yields a weight vector upon normalization, which is a vector of
$1\times 10$ order (Table
9).
| Criteria |
EXT1 |
EXT2 |
EXT3 |
EXT4 |
EXT5 |
| CRT4 |
0.772870662 |
1 |
0 |
0.772870662 |
1 |
| CRT5 |
0.871972318 |
0.871972318 |
0.269896194 |
0 |
1 |
| CRT6 |
1 |
1 |
0.264150943 |
0 |
1 |
| CRT7 |
1 |
1 |
0.264150943 |
0 |
1 |
| CRT8 |
0.432653061 |
1 |
0.114285714 |
0 |
0.432653061 |
| CRT9 |
1 |
1 |
0 |
0 |
0.30952381 |
| CRT10 |
1 |
1 |
0 |
0 |
0 |
| CRT11 |
0.82464455 |
0.82464455 |
0 |
0.658767773 |
1 |
| CRT15 |
0.82464455 |
1 |
0 |
0.82464455 |
1 |
| CRT16 |
0.82464455 |
1 |
0 |
0 |
0.658767773 |
Table 10
Objective weights by HyF-LOPCOW.
| PV |
Criteria weight |
| 77.34229094 |
CRT4: 0.138671694 |
| 60.27494807 |
CRT5: 0.108070618 |
| 59.23576519 |
CRT6: 0.106207404 |
| 59.23576519 |
CRT7: 0.106207404 |
| 41.60836661 |
CRT8: 0.07460217 |
| 35.56630127 |
CRT9: 0.063768983 |
| 25.54128119 |
CRT10: 0.045794515 |
| 76.46759595 |
CRT11: 0.137103401 |
| 78.67431212 |
CRT15: 0.141059956 |
| 43.79005707 |
CRT16: 0.078513855 |
From Eqs. (
11)–(
12), the results in Tables
9 and
10 are depicted. From Table
9, data is given to the LOPCOW for calculating the objective criteria weights (refer to Table
10). Further, data in Table
8 is provided to Eqs. (
13)–(
14) for determining the subjective criteria weights using the RANCOM method (Table
11).
Table 11
MAC values – RANCOM method.
|
CRT4 |
CRT5 |
CRT6 |
CRT7 |
CRT8 |
CRT9 |
CRT10 |
CRT11 |
CRT15 |
CRT16 |
| EXT1 MAC |
|
|
|
|
|
|
|
|
|
|
| CRT4 |
0.5 |
0 |
1 |
1 |
1 |
0 |
0 |
0 |
0 |
0 |
| CRT5 |
1 |
0.5 |
1 |
1 |
1 |
0.5 |
0.5 |
0.5 |
0.5 |
0.5 |
| CRT6 |
0 |
0 |
0.5 |
0.5 |
0.5 |
0 |
0 |
0 |
0 |
0 |
| CRT7 |
0 |
0 |
0.5 |
0.5 |
0.5 |
0 |
0 |
0 |
0 |
0 |
| CRT8 |
0 |
0 |
0.5 |
0.5 |
0.5 |
0 |
0 |
0 |
0 |
0 |
| CRT9 |
1 |
0.5 |
1 |
1 |
1 |
0.5 |
0.5 |
0.5 |
0.5 |
0.5 |
| CRT10 |
1 |
0.5 |
1 |
1 |
1 |
0.5 |
0.5 |
0.5 |
0.5 |
0.5 |
| CRT11 |
1 |
0.5 |
1 |
1 |
1 |
0.5 |
0.5 |
0.5 |
0.5 |
0.5 |
| CRT15 |
1 |
0.5 |
1 |
1 |
1 |
0.5 |
0.5 |
0.5 |
0.5 |
0.5 |
| CRT16 |
1 |
0.5 |
1 |
1 |
1 |
0.5 |
0.5 |
0.5 |
0.5 |
0.5 |
| EXT2 MAC |
|
|
|
|
|
|
|
|
|
|
| CRT4 |
0.5 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
0.5 |
0.5 |
| CRT5 |
0 |
0.5 |
1 |
1 |
1 |
0.5 |
0.5 |
0.5 |
0 |
0 |
| CRT6 |
0 |
0 |
0.5 |
0.5 |
0 |
0 |
0 |
0 |
0 |
0 |
| CRT7 |
0 |
0 |
0.5 |
0.5 |
0 |
0 |
0 |
0 |
0 |
0 |
| CRT8 |
0 |
0 |
1 |
1 |
