13543


FACTA UNIVERSITATIS  
Series: Mechanical Engineering  
https://doi.org/10.22190/FUME250311025H 

© 2025 by University of Niš, Serbia | Creative Commons License: CC BY-NC-ND 

Original scientific paper 

ASSESSMENT OF THE QUALITY INSPECTORS FOR THE 

RAILWAY MANUFACTURING INDUSTRY IN INTERVAL-

VALUED Q-RUNG ORTHOPAIR FUZZY ENVIRONMENT 

Ömer Faruk Görçün1, Cem Niyazi Durmuş2, Mustafa Çanakçıoğlu3 

1Logistics Department, Faculty of Applied Science, Kadir Has University, Türkiye 
2Department of Business Administration, Faculty of Economics, Administration, and Social 

Sciences, Kadir Has University, Türkiye 
3International Trade Department, Faculty of Applied Sciences,  

Istanbul Gelişim University, Türkiye 

Abstract. Selecting an independent quality control, test, and inspection firm (IQCTIF) 

as a strategic partner in railway wagons and locomotive manufacturing is critical for 

safety, compliance, and efficiency, as errors can lead to accidents, high maintenance 

costs, and reputational damage. Recent railway accidents in Germany, Spain, China, and 

Turkey highlight the risks of inadequate quality control. To mitigate these risks, multi-

criteria decision-making (MCDM) approaches help balance security tests, certifications, 

cost, impartiality, and technological infrastructure. Despite its importance, optimizing 

these processes through outsourcing remains an underexplored research area. This study 

proposes an IVq-ROFS-based CRITIC-WASPAS model to identify the most suitable 

strategic partners in railway manufacturing. The proposed model was preferred in this 

study due to its advantages, such as having an extremely flexible structure, providing 

results at a high level of accuracy, and allowing effective and successful management of 

uncertainties. According to the results, "Railway Certifications" (C2) is the most critical 

criterion, and TÜV SÜD is the most suitable partner for the railway manufacturing 

industry. A comprehensive robustness check confirmed the model's reliability. 

Key words: Railway manufacturing industry, Independent audit & quality control, test, 

and inspection firm (IQCTIF), CRITIC, WASPAS, Interval-Valued Q-Rung 

Orthopair Fuzzy Set 

                                                           
Received: March 11, 2025 / Accepted July 14, 2025  
Corresponding author: Ömer Faruk Görçün  

Logistics Department, Faculty of Applied Science, Kadir Has University, Kadir Has Street, No:1, B-203 Cibali, 

Fatih – İstanbul 34083, Türkiye  
E-mail: omer.gorcun@khas.edu.tr 



2 Ö.F. GÖRÇÜN, C.N. DURMUŞ, M. ÇANAKÇIOGLU 

  1. INTRODUCTION 

Failures in railway vehicle manufacturing quality control processes have recently caused 

fatal accidents, injuries, financial losses, and damage to trust and reputation. In 1998, 101 

people were killed, and 88 passengers were injured because of a high-speed train derailment 

in Germany [1]. Post-accident investigations showed that factors such as defects in the 

materials used in the production of the high-speed train (such as metal fatigue) [2] and poor 

management of quality control processes were primarily responsible for the accident.  

The Wenzhou train accident in China in 2011 resulted in the death of more than 40 

people due to a lack of quality control in the signaling system [3]. Official reports on this 

accident have cited serious design flaws and a lack of supervision and control as the main 

culprits [4]. Then, in the train accident that occurred in Spain in 2013, in which eighty 

people lost their lives [5], the railway authority claimed that the fault was with the train 

personnel, while technical reports cited inadequate testing of the brake systems as the most 

crucial cause of the accident [6]. Recently, railway accidents have occurred in some rail 

system projects in Turkey due to a lack of certification, resulting in significant losses [7]. 

While collision-type accidents in railway transportation generally occur due to human 

errors, the factors that cause derailment can be listed as deterioration in the wheels of the 

railway vehicle, deterioration on the rail surface, deterioration of the track geometry, etc. 

[8]. Therefore, derailment-type accidents are caused mainly by systemic problems. Cannon 

et al. [9] highlighted that the real cause of such accidents is improperly structured quality 

control and monitoring systems for rolling stock. According to the statistical data published 

by UIC, considering the accidents that occurred only in Turkey, more than three times as 

many derailment-type accidents took place as collision-type accidents. 

A well-structured quality control and monitoring system enables the production of 

reliable locomotives and components that fully comply with international standards. This 

situation is critical in reducing risks and accidents in railway transportation and creating a 

safe, reliable, comfortable, and efficient transportation system [10]. The integration of 

preventive maintenance and production planning, particularly within the framework of 

Industry 4.0 and smart manufacturing, has been shown to significantly improve production 

efficiency and reduce operational disruptions, as emphasized by Babaeimorad et al. [11]. 

In this direction, accidents and externalities caused by production processes that do not 

comply with the standards, regulations, and certifications determined by international 

railway authorities or cannot meet the requirements specified in these regulations, and the 

defects of the wagons, locomotives, and bogies produced cause severe economic losses in 

addition to loss of trust and reputation in the eyes of all stakeholders of the industry [12]. 

A properly configured quality control and assurance system improves supply chain 

efficiency and effectiveness in the rolling stock manufacturing industries [13], optimizing 

the waste of materials used in production and maintenance and repair costs [14]. 

However, quality control, monitoring, auditing, and sustainability practices have 

expanded international and national legal regulations regarding the number and content. In 

this context, they have become more complex and sophisticated due to international 

organizations' and governments' increasing sanctions and pressures on safety, security, and 

sustainability [15]. In addition to the railway industry, it has become almost impossible for 

the departments and units to be established within the enterprise to undertake the 

responsibilities regarding these applications in nearly every sector and successfully manage 

these processes [16].  



 Assessment of the Quality Inspectors for the Railway Manufacturing Industry in... 3 

Therefore, manufacturers must meet these requirements, especially in the railway 

sector, through outsourcing and strategic partnerships with professional quality service 

providers [17]. In this context, selecting a strategic partner for quality control and process 

management of production enterprises in the railway industry is a critical and strategic 

decision regarding railway transportation safety, security, and sustainability [18]. This 

methodical technique improves motor selection and can be used as a template for similar 

assessments in other technical contexts, including strategic partner evaluation and process 

optimization in highly regulated industries [19]. 

On the other hand, it may be more rational to outsource these services to internationally 

professionalized sources, providing them with higher quality, more convenient, and 

continuous access [20]. First, professional organizations continuously and in real-time 

follow international standards related to quality control, sustainability, and safety 

associated with rolling stock production. They have deep and extensive expertise in this 

field. Accordingly, manufacturers adapt more quickly to changing and differentiating 

regulations in different markets [21] while increasing their competitiveness tremendously. 