0.5 |
0 |
0 |
0 |
0 |
0 |
| CRT9 |
0 |
0.5 |
1 |
1 |
1 |
0.5 |
0.5 |
0.5 |
0 |
0 |
| CRT10 |
0 |
0.5 |
1 |
1 |
1 |
0.5 |
0.5 |
0.5 |
0 |
0 |
| CRT11 |
0 |
0.5 |
1 |
1 |
1 |
0.5 |
0.5 |
0.5 |
0 |
0 |
| CRT15 |
0.5 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
0.5 |
0.5 |
| CRT16 |
0.5 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
0.5 |
0.5 |
| EXT3 MAC |
|
|
|
|
|
|
|
|
|
|
| CRT4 |
0.5 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
| CRT5 |
1 |
0.5 |
1 |
1 |
1 |
1 |
0.5 |
0.5 |
0.5 |
0.5 |
| CRT6 |
1 |
0 |
0.5 |
0.5 |
0.5 |
0.5 |
0 |
0 |
0 |
0 |
| CRT7 |
1 |
0 |
0.5 |
0.5 |
0.5 |
0.5 |
0 |
0 |
0 |
0 |
| CRT8 |
1 |
0 |
0.5 |
0.5 |
0.5 |
0.5 |
0 |
0 |
0 |
0 |
| CRT9 |
1 |
0 |
0.5 |
0.5 |
0.5 |
0.5 |
0 |
0 |
0 |
0 |
| CRT10 |
1 |
0.5 |
1 |
1 |
1 |
1 |
0.5 |
0.5 |
0.5 |
0.5 |
| CRT11 |
1 |
0.5 |
1 |
1 |
1 |
1 |
0.5 |
0.5 |
0.5 |
0.5 |
| CRT15 |
1 |
0.5 |
1 |
1 |
1 |
1 |
0.5 |
0.5 |
0.5 |
0.5 |
| CRT16 |
1 |
0.5 |
1 |
1 |
1 |
1 |
0.5 |
0.5 |
0.5 |
0.5 |
| EXT4 MAC |
|
|
|
|
|
|
|
|
|
|
| CRT4 |
0.5 |
1 |
1 |
1 |
1 |
1 |
1 |
0.5 |
0 |
1 |
| CRT5 |
0 |
0.5 |
1 |
1 |
1 |
0.5 |
0 |
0 |
0 |
0 |
| CRT6 |
0 |
0 |
0.5 |
0.5 |
0.5 |
0 |
0 |
0 |
0 |
0 |
| CRT7 |
0 |
0 |
0.5 |
0.5 |
0.5 |
0 |
0 |
0 |
0 |
0 |
| CRT8 |
0 |
0 |
0.5 |
0.5 |
0.5 |
0 |
0 |
0 |
0 |
0 |
| CRT9 |
0 |
0.5 |
1 |
1 |
1 |
0.5 |
0 |
0 |
0 |
0 |
| CRT10 |
0 |
1 |
1 |
1 |
1 |
1 |
0.5 |
0 |
0 |
0.5 |
| CRT11 |
0.5 |
1 |
1 |
1 |
1 |
1 |
1 |
0.5 |
0 |
1 |
| CRT15 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
0.5 |
1 |
| CRT16 |
0 |
1 |
1 |
1 |
1 |
1 |
0.5 |
0 |
0 |
0.5 |
| EXT5 MAC |
|
|
|
|
|
|
|
|
|
|
| CRT4 |
0.5 |
0.5 |
1 |
1 |
1 |
1 |
1 |
0.5 |
0.5 |
1 |
| CRT5 |
0.5 |
0.5 |
1 |
1 |
1 |
1 |
1 |
0.5 |
0.5 |
1 |
| CRT6 |
0 |
0 |
0.5 |
0.5 |
0.5 |
0.5 |
0.5 |
0 |
0 |
0 |
| CRT7 |
0 |
0 |
0.5 |
0.5 |
0.5 |
0.5 |
0.5 |
0 |
0 |
0 |
| CRT8 |
0 |
0 |
0.5 |
0.5 |
0.5 |
0.5 |
0.5 |
0 |
0 |
0 |
| CRT9 |
0 |
0 |
0.5 |
0.5 |
0.5 |
0.5 |
0.5 |
0 |
0 |
0 |
| CRT10 |
0 |
0 |
0.5 |
0.5 |
0.5 |
0.5 |
0.5 |
0 |
0 |
0 |
| CRT11 |
0.5 |
0.5 |
1 |
1 |
1 |
1 |
1 |
0.5 |
0.5 |
1 |
| CRT15 |
0.5 |
0.5 |
1 |
1 |
1 |
1 |
1 |
0.5 |
0.5 |
1 |
| CRT16 |
0 |
0 |
1 |
1 |
1 |
1 |
1 |
0 |
0 |
0.5 |
Table
12 presents the subjective weight values from each expert, which are further used for determining the subjective weights of criteria. Eq. (
14) determines the weights, and it is shown in Table
13.
Table 12
Subjective criteria weights by HyF-RANCOM.
| Criteria |
EXT1 |
EXT2 |
EXT3 |
EXT4 |
EXT5 |
Average |
| CRT4 |
0.07 |
0.17 |
0.01 |
0.16 |
0.16 |
0.114 |
| CRT5 |
0.14 |
0.1 |
0.15 |
0.08 |
0.16 |
0.126 |
| CRT6 |
0.03 |
0.02 |
0.06 |
0.03 |
0.05 |
0.038 |
| CRT7 |
0.03 |
0.02 |
0.06 |
0.03 |
0.05 |
0.038 |
| CRT8 |
0.03 |
0.05 |
0.06 |
0.03 |
0.05 |
0.044 |
| CRT9 |
0.14 |
0.1 |
0.06 |
0.08 |
0.05 |
0.086 |
| CRT10 |
0.14 |
0.1 |
0.15 |
0.12 |
0.05 |
0.112 |
| CRT11 |
0.14 |
0.1 |
0.15 |
0.16 |
0.16 |
0.142 |
| CRT15 |
0.14 |
0.17 |
0.15 |
0.19 |
0.16 |
0.162 |
| CRT16 |
0.14 |
0.17 |
0.15 |
0.12 |
0.11 |
0.138 |
The results in Table
10 and Table
12 are used for determining the combined weights of criteria by considering the step size as 0.50. The weights are calculated as: CRT4: 0.126, CRT5: 0.117, CRT6: 0.072, CRT7: 0.072, CRT8: 0.059, CRT9: 0.075, CRT10: 0.079, CRT11: 0.140, CRT15: 0.152, and CRT16: 0.108, respectively.
Step 6: Apply the procedure in Section
3.4 for determining the individualistic and combined ranks of alternatives by considering data from Step 3. A rank vector of
$1\times 5$ is obtained.
Eqs. (
15)–(
20) are applied for determining the ranks of alternative suppliers. Note that the ranks from each expert’s data are obtained, and the combined ranks are also determined using the Copeland strategy. We present the results from the DEPART method for one expert, and the combined ranks of alternative suppliers are presented from Eq. (
20) and the Copeland strategy.
Table 13
DEPART decision parameters for rating from EXT1.