A professional IQCTIF conducts objective evaluations and identifies issues impartially, 

thanks to its independence [22]. In addition, professional businesses also have relationships 

with different industries and provide services for these industries as well. Accordingly, it 

can also use other industry experiences and practices for companies that are railway vehicle 

manufacturers, thus providing critical advantages. 

In addition to the accelerating development of technology, the diversification and 

complexity of legal regulations have incredibly complicated the quality control and 

inspection processes, and accordingly, it has become challenging for production enterprises 

to produce these services by establishing departments within their bodies [23]. Considering 

the costs to be incurred for the establishment of the department in the first place, the 

employment of expert personnel to work in these departments and the costs of continuing 

education for these specialists, the provision of technologically advanced and highly 

sophisticated equipment and tools used in quality control processes, as well as the costs to 

carry out certification processes, such an approach can lead to excessively high and 

unbearable expenses [24]. On the other hand, professional businesses only demand 

payment from production enterprises for the services they provide, as they cover 

installation costs, etc. Therefore, production enterprises can provide higher-quality control 

and inspection services at very reasonable costs.  

In addition, professional independent quality control, test, and inspection firms 

(IQCTIFs) produce and complete these services quickly and effectively as they standardize 

and simplify their quality control and inspection activities with the advantage of the 

experience they have gained over many years [25]. In the railway production industry, 

enterprises can obtain a significant competitive advantage by supplying their products to 

the market more easily and quickly, depending on the inspection processes that are 

completed quickly. Therefore, the services produced by such enterprises also increase the 

trust and reputation of the manufacturer regarding the products they make at an 

extraordinary level. More importantly, professional organizations produce more precise, 

detailed, and high-quality testing services by continuously investing in advanced 

technologies required for tests and inspections, as they have determined quality control and 

inspection activities as their main activities [26]. Establishing in-house infrastructure is 

costly, and equipment may quickly become outdated. 



4 Ö.F. GÖRÇÜN, C.N. DURMUŞ, M. ÇANAKÇIOGLU 

Regarding production enterprises, selecting the appropriate quality control and inspection 

company involves critical challenges and risks. Focusing solely on selecting IQCTIFs based 

on economic criteria and determining the most suitable option through static assessment 

models often reflects a tendency to address the short-term needs of businesses. For instance, 

practitioners may base their choices on subjective assessments and prioritize a criterion of 

limited relevance for longstanding objectives. Thereby, they risk overlooking critical factors 

and key criteria for sustainable success. Such an approach significantly hinders 

manufacturing enterprises from effectively achieving their long-term strategic goals. 

The lack of a structured roadmap for selecting IQCTIFs can lead to critical challenges 

in modeling and managing existing and potential risks associated with the selection 

process. Failing to evaluate audit firms based on essential factors identified within a 

strategic framework increases the likelihood of making deficient choices. Such missteps 

can significantly increase the business's operational, financial, and reputational risks and 

have long-term consequences. 

Evaluating IQCTIFs without a structured roadmap poses serious challenges and risks. 

Such an approach may expose businesses to inconsistency and indecisiveness in decision-

making processes. Additionally, decisions made without a well-structured framework are 

prone to subjective biases, which can undermine the credibility and reliability of the 

outcomes. Moreover, this lack of transparency can tarnish the company's reputation among 

stakeholders, significantly erasing trust and credibility. This inefficiency can lead to wasted 

time and other resources that decision-makers could have utilized more effectively. 

Consequently, such mismanagement results in substantial time and labor losses and 

imposes significant financial costs on the organization. 

In addition, determining whether stakeholders should outsource activities related to 

appropriate quality control and process management for production enterprises is a 

decision-making problem that is affected by highly complex uncertainties and needs to be 

balanced by considering contradictory criteria. Similarly, the presence of diverse and 

distinct service features in various application domains — such as e-services of brokerage 

firms — has resulted in multi-criteria decision-making dilemmas for users, as emphasized 

by Jana et al. [27]. Moreover, when addressing this decision-making problem, linear and 

nonlinear interactions and relationships between criteria also need to be considered. For 

example, C4 (Technological infrastructure and equipment) directly affects C3 (Safety 

testing capability). The development of technological infrastructure increases the accuracy 

of security tests. Likewise, there can be a nonlinear relationship between C7 (Cost and 

pricing) and C8 (Service timeliness and flexibility). Services with higher costs can often 

be faster, but after a certain level of cost, the increase in speed may become limited. In this 

context, IVq-ROF clusters precisely reflect nonlinear threshold effects and complex 

interactions by defining membership, anti-membership, and degrees of uncertainty over a 

wide range. Thanks to its capacity to manage ambiguities, it can analyze linear and 

nonlinear dependencies between criteria flexibly and dynamically. Hence, it produces more 

accurate and reliable results in multi-criteria decision-making processes. 

In this context, selecting the most appropriate stakeholder requires using a robust, 

consistent, and reliable decision-making tool extended based on an advanced fuzzy set to 

model and manage uncertainties at a perfect level. At the same time, this model should 

handle the interactions between the selection criteria and be able to perform 

multidimensional and comprehensive analysis. 



 Assessment of the Quality Inspectors for the Railway Manufacturing Industry in... 5 

According to the authors' knowledge, no study has focused on selecting quality control 

and process management companies using multi-criteria decision-making approaches in 

the relevant literature. In recent literature, hybrid MCDM models that combine weight 

determination and ranking phases, such as the DIBR II–Rough MABAC method, have 

proven effective in evaluating organizational and technical strategies under uncertain and 

resource-constrained environments [28]. Generally, researchers have focused on issues 

such as inspection procedures in production processes [29], inspection and quality costs in 

the manufacturing sector, and the effects of quality management practices on performance 

and competitive advantage [30]. In conclusion, even though the selection of IQCTIF is a 

significant and critical research problem, it is an issue that has been largely neglected and 

ignored by members of the research community. 

Accordingly, considering the above requirements and critical research gaps, this study 

aimed to develop and recommend a reliable, robust, and consistent decision-making tool 

for decision-makers of all manufacturing enterprises, especially the railway vehicle 

manufacturing industry. This proposed decision-making framework should also include an 

advanced fuzzy set to manage uncertainties effectively.  

Following these requirements, this study developed an interval-valued q-ROF (q-Rung 

Orthopair Fuzzy) set based on CRiteria Importance Through Intercriteria Correlation 

(CRITIC) developed by Diakoulaki et al. [31] and Weighted Aggregated Sum Product 

Assessment (WASPAS) approaches introduced by Zavadskas et al. [32] to address this 

decision-making problem. Cronbach's alpha was calculated to verify the validity and 

relevance of the selected criteria, ensuring that the evaluation was based on relevant and 

influential factors. In this context, each of the nine experts was asked 14 questions to 

evaluate the criteria, and for each question, the experts were asked to rate between 1 and 

10. Here, the total variance was calculated as 21.6944, while the variance value of the total 

scores was determined as 91.5. Then, using the formulation of the Cronbach alpha 

technique, the Cronbach alpha value was calculated as 0.82159. When the results are 

between 0.80 and 1.00, they are highly reliable [33]. The subjective weight coefficients 

derived from the mathematical framework of the fuzzy set were combined with the weights 

obtained by the CRITIC method. A range-valued q-ROF-based WASPAS method was 

used to rank and prioritize strategy alternatives. 

The suggested model has a practical and straightforward procedure that allows 

practitioners to employ it effectively without requiring advanced mathematical knowledge. 

It is also highly trustworthy and robust for modeling ambiguities, structuring decision 

issues, and delivering consistent and dependable conclusions. These features make the 

model well-suited for applications that require precision and adaptability in complex 

decision-making scenarios. 

The proposed model has identified ten alternatives and fourteen evaluation criteria for 

selecting an IQCTIF. The findings show that risk management practices emerged as the 

most critical and practical criterion, while the Independence and Impartiality Strategy was 

determined as the most appropriate strategic approach. The contributions of this study are 

essential and multifaceted. First, the integrated model proposed in this research improves 

the decision-making processes of enterprises by providing a more structured and practical 

framework for selecting IQCTIFs. 

Furthermore, the versatile model can be adapted to address similar decision-making 

challenges in other industries, demonstrating its broader applicability. Furthermore, the 

proposed model provides a well-structured, effective, and reliable strategy-based 



6 Ö.F. GÖRÇÜN, C.N. DURMUŞ, M. ÇANAKÇIOGLU 

framework, ensuring that resources are appropriately allocated and that evaluation 

processes are carried out systematically. It supports better decision-making and improves 

organizations' strategic alignment and operational efficiency. 

In addition, the IVq-ROF-based Subjective & CRITIC & WASPAS integrated model 

proposed in the study has not been used in the relevant literature before, but has been developed 

for the first time to solve the decision problem addressed in this study. As such, it represents a 

comprehensive hybrid decision-making approach that is rare in the available literature. 

This study has some critical managerial and political implications. Considering the 

findings and conclusions obtained in this study, decision-makers can strategically structure 

their decision-making processes rationally and systematically, especially regarding the 

selection of IQCTIFs. In addition, the study provides a comprehensive roadmap for 

decision-makers, emphasizing the need to focus on sustainable growth and long-term 

alliances, not just short-term operational goals. In addition, the results obtained in the study 

can further increase the trust environment in the sector by making the evaluation processes 

more transparent based on business models and determined strategies. 

First, it underlines the need for businesses to adopt a more holistic framework for their 

decision-making processes while at the same time identifying the critical and practical 

criteria that affect the choice of IQCTIF and ensuring that the decision-making problem is 

structured more accurately and appropriately.  

Given the identified research gap and objectives, this study aims to address the 

following key research questions: RQ1. What are the most critical evaluation strategies for 

selecting IQCTIFs in an Interval-Valued Q-Rung Orthopair Fuzzy (IVq-ROF) 

environment? RQ2. How do the CRITIC and WASPAS methods improve decision-making 

when selecting IQCTIFs? RQ3. How does the proposed model compare to other MCDM 

approaches regarding robustness, reliability, and accuracy? 

After a comprehensive introduction, the rest of the study is structured as follows. Part 

2 presents the results of a detailed literature review. Chapter 3 introduces the proposed 

integrated decision-making model and illustrates the implementation steps and 

mathematical operations. Chapter 4 describes the implications of the proposed decision-

making model for addressing and resolving the decision-making problem related to 

evaluating and prioritizing IQCTIFs' choices. Chapter 5 summarizes and discusses the 

results obtained. Chapter 6 concludes the study and shows the limitations of the study and 

research guidelines for future studies. 

2. SUGGESTED FRAMEWORK 

This section outlines the mathematical formulation and implementation steps of the 

proposed IVq-ROFNs-based decision-making model. The model was chosen to identify 

strategies for IQCTIF selection, the core of the decision-making problem, and was designed 

to address certain structural limitations. The following subsections present the proposed 

approach's structural features, fundamental algorithms, and step-by-step implementation. 

2.1 Preliminary Information about the IVq-ROFNs 

Yager [34] introduced q-ROFSs, defined by the pair (q, ν), to manage complex 

uncertainties in decision-making. However, due to structural limitations, they may not fully 

capture or process uncertainties [35]. To overcome these issues, Joshi et al. [36] proposed 



 Assessment of the Quality Inspectors for the Railway Manufacturing Industry in... 7 

IVq-ROFSs as an improved version. Their flexible structure offers a broader and more 

accurate approach to handling uncertainty. The following section introduces the basics of 

IVq-ROFSs and their primary algebraic operations. A q-ROFS on the universal set X is 

given below [35]:  

            0,1 , 0,1 ,0 1
q q

F F F Fx x x x         (1) 

       , ,
q q

F FF x x x x X    (2) 

Here, ϛF(x) is the membership degree and υF(x) depicts the non-membership degree of x ∈ 
X. On the other hand, the degree of indeterminacy is calculated as: 

    1
q qq

F F Fx x      (3) 

An IV-q-ROFS on the universal set X is signified below [34, 35]:  

                   , 0,1 , , 0,1 ,0 1
H H H H H H

q q
U U U UL Lx x x x x x                 (4) 

         , , , ,
H H H H

q q q q
U UL LH x x x x x x X       

   
 (5) 

In Eq. (5), the membership degree's lower and upper bound's lower and upper bounds 

of the non-membership degree are exhibited, respectively. Moreover, the indeterminacy 

membership degree is defined as follows:  

            , 1 , 1
H H H H H H

q q q qq qU U UL L L
F x x x x x x                 

 (6) 

The IV-q-ROF number (IV-q-ROFN) can be written as φ= ([α, β], [γ, δ]) for simplicity. 

Moreover, the conditions given below are satisfied [34]. 

        , 0,1 , , 0,1 ,0 1q q           (7) 

Let φ1= ([α1, β1], [γ1, δ1]) and φ2= ([α2, β2], [γ2, δ2]) be two IV-q-ROFNs. Next, some 

operations, score, and accuracy functions on IV-q-ROFSs are outlined below: ζ > 0, q ≥1 

[34–36]. 