|
AL1 |
AL2 |
AL3 |
AL4 |
AL5 |
| Normalized matrix |
| CRT4 |
0.1618 |
0.31623 |
0.31623 |
0.31623 |
0.1618 |
| CRT5 |
0.47837 |
0.31623 |
0.31623 |
0.31623 |
0.47837 |
| CRT6 |
0.1618 |
0.31623 |
0.31623 |
0.31623 |
0.1618 |
| CRT7 |
0.1618 |
0.31623 |
0.31623 |
0.31623 |
0.1618 |
| CRT8 |
0.1618 |
0.31623 |
0.31623 |
0.31623 |
0.1618 |
| CRT9 |
0.26381 |
0.31623 |
0.31623 |
0.31623 |
0.26381 |
| CRT10 |
0.26381 |
0.31623 |
0.31623 |
0.31623 |
0.26381 |
| CRT11 |
0.26381 |
0.31623 |
0.31623 |
0.31623 |
0.26381 |
| CRT15 |
0.47837 |
0.31623 |
0.31623 |
0.31623 |
0.47837 |
| CRT16 |
0.47837 |
0.31623 |
0.31623 |
0.31623 |
0.47837 |
| d_plus |
| CRT4 |
0 |
0 |
0 |
0 |
0 |
| CRT5 |
0.31657 |
0 |
0 |
0 |
0.31657 |
| CRT6 |
0 |
0 |
0 |
0 |
0 |
| CRT7 |
0 |
0 |
0 |
0 |
0 |
| CRT8 |
0 |
0 |
0 |
0 |
0 |
| CRT9 |
0.10201 |
0 |
0 |
0 |
0.10201 |
| CRT10 |
0.10201 |
0 |
0 |
0 |
0.10201 |
| CRT11 |
0.10201 |
0 |
0 |
0 |
0.10201 |
| CRT15 |
0.31657 |
0 |
0 |
0 |
0.31657 |
| CRT16 |
0.31657 |
0 |
0 |
0 |
0.31657 |
| d_minus |
| CRT4 |
0.31657 |
0 |
0 |
0 |
0.31657 |
| CRT5 |
0 |
0 |
0 |
0 |
0 |
| CRT6 |
0.31657 |
0 |
0 |
0 |
0.31657 |
| CRT7 |
0.31657 |
0 |
0 |
0 |
0.31657 |
| CRT8 |
0.31657 |
0 |
0 |
0 |
0.31657 |
| CRT9 |
0.21456 |
0 |
0 |
0 |
0.21456 |
| CRT10 |
0.21456 |
0 |
0 |
0 |
0.21456 |
| CRT11 |
0.21456 |
0 |
0 |
0 |
0.21456 |
| CRT15 |
0 |
0 |
0 |
0 |
0 |
| CRT16 |
0 |
0 |
0 |
0 |
0 |
| e_plus |
| AL1 |
1 |
0.7401 |
0.7401 |
0.7401 |
1 |
| AL2 |
1.47134 |
1 |
1 |
1 |
1.47134 |
| AL3 |
1.47134 |
1 |
1 |
1 |
1.47134 |
| AL4 |
1.47134 |
1 |
1 |
1 |
1.47134 |
| AL5 |
1 |
0.7401 |
0.7401 |
0.7401 |
1 |
| e_minus |
| AL1 |
1 |
1.52866 |
1.52866 |
1.52866 |
1 |
| AL2 |
0.71658 |
1 |
1 |
1 |
0.71658 |
| AL3 |
0.71658 |
1 |
1 |
1 |
0.71658 |
| AL4 |
0.71658 |
1 |
1 |
1 |
0.71658 |
| AL5 |
1 |
1.52866 |
1.52866 |
1.52866 |
1 |
| e_eta_0.5 |
| AL1 |
1 |
1.13438 |
1.13438 |
1.13438 |
1 |
| AL2 |
1.09396 |
1 |
1 |
1 |
1.09396 |
| AL3 |
1.09396 |
1 |
1 |
1 |
1.09396 |
| AL4 |
1.09396 |
1 |
1 |
1 |
1.09396 |
| AL5 |
1 |
1.13438 |
1.13438 |
1.13438 |
1 |
Table
13 depicts the results of the DEPART method by considering the rating from expert EXT1. Likewise, results are determined for other experts’ rating data, and the ranks at 0.50 are depicted in Table
14 for all five experts. Eq. (
15)–(
19) is used on the rating data provided in Table
7. Each parameter of DEPART is determined and shown in Table
14. Table
15 shows the rank values of alternative suppliers by considering data from each expert and strategy value at 0.50.