                  1 2 1 2 1 2 1 22 21 22 1 2 1 2, , ,
q q q q q q q qq q             

           
 (8) 

                  1 2 1 2 1 2 1 2 1 2 1 2 1 2, , ,
q q q q q q q qq q             

           
 (9) 

          1 1 1 1 11 1 , 1 1 , ,
q qq q

 
 

    
  

         
  

 (10) 



8 Ö.F. GÖRÇÜN, C.N. DURMUŞ, M. ÇANAKÇIOGLU 

          1 1 1 1 1, , 1 1 , 1 1 , 0,
q qq q

 
      

  
          

  
 (11) 

       1 1 1 1 1, , , ,
c

      (12) 

  
       

   
1 1 1 1

1 1

1 1
; 0,1

4

q q q q

S S
   

 
    

   (13) 

  
       

   
1 1 1 1

1 1; 0,2
2

q q q q

A A
   

 
 

   (14) 

The IVq-ROF Weighted Arithmetic Average (IVq-ROFWAA) operator is denoted 

below: Here, φi = φ1,φ2,…, φm, 0 ≤ ζi ≤ 1. The sum of ζi should be equal to 1. 

 

 

         

1 2

1 1 1 1

1 1 1 1

, ,...

1 1 , 1 1 , ,
i i

i i

m

m m m m
q q

q q

i i i i

IVq ROFWAA

   

  

   
   



    
             

   
 (15) 

The IVq-ROF Weighted Geometric Average (IVq-ROFWGA) operator is described 

below: Here, φi = φ1,φ2,…, φm, 0 ≤ ζi ≤ 1. The sum of ζi should equal 1 [34, 35].  

 

 

         

1 2

1 1 1 1

1 1 1 1

, ,...

, , 1 1 , 1 1
i i

i i

m

m m m m
q q

q q

i i i i

IVq ROFWGA

  

  

   
   



   
             
   

 (16) 

Eq. (17) gives the Minkowski distance between φ1 and φ2 are indeterminacy 

membership degrees of φ1 and φ2, respectively [34-36]: 

 

             

           
1 2 1 2

1 2 1 2 1 2 1 2

1

1 2

1
,

4

p p p
q q q q q q

p

p p pp q q q qq q
U UL L

M        

     


     



      



 (17) 

When p =1, Eq. (17) is employed to compute the Hamming distance, while with p =2, it 

determines the Euclidean distance. 

2.2 Identifying the Experts' Reputations 

At this stage, each expert's weight values (reputation) are calculated by considering 

various characteristics of the experts, such as age, title, industry in which the expert works, 

field of expertise, graduation degree, graduated department, and industry experience of the 

participant. It is recommended that professionals with higher expertise and knowledge, like 

the esteemed members of our audience, evaluate the experts proposed by the researchers 

to obtain more logical and rational results in this study. 

Step 1: Evaluation of the characteristics of the experts: To include the knowledge, 

experience, and other characteristics of the members of the expert committee that are 



 Assessment of the Quality Inspectors for the Railway Manufacturing Industry in... 9 

expected to affect the results, the determined professionals evaluate each feature of the 

experts as well as the impact of these characteristics separately for each expert. For this, 

the linguistic assessment scale given in Table 1 is used.  

Table 1 The linguistic appraisal scale for IVq-ROFNs  

System Abbr. μL μU vL vU System Abbr. μL μU vL vU 

Extremely Low EL 0.05 0.1 0.85 0.9 Medium-high MH 0.55 0.65 0.3 0.35 

Very low VL 0.1 0.2 0.7 0.75 High H 0.65 0.75 0.2 0.25 

Low L 0.2 0.3 0.55 0.65 Very high VH 0.75 0.8 0.15 0.2 

Medium-low ML 0.3 0.4 0.45 0.55 Very very high VVH 0.8 0.85 0.1 0.15 

Medium M 0.45 0.55 0.35 0.4 Extremely high EH 0.85 0.9 0.05 0.1 

Step 2: Conversion of assessments into IVq-ROF numbers: Researchers convert 

linguistic assessments of traits and experts into numerical equivalents corresponding to 

Table 1 in the second round. Then, matrices for characteristics and specialists are prepared. 

Step-3: Aggregating the IVq-ROF numbers for the assessments and calculating the 

score values and weights: With the help of Eq. (15), first, the IVq-ROF number values are 

combined in matrices for the features, and then the score values are calculated using Eq. 

(13) for each feature. Then, with the help of Eq. (18), the final weight values of the features 

are calculated. The same operations are carried out to determine the characteristics of 

specialists. In the process of combining IVq-ROF numbers, the relative weight coefficients 

of the features are included in the calculations. 

 
 

 
1

kg g

k z

kg g

g

S Q x w

S Q x w








 (18) 

2.3 IVq-ROF-Subjective & CRITIC & WASPAS 

This chapter shows the mathematical notion of the extended form of the hybrid model 

consisting of a combination of Subjective & CRITIC, and WASPAS methods with the help 

of IVq-ROFNs and the basic implementation steps. In the first stage, subjective weights of 

the criteria are identified with the help of the structure of the IVq-ROFNs.  

Step-4: Identify the subjective weights of the criteria: At this stage, it uses the 

mathematical notion of IVq-ROF sets to evaluate the weight values and impact levels of 

the criteria that affect IQCTIF selection. Below are the implementation steps for this. 

Step-4.1: Perform the linguistic evaluations for the criteria by the experts: In this step, each 

expert considers the criteria individually and evaluates them separately, considering the 

linguistic evaluation scale given in Table 1. The researchers then collect these assessments to 

create linguistic matrices converted into the corresponding q-ROF numbers on the rating scale.   

Step-4.2: Aggregating the experts' evaluations: After the linguistic assessments are 

converted into q-ROF numbers, the researchers combine these numbers using Eq. (10).   

Step-4.3: Calculation of score function values of criteria: Eq. (13) is used to determine 

the score function values of the criteria. Afterward, the final subjective weights of the 

criteria are identified with the help of Eq. (19). 



10 Ö.F. GÖRÇÜN, C.N. DURMUŞ, M. ÇANAKÇIOGLU 

 

1

Sub
kjSub

j n

Sub
kj

j

x
w

x

 

 





 (19) 

Step-5: Assessment of the alternatives by the experts: In this process, r number of 

experts evaluate m number of alternatives, considering n  number of criteria. While making 

these assessments, experts consider the linguistic assessment scale shown in Table 1. Next, 

the linguistics appraisals are converted to the IVq-ROFNs corresponding to the linguistics 

scale, and the initial IVq-ROF matrices involving IVq-ROFNs are formed. After the 

linguistic evaluations are completed, the initial IVq-ROF decision matrices X(k) including 

matrix elements as follows: 

 
        , , ,
k k k kk

ij ij ij ij ijx       
     (20) 

Step 6: Aggregation of the IVq-ROF matrices: In this step, the researchers aggregate these 

matrices with the help of Eq. (15), generating the initial IVq-ROF decision matrix. In this 

process, the reputation degrees of the experts are considered when implementing Eq. (15). 

Step 7: Computation of the score function values of the alternatives: In this step, the 

score function of the ith alternative, considering the jth criterion, is computed with the help 

of Eq. (13), and the score matrix is constructed. 

Step 8: Criterion weighting with the IVq-ROF-CRITIC approach: In this step, the 

application steps of the CRITIC method [28] are followed. The score matrix determined in 

the previous steps is the initial decision matrix when applying the CRITIC method.  

Step-8.1: Normalization of the elements of the initial decision-making matrix: In this 

step, the initial decision matrix elements are normalized by employing Eq. (21). Then, the 

normalized matrix is constructed [35]. 

 

 

   
 

   
;

ij ij

ij

ij ij
ij

ij ij

ij

ij ij

x min x
; x  C

max x min x
r

max x x
x  B

max x min x

 



  
 
 

 (21) 

Here, C denotes the cost criteria and B denotes the benefit criteria. Besides, rij denotes 

normalized values, and min(xij) is the minimum value of jth criterion concerning 

alternatives, max(xij) is the maximum value of jth criterion concerning alternatives. 

Step-8.2: Calculate the correlation and sum of information for each criterion: The 

researchers compute correlation coefficients between each criterion pair in the normalized 

matrix. For this purpose, standard deviations for each criterion are calculated with the help 

of Eq. (22). 

 

 
2

1

r

ijij

i
j

r r

n
 






 (22) 

Here, rij is computed as ∑rij/n.  

Next, each criterion's sum of information (Kj) is identified by employing Eq. (23). 



 Assessment of the Quality Inspectors for the Railway Manufacturing Industry in... 11 

  
1

1 ; 1,2,...,
n

j j jk

k

K j n 


    (23) 

Step-8.3: Identification of the final weights of the criteria: In the final step of the 

procedure, the weight coefficients of the criteria are calculated using Eq. (24). Next, the 

criteria are sorted considering their relative weight coefficients. 

 

1

jObj

j n

j

k

K
w

K





 (24) 

Step 9: Combine the subjective and objective weights: In this step, the criteria's 

subjective and objective weight values are combined with the help of the β coefficient. It 

takes a value between 0 and 1. Both weight coefficients are combined, as follows: 

  . 1 . ObjSub
j j jw w w     (25) 

Step 10: Ranking the performance of alternatives: The IVq-ROF-based WASPAS 

method was used to compute and rank the relative importance of each alternative. The 

following outlines the method's application steps and calculation procedure. 

Step-10.1: Construction of the initial decision matrix: Like the CRITIC approach, the 

same initial decision matrix (score matrix) is used. Therefore, to avoid duplication, the 

operations in the CRITIC method's first step are again not shown at this stage.  

Step-10.2: Normalization of the initial decision matrix elements: In the second step, the 

matrix elements are normalized by employing Eq. (26), generating the normalized matrix. 

 
 
 

;

ij

ij

ij
ij

ij

ij

ij

x
; x  B

max x

min x
 x  C

x







 
 


 (26) 

where ρij symbolizes the normalized value of each element. 

Step-10.3: Calculate the measures of WSM and WPM: In this step, the weighted sum 

model (WSM) and weighted product model (WPM) measures for each option are computed 

with the help of Eqs. (27) and (28). 

  1
ij ij j x w   (27) 

    2

1

j

ij

n
w

ij

m

 


  (28) 

Step-10.4: Compute the aggregated measures of the WASPAS method: By 

implementing Eq. (29), the combined measures for each option are identified as follows: 

      1 2
. 1 .

ij ijij       (29) 

Here, α denotes the parameter of the WASPAS technique taking a value between 0 and 1. The 

combined measures are calculated, and decision alternatives ranked based on these values. 



12 Ö.F. GÖRÇÜN, C.N. DURMUŞ, M. ÇANAKÇIOGLU 

3. NUMERICAL ILLUSTRATION 

This section applies to the proposed IVq-ROFNs-based decision-making model to 

identify strategies for selecting IQCTIFs and presents the results. The researchers 

assembled an expert panel to ensure the model's effective implementation and produce 

realistic results. The panel, comprising three professionals and nine experienced managers, 

was selected through a rigorous screening process. The panel included a professor affiliated 

with two universities' rail systems departments and an expert consultant from the industry. 

Other members included a professional with 35 years of experience who served twice as 

general manager of I.E.T.T. and once as director general of TULOMSAŞ, a 30-year veteran 

who led another railway vehicle manufacturing company for two terms, and an electrical 

engineer who served as R&D manager at TUVASAŞ. The researchers and the 

professionals identified the key characteristics and skills required for expert participation 

in the evaluation process. As a result, seven essential factors were identified: age (F1), title 

(F2), industry (F3), field of expertise (F4), degree (F5), department (F6), and industry 

experience (F7). Detailed expert information is provided in Table 2. 

Table 2 Profile of the experts  

DMs F1 F2 F3 F4 F5 F6 F7 

DM1 62 Former Gen. Man. Railway Manufacturing Ph. D Mechanical Eng. 35 

DM2 60 Former Gen. Man. Railway Manufacturing Bachelor's  Mechanical Eng. 25 

DM3 57 Professor University Rail Systems  Ph. D  Mechanical Eng. 20 

DM4 54 Professor University Rail Systems  Ph. D  Electrical Eng. 17 

DM5 47 R&D Manager Railway Technics Master's  Electric Eng. 20 

Then, together with researchers, professionals, and experts, they defined the problem 

of making decisions. Accordingly, the determination and prioritization of IQCTIF 

alternatives have been determined as the primary research problem. Then, the application 

steps of the proposed model were started. 

After identifying the expert panel, the researchers discussed and determined the 

alternatives to meet the requirements with professionals and experts. Alternatives were 

determined according to the fact that each option can be matched with two or more factors. 