Table 14
Expert-wise ranking of alternative suppliers.
| EW |
0.201 |
0.198 |
0.188 |
0.212 |
0.202 |
| Comb-factor (0.50) |
EXT1 |
EXT2 |
EXT3 |
EXT4 |
EXT5 |
| AL1 |
0.204913 |
0.188721 |
0.198582 |
0.195679 |
0.212133 |
| AL2 |
0.196725 |
0.206215 |
0.174003 |
0.16984 |
0.173641 |
| AL3 |
0.196725 |
0.204595 |
0.206566 |
0.201943 |
0.221191 |
| AL4 |
0.196725 |
0.200265 |
0.200513 |
0.230497 |
0.196585 |
| AL5 |
0.204913 |
0.200204 |
0.220337 |
0.202042 |
0.196449 |
| Order |
AL1 > AL5 > AL2 > AL3 > AL4 |
AL2 > AL3 > AL4 > AL5 > AL1 |
AL5 > AL3 > AL4 > AL1 > AL2 |
AL4 > AL5 > AL3 > AL1 > AL2 |
AL3 > AL1 > AL4 > AL5 > AL2 |
From Table
14, it is clear that supplier ‘AL2’ is the least preferred by five experts, and the conclusion on the top alternative supplier varies across experts. To arrive at a consensus, we apply the Copeland strategy, and the results are shown in Table
15.
Table 15
Combined ranking of alternative suppliers by HyF-DEPART.
| Wcomb |
EXT1 |
EXT2 |
EXT3 |
EXT4 |
EXT5 |
M |
max-M |
FinalR |
| AL1 |
0.201 |
0.990 |
0.752 |
0.848 |
0.404 |
3.195 |
0.616 |
RANK 4 |
| AL2 |
0.603 |
0.198 |
0.940 |
1.060 |
1.010 |
3.811 |
0 |
RANK 5 |
| AL3 |
0.804 |
0.396 |
0.376 |
0.636 |
0.202 |
2.414 |
1.397 |
RANK 1 |
| AL4 |
1.005 |
0.594 |
0.564 |
0.212 |
0.606 |
2.981 |
0.830 |
RANK 3 |
| AL5 |
0.402 |
0.792 |
0.188 |
0.424 |
0.808 |
2.614 |
1.197 |
RANK 2 |
From Table
15, the combined ranks of alternative suppliers are clear. Alternative ‘AL3’ is most preferred, while ‘AL2’ is least preferred. From the Copeland strategy, we are able to arrive at a consensus on the top priority and the least priority alternative. In the earlier situation, it was difficult as each expert’s ranking provided a new rank order that led to non-consensus in the final priority of alternatives. Besides, this approach facilitates the understanding of ranking by each expert, which otherwise ceases to exist. This improvement in rank determination is lacking in extant models.
4.1 Illustration of the Computational Steps (Worked Example)
To illustrate how the framework operates, the principal computational steps are demonstrated below using the case-study data; the complete intermediate values are reported in Tables
3–
16.
-
(a) From linguistic rating to a normalized score. Each linguistic rating is converted to a hyperbolic fuzzy number (HyFN) and then to a crisp score using the score function in Eq. (
8). The resulting score vector of every criterion is rescaled by the min–max normalization in Eq. (
10). For criterion CRT4, the five expert ratings (5, 7, 2, 5, 7) give, after the HyFN transformation and Eq. (
10), the normalized vector (0.773, 1.000, 0.000, 0.773, 1.000), as reported in Table
9.
-
(b) Objective weights (LOPCOW). For each criterion, the percentage value is obtained from Eq. (
11), with d = 5 experts and
${\sigma _{j}}$ the standard deviation. The percentage values of the ten criteria are 77.342, 60.275, 59.236, 59.236, 41.608, 35.566, 25.541, 76.468, 78.674, and 43.790, summing to 557.736. Normalizing with Eq. (
12), gives, for example, w(CRT4) = 77.342 / 557.736 = 0.139 and w(CRT15) = 78.674 / 557.736 = 0.141, the largest objective weight.
-
(c) Subjective weights (RANCOM). Each expert ranks the criteria, and the pairwise ranking-comparison matrix (MAC) is formed by Eq. (
13) with entries 1, 0.5, or 0. Summing each criterion’s row and normalizing by Eq. (
14), and averaging over the five experts, yields the subjective weights in Table
12; for instance, CRT15 attains the highest value (0.162), and CRT6 and CRT7 attain the lowest (0.038).
-
(d) Combined weights. The objective and subjective weights are merged through a convex combination with $z=0.50$, ${w_{j}}(comb)=z\cdot {w_{j}}(obj)+(1-z)\cdot {w_{j}}(sub)$, giving CRT4 = 0.126, CRT5 = 0.117, CRT6 = 0.072, CRT7 = 0.072, CRT8 = 0.059, CRT9 = 0.075, CRT10 = 0.079, CRT11 = 0.140, CRT15 = 0.152 and CRT16 = 0.108.
-
(e) Expert weights (entropy). The Shannon entropy of each expert’s rating distribution is computed as in Section
3.3.3 and normalized across experts, giving the expert-weight vector (0.201, 0.198, 0.188, 0.212, 0.202) for EXT1–EXT5 (Table
14).
-
(f) Ranking by HyF-DEPART and aggregation. For each expert, the positive and negative deviation matrices follow from Eqs. (
15)–(
16); the pairwise deviation ratios from Eqs. (
17)–(
18); and the net pairwise value with z = 0.50 from Eq. (
19). The alternative score is the normalized row sum in Eq. (
20). Using the data of EXT1 (Table
13), the row sums are 5.403 for AL1 and AL5 and 5.188 for AL2, AL3 and AL4 (total 26.370), so the normalized score of AL1 is 5.403 / 26.370 = 0.205. Aggregating the five expert rankings with the Copeland strategy and the expert weights gives the consensus order AL3 > AL5 > AL4 > AL1 > AL2, i.e. AL3 is the most and AL2 the least preferred supplier, in agreement with Table
15.
6 Implications
6.1 Managerial Implications
As discussed above, the proposed framework helps a real-world logistics manager make better decisions. This study also has crucial managerial implications for companies operating in the aerated concrete industry and their supplier decision-makers. Firstly, the selection of suppliers based on a CE approach should not be limited to environmental indicators alone, but should also consider factors such as corporate reputation, technological competence, and financial flexibility. In other words, the flexibility a company offers in payment, its position within the sector, and its technological capabilities are as important as environmental indicators in aerated concrete supply. Therefore, companies should increase their technological capacity and demonstrate a strong corporate stance to establish sustainable business relationships. Additionally, the high importance of criteria such as energy efficiency and compliance with environmental regulations will require manufacturing companies to revise their production processes to produce energy-efficient and regulatory-compliant products. Companies that implement this will both gain a cost advantage and become an important link in the supply chain. Companies operating in compliance with environmental regulations and legislation will both overcome increasing public pressure and position themselves well in the face of legal regulations, and be preferred due to the trust they build. The research results also show an increasing importance of green supply chain and logistics processes. In this situation, manufacturers need to consider environmental impacts not only during the product’s manufacturing phase but also during its delivery to the customer. Optimal route selection in logistics processes, and the use of gasoline, hybrid, or electric vehicles instead of diesel vehicles, stand out as elements that strengthen CE performance in the supply chain. However, the fact that criteria such as recycling of material or waste management are given less importance compared to others indicates a lack of sufficient awareness in this area. Therefore, suppliers prioritizing this area will help decision-makers achieve circular economy goals. Furthermore, the proposed framework helps a real-world logistics manager make better decisions.
6.2 Policy Implications
This study offers important insights for public authorities and regulators on how to more effectively implement CE-focused criteria in building construction processes. Firstly, the importance of criteria such as energy efficiency and environmental compliance has begun to influence current selection decisions. This necessitates a firm commitment to achieving public goals such as energy efficiency and carbon emission reduction, and the strengthening of regulations in this direction. The significant role of certification and regulatory compliance criteria in supplier selection suggests that policymakers can guide suppliers by developing standards in this area. Labelling systems that measure and numerically compare the circular performance of building materials can be an incentive for companies to achieve these goals. Once such regulations are implemented, a more transparent market environment will be created, and environmentally friendly companies will gain a competitive advantage under increasing cost pressures. Besides, the research findings show that areas such as the use of recycled materials or waste management are not yet sufficiently emphasized in supplier selection. This creates an important area for intervention for authorities. Through regulations, authorities can implement incentives, tax breaks, or priority in public procurement for the use of such materials. This could pave the way for the development of these areas through public means.