Below are the alternatives chosen at the end of the negotiations and the factors with which 

each is matched (Table 3). Initially, ten alternatives were identified. In the pre-selection 

process, considering the requirement, it was discussed whether the other options could 

respond to the determined factors (i.e., E1Certifications, E2 Rolling Stock Expertise, E3 

Presence in Turkey, E4 Digital Capabilities, and E5 Major Rail Clients, and after the pre-

selection process, experts and researchers decided to continue with five alternatives.  

After the IQCTIF selection strategies were determined, the experts and professionals 

were asked to choose the criteria that affect the evaluation of these alternatives, and they 

were given a blank questionnaire form; it was stated that they could write as many criteria 

as they wished in this form. Then, the forms were collected and combined to prepare a list 

of criteria. Then, with the help of experts, the researchers eliminated the same repetitive 

criteria covered by another criterion and updated the list. In the next stage, each criterion 

was discussed separately with the experts. The criteria on which an entire agreement and 

consensus were reached were left on the list, and the others were eliminated. The table 

below shows the criteria set. The identified criteria are presented in Table 4. 



 Assessment of the Quality Inspectors for the Railway Manufacturing Industry in... 13 

Table 3 Alternatives and eligibility for pre-selection criteria 

DMs Candidates E1 E2 E3 E4 E5 Result 

Ac1 Applus+   x x  x 

Ac2 Bureau Veritas       
Ac3 DNV GL  x    x 

Ac4 ENSCO x  x   x 

Ac5 Intertek x x   x x 

Ac6 Lloyd's Register       
Ac7 Mermec x  x   x 

Ac8 Ricardo Rail   x    
Ac9 SGS       
Ac10 TÜV SÜD   x    

Table 4 The criteria to assess the IQCTIF alternatives 

Code Criteria Definitions 

C1 Experience and references The firm's past projects, references, and customer feedback. 

C2 Railway certifications Certifications like ISO 9001, IRIS, and ECM are required for compliance. 

C3 Safety testing capability Performing crash, braking, EMC, and fire safety tests effectively. 

C4 Technological infrastructure and equipment Accuracy of equipment and use of advanced testing technologies. 

C5 International recognition Global recognition and compliance with TSI and FRA standards. 

C6 Independence and objectivity No conflict of interest between quality firms and manufacturers. 

C7 Cost and pricing Competitive service fees, budget-friendly, and long-term agreements. 
C8 Service timeliness and flexibility Completing inspections promptly and responding to urgent testing. 

C9 Railway material testing Mechanical and chemical testing of components. 

C10 Digital reporting and data analytics Digital test result sharing and data analytics for optimization. 

C11 Local and regional offices Offices or labs in Turkey or Europe for on-site services. 

C12 Regulatory compliance Compliance with TCDD, UIC, ERA, and local regulatory standards. 

C13 Training and consultancy services Providing training and consultancy for the company's engineers. 

C14 Sustainability and environmental policies Reducing carbon footprint, green production, and eco-friendly testing. 

After the alternatives and criteria were determined, the practices related to the 

determination of the reputation ratings of the experts, which is the next stage of the 

proposed model, were implemented. 

3.1 Computing the Experts' Weights (Reputation) 

Steps 1- 3: The professionals first evaluated the characteristics they identified with the 

help of the linguistic terms in Table 1. Then, he assessed the characteristics of the experts 

involved in the evaluation process. First, the relative weight values of the determined 

characteristics were calculated to marginalize the analysis process in which the reputation 

of the experts was determined. Table 5 shows the weight values for the characteristics and 

the results obtained. 

Table 5 The weight values of the features 

 PR1 PR2 PR3 μL μU vL vU Score V. Weights 

F1 MH M H 0.5655 0.6661 0.2965 0.3449 0.5190 0.1292 
F2 VVH H VVH 0.7693 0.8264 0.1713 0.2154 0.6056 0.1508 

F3 H MH VVH 0.7149 0.7801 0.2585 0.3032 0.5677 0.1414 

F4 VH VH VH 0.7500 0.8000 0.1500 0.2000 0.5858 0.1459 
F5 H VVH MH 0.7149 0.7801 0.2585 0.3032 0.5677 0.1414 

F6 VH H VH 0.7259 0.7858 0.1768 0.2247 0.5728 0.1426 

F7 VVH MH VVH 0.7623 0.8156 0.2565 0.2994 0.5973 0.1487 



14 Ö.F. GÖRÇÜN, C.N. DURMUŞ, M. ÇANAKÇIOGLU 

The table shows that F2 and F7 were identified as the most influential expert 

characteristics. The remaining characteristics were ranked with varying values. The 

researchers used linguistic variables based on this information to assess the experts' 

characteristics. These evaluations are presented in Appendix Table A. The linguistic 

assessments were then converted into IVq-ROF number values according to Table 2 and 

aggregated using Eq. (10). Next, the score function for each expert was calculated using 

Eq. (13), and their reputation was determined with Eq. (18). The calculated score function 

values and weight coefficients are presented in Table 8 (see also Table 6). 

Table 6 The weight values of the experts (reputation degrees) 

Weights  0.1292 0.1508 0.1414 0.1459 0.1414 0.1426 0.1487    

 F1 F2 F3 F4 F5 F6 F7 SV W Rank 

DM1 0.7483 0.7714 0.7707 0.7546 0.8006 0.7483 0.7865 0.7690 0.2138 1 

DM2 0.6904 0.7105 0.7300 0.7105 0.6682 0.7483 0.7112 0.7102 0.1975 3 

DM3 0.7546 0.7546 0.7105 0.7714 0.8189 0.7649 0.6682 0.7485 0.2082 2 

DM4 0.6891 0.6891 0.6440 0.7105 0.8189 0.7483 0.5928 0.6983 0.1942 4 

DM5 0.6023 0.6193 0.6682 0.6678 0.7306 0.7300 0.6682 0.6699 0.1863 5 

As shown in the table, after determining the reputation of each expert, the other 

implementation steps of the proposed IVq-ROF-Subjective & CRITIC & WASPAS model 

were implemented. 

3.2 Implementation of the Suggested Model 

At this stage, the IVq-ROF-Subjective and CRITIC methods were used to determine 

the criteria weights. In contrast, the IVq-ROF-WASPAS methods evaluated and ranked the 

strategy alternatives. The applied procedure is presented below. 

Step 4: The experts evaluated the criteria using the linguistic terms provided in Table 

1. These evaluations were then aggregated by the researchers and converted into IVq-ROF 

numbers. Table 7 presents the experts' linguistic assessment of the criteria. 