6.3 Theoretical Implications
The framework proposed in this work combines different decision methods to arrive at a rational decision by reducing human intervention. Specifically, decision parameters such as weights or importance of experts, weights or importance of criteria, and ranks of alternative suppliers are determined methodically, which eventually reduces inaccuracies and bias in value assignment to decision parameters. By extending a decision method to the HyFS, we make the choice to extend considering the merit value it adds to the decision process. Entropy is used for expert weight calculation, as it captures hesitation and the depth of information an expert offers to the decision process. Likewise, LOPCOW and RANCOM are extended for determining the combined criteria weights, as LOPCOW has the ability to nullify extreme values and offers effective discrimination of criteria. RANCOM is a simple and straightforward subjective method, which outperforms different state-of-the-art subjective methods as clarified by Wieckowski et al. (2023). Finally, suppliers are ranked based on expert-wise data and combined grading by HyF-DEPART, which offers both individualistic and cumulative sense of ranking of alternative suppliers.
By calculating key decision parameters, we not only reduce subjectivity/bias but also make the process explainable, which is currently essential in AI systems. The step-by-step procedure offers transparency in the process, and stakeholders can readily apply changes to realize its impact on the final choices. Such perturbations are computationally viable given the flexible design of the proposed framework, which is both scalable and logically connected to yield rational decisions.
7 Conclusion
This research focuses on supplier selection in the construction supply chain for the aerated concrete industry, considering CE drivers. To do this, we introduced the HyF-LOPCOW-RANCOM-DEPART framework, which allows for a more systematic and transparent approach to supplier selection, addressing uncertainty and subjective evaluations. The study contributes to the supply chain process by providing a practical tool for incorporating CE applications into the decision-making process in the construction materials industry. Another significant contribution of the study is that it clearly demonstrates that CE-based supplier selection is not solely based on environmental indicators. The research results emphasize that factors such as technological capability, management structure, and corporate reputation are at least as important as environmental criteria. The proposed HyF-LOPCOW-RANCOM-DEPART decision support approach for CE-focused supplier selection produces more systematic and balanced results by considering the characteristics of experts. Thanks to this model, which makes a significant methodological contribution to the literature, intuitive decisions are replaced by consistent evaluations. In this respect, the proposed model can be used not only for the aerated concrete sector but also for other sectors with similar characteristics.
Whereas the research offers valuable contributions, it also has some limitations. First, the study is based on the assessments of a limited number of experts. Although the expert panel consisted of individuals with extensive field experience, increasing the number of experts could strengthen the representativeness of the results. Another limitation is that the research was conducted within a specific industry and a limited number of firms. This limits generalization to other construction materials or different sub-industries. Although the present study focuses on the aerated concrete sector in Türkiye, the proposed decision-making framework is flexible and can be adapted to different geographic and industrial contexts. The methodology is not limited to a specific country or market structure, and the evaluation criteria may be revised according to regional regulations, environmental policies, supply chain characteristics, and market conditions. Future studies may apply the proposed framework to different construction material sectors, such as insulation materials or prefabricated building components, and compare circular economy priorities across developed and developing countries. Furthermore, applications in different developed and developing countries and regional contexts could reveal the impact of regulatory frameworks and market conditions on supplier selection outcomes. Third, this research provides a static assessment and does not consider changes in supplier performance over time. Future research could analyse the development of suppliers’ CE performance over the years using dynamic evaluation models. Fourth, the proposed framework assumes that the data is fully available, which might not always be practically viable. In such cases, the present model cannot handle the non-availability of data. Partial information about decision parameters, such as criteria and alternatives, cannot be embedded in the present framework. These limitations will be handled in the future. Furthermore, plans are made to extend the proposed framework for other decision applications in the field of logistic service providers, renewable energy-based transit mode selection, technology intervention assessment in supply chains, resilience, and humanitarian supply chain evaluation. Novel fuzzy variants, such as pentagonal fuzzy set, bipolar fuzzy set, quantum fuzzy set, etc., may also be explored for data interpretation, and novel decision models can be developed under these fuzzy constructs for rational decision-making with better modelling of uncertainty. Finally, plans are made to integrate machine learning methods with a decision support system for carrying out data-driven decision activities with the help of a larger volume of data.