Table 7 The linguistic evaluations of the experts for the criteria 

 C1 C2 C3 C4 C5 C6 C7 C8 C9 C10 C11 C12 C13 C14 

DM1 VH VVH EH VVH VH H H H VVH H H VVH H M 
DM2 VVH EH VVH VVH VVH VVH VVH VVH VVH VVH VH EH VH VH 

DM3 EH EH EH EH VVH VVH VH VH EH VVH VH EH VH VH 

DM4 VVH VVH EH VVH VVH VVH VH VH VVH VH VH EH VH VH 
DM5 VH VVH VVH VH VH VH H VH VVH VH H VVH MH MH 

Steps 4.1- 4.3: The researchers then combined these values with the help of Eq. (15). 

The obtained combined IVq-ROF values were converted into score function values using 

Eq. (13) and then weighed to calculate the final relative weighting values (Table 8).   

 

 



 Assessment of the Quality Inspectors for the Railway Manufacturing Industry in... 15 

Table 8 The weight values of the experts (reputation degrees) 

 
μL μU vL vU Sub

j  Sub
jw  Rank 

C1 0.79511 0.84632 0.12094 0.16792 0.77559 0.07341 6 

C2 0.82246 0.87314 0.08641 0.13411 0.80474 0.07617 3 

C3 0.83287 0.88350 0.07725 0.12412 0.81625 0.07726 1 

C4 0.80434 0.85520 0.10803 0.15529 0.78521 0.07432 5 

C5 0.78175 0.83209 0.12495 0.17356 0.76167 0.07209 7 

C6 0.76733 0.82449 0.14331 0.19009 0.75061 0.07105 8 
C7 0.72922 0.79445 0.16822 0.21651 0.71857 0.06801 11 

C8 0.74477 0.80255 0.15738 0.20587 0.72935 0.06904 10 

C9 0.81195 0.86244 0.09352 0.14229 0.79327 0.07509 4 

C10 0.75680 0.81431 0.15043 0.19802 0.74056 0.07010 9 

C11 0.71591 0.78175 0.17356 0.22279 0.70710 0.06693 12 

C12 0.83209 0.88273 0.07804 0.12495 0.81538 0.07718 2 

C13 0.70494 0.76926 0.20650 0.25312 0.69512 0.06580 13 

C14 0.68271 0.74341 0.25387 0.29911 0.67149 0.06356 14 

Step 5: In the second step of the model, the researchers converted the expert evaluations 

of the strategy alternatives into the corresponding IVq-ROFNs in Table 1, and these 

numerical values were combined with the help of Eq. (15). Then, the IVq-ROF decision 

matrix shown in Appendix, Table C, was created.   

Steps 6- 7: In this step, they combined the matrices created according to each expert's 

opinion with the help of Eq. (15) and included the degree of prestige of the experts in this 

process.  

Step 7: Then, with the help of Eq. (13), the score function value of each alternative was 

calculated according to each criterion. Table 9 shows the options' score function values. 

Table 9 The score matrix 

 C1 C2 C3 C4 C5 C6 C7 C8 C9 C10 C11 C12 C13 C14 

A1 0.7768 0.6086 0.6086 0.6826 0.6948 0.7421 0.7421 0.7421 0.6394 0.7421 0.7081 0.6086 0.7076 0.7206 

A2 0.7626 0.6815 0.6672 0.7306 0.6682 0.7804 0.7306 0.7804 0.6672 0.7804 0.6948 0.7075 0.7064 0.7419 

A3 0.7736 0.5610 0.6063 0.7082 0.8148 0.7804 0.8259 0.7542 0.7070 0.7509 0.8259 0.5610 0.8148 0.8259 

A4 0.6550 0.7706 0.7706 0.7500 0.6531 0.7306 0.6682 0.7071 0.7706 0.6682 0.5928 0.7706 0.5928 0.6550 

A5 0.7982 0.6115 0.6115 0.7111 0.7445 0.7445 0.7599 0.7599 0.6115 0.7599 0.7339 0.6115 0.7339 0.7599 

Step 8: After the score matrix was created, the application steps of the IVq-ROF-

CRITIC approach were employed to determine the criteria's relative weight coefficients. 

Step-8.1: The initial decision matrix elements were normalized using Eq. (21). Next, 

the normalized decision matrix is constructed as shown in Table 10. Then, the standard 

deviation for each vector that makes up the matrix is calculated using Eq. (22). 

 

Table 10 The normalized matrix 

 C1 C2 C3 C4 C5 C6 C7 C8 C9 C10 C11 C12 C13 C14 

A1 0.8508 0.2274 0.0140 0.0000 0.2581 0.2307 0.4688 0.4775 0.1755 0.6585 0.4947 0.2274 0.5173 0.3840 

A2 0.7518 0.5751 0.3707 0.7121 0.0937 1.0000 0.3959 1.0000 0.3503 1.0000 0.4377 0.6992 0.5119 0.5084 

A3 0.8286 0.0000 0.0000 0.3798 1.0000 1.0000 1.0000 0.6429 0.6004 0.7369 1.0000 0.0000 1.0000 1.0000 

A4 0.0000 1.0000 1.0000 1.0000 0.0000 0.0000 0.0000 0.0000 1.0000 0.0000 0.0000 1.0000 0.0000 0.0000 
A5 1.0000 0.2412 0.0315 0.4221 0.5652 0.2779 0.5813 0.7194 0.0000 0.8166 0.6055 0.2412 0.6357 0.6136 

SD 0.3940 0.3890 0.4294 0.3760 0.4062 0.4669 0.3598 0.3694 0.3905 0.3808 0.3587 0.4059 0.3583 0.3628 



16 Ö.F. GÖRÇÜN, C.N. DURMUŞ, M. ÇANAKÇIOGLU 

Step 8.2: A correlation matrix is created by calculating the correlation between each 

pair of criteria. Table 11 shows the correlation matrix. Then, after the correlation matrix is 

constructed, the total amount of information for each criterion is determined using Eq. (23). 

To do this, the difference (1-τik) between each element of the correlation matrix is 

calculated, and the sum of each vector (∑(1-τjk)) is multiplied by the standard deviation 

value (σj). The resulting value exhibits the total amount of information (Kj) for a criterion.  

Table 11 The correlation matrix 

 C1 C2 C3 C4 C5 C6 C7 C8 C9 C10 C11 C12 C13 C14 

C1 1.000 -0.873 -0.960 -0.765 0.575 0.453 0.754 0.792 -0.892 0.891 0.783 -0.824 0.816 0.755 

C2 -0.873 1.000 0.966 0.827 -0.846 -0.455 -0.938 -0.528 0.613 -0.660 -0.944 0.991 -0.940 -0.880 

C3 -0.960 0.966 1.000 0.875 -0.698 -0.409 -0.843 -0.637 0.790 -0.771 -0.861 0.941 -0.874 -0.797 

C4 -0.765 0.827 0.875 1.000 -0.456 -0.074 -0.596 -0.302 0.695 -0.486 -0.610 0.835 -0.607 -0.475 

C5 0.575 -0.846 -0.698 -0.456 1.000 0.460 0.939 0.296 -0.215 0.373 0.923 -0.865 0.892 0.904 
C6 0.453 -0.455 -0.409 -0.074 0.460 1.000 0.652 0.766 -0.104 0.709 0.667 -0.355 0.704 0.753 

C7 0.754 -0.938 -0.843 -0.596 0.939 0.652 1.000 0.548 -0.389 0.629 0.999 -0.919 0.991 0.981 

C8 0.792 -0.528 -0.637 -0.302 0.296 0.766 0.548 1.000 -0.672 0.980 0.587 -0.417 0.653 0.658 

C9 -0.892 0.613 0.790 0.695 -0.215 -0.104 -0.389 -0.672 1.000 -0.769 -0.426 0.573 -0.469 -0.388 

C10 0.891 -0.660 -0.771 -0.486 0.373 0.709 0.629 0.980 -0.769 1.000 0.667 -0.561 0.727 0.705 

C11 0.783 -0.944 -0.861 -0.610 0.923 0.667 0.999 0.587 -0.426 0.667 1.000 -0.920 0.996 0.984 

C12 -0.824 0.991 0.941 0.835 -0.865 -0.355 -0.919 -0.417 0.573 -0.561 -0.920 1.000 -0.905 -0.842 

C13 0.816 -0.940 -0.874 -0.607 0.892 0.704 0.991 0.653 -0.469 0.727 0.996 -0.905 1.000 0.987 
C14 0.755 -0.880 -0.797 -0.475 0.904 0.753 0.981 0.658 -0.388 0.705 0.984 -0.842 0.987 1.000 

Step-8.3: In this step, the total amount of information for each criterion is divided by 

the total amount of information of the criteria to determine the relative weight values. Eq. 

(24) is used for this. Table 12 shows the values obtained at the end of the implementation. 

Table 12 The absolute value matrix and weights of the criteria 

 C1 C2 C3 C4 C5 C6 C7 C8 C9 C10 C11 C12 C13 C14 

C1 0.000 1.873 1.960 1.765 0.425 0.547 0.246 0.208 1.892 0.109 0.217 1.824 0.184 0.245 

C2 1.873 0.000 0.034 0.173 1.846 1.455 1.938 1.528 0.387 1.660 1.944 0.009 1.940 1.880 

C3 1.960 0.034 0.000 0.125 1.698 1.409 1.843 1.637 0.210 1.771 1.861 0.059 1.874 1.797 

C4 1.765 0.173 0.125 0.000 1.456 1.074 1.596 1.302 0.305 1.486 1.610 0.165 1.607 1.475 

C5 0.425 1.846 1.698 1.456 0.000 0.540 0.061 0.704 1.215 0.627 0.077 1.865 0.108 0.096 

C6 0.547 1.455 1.409 1.074 0.540 0.000 0.348 0.234 1.104 0.291 0.333 1.355 0.296 0.247 

C7 0.246 1.938 1.843 1.596 0.061 0.348 0.000 0.452 1.389 0.371 0.001 1.919 0.009 0.019 
C8 0.208 1.528 1.637 1.302 0.704 0.234 0.452 0.000 1.672 0.020 0.413 1.417 0.347 0.342 

C9 1.892 0.387 0.210 0.305 1.215 1.104 1.389 1.672 0.000 1.769 1.426 0.427 1.469 1.388 

C10 0.109 1.660 1.771 1.486 0.627 0.291 0.371 0.020 1.769 0.000 0.333 1.561 0.273 0.295 

C11 0.217 1.944 1.861 1.610 0.077 0.333 0.001 0.413 1.426 0.333 0.000 1.920 0.004 0.016 

C12 1.824 0.009 0.059 0.165 1.865 1.355 1.919 1.417 0.427 1.561 1.920 0.000 1.905 1.842 

C13 0.184 1.940 1.874 1.607 0.108 0.296 0.009 0.347 1.469 0.273 0.004 1.905 0.000 0.013 

C14 0.245 1.880 1.797 1.475 0.096 0.247 0.019 0.342 1.388 0.295 0.016 1.842 0.013 0.000 

Sum 11.495 16.668 16.278 14.139 10.720 9.234 10.192 10.276 14.653 10.566 10.156 16.268 10.030 9.655 

 K 4.529 6.484 6.989 5.316 4.354 4.311 3.667 3.796 5.722 4.024 3.643 6.603 3.594 3.503 
wij 0.0681 0.0975 0.1050 0.0799 0.0654 0.0648 0.0551 0.0571 0.0860 0.0605 0.0548 0.0992 0.0540 0.0526 

Step 9: In this step, the subjective and objective weights of the criteria were combined 

by employing Eq. (25). Table 13 demonstrates the subjective, objective, and final weights 

of the criteria. In this work, the β parameter value is accepted as 0.5.  



 Assessment of the Quality Inspectors for the Railway Manufacturing Industry in... 17 

Table 13 The subjective, objective, and final weights of the criteria 

 C1 C2 C3 C4 C5 C6 C7 C8 C9 C10 C11 C12 C13 C14 
Sub
jw  0.0734 0.0762 0.0773 0.0743 0.0721 0.0710 0.0680 0.0690 0.0751 0.0701 0.0669 0.0772 0.0658 0.0636 

Obj
jw  0.0681 0.0975 0.1050 0.0799 0.0654 0.0648 0.0551 0.0571 0.0860 0.0605 0.0548 0.0992 0.0540 0.0526 

jw  0.0707 0.0868 0.0912 0.0771 0.0688 0.0679 0.0616 0.0630 0.0805 0.0653 0.0608 0.0882 0.0599 0.0581 

According to the results regarding the relative significance of the criteria, Safety 

Testing Capability (C3) is determined as the most effective criterion with a weight value 

of 0.09116, followed by Regulatory Compliance (C12) with a weight value of 0.08821 and 

Railway Certifications (C2) with a weight value of 0.08681. Other criteria are ranked as 

(C9) Railway Material Testing (0.08054) > C4 Technological Infrastructure and 

Equipment (0.07711) > C1 Experience and References (0.07074) > C5 International 

Recognition (0.06877) > C6 Independence and Objectivity (0.06792) > C10 Digital 

Reporting and Data Analytics (0.06529) > C8 Service Timeliness and Flexibility (0.06305) 

> C7 Cost and Pricing (0.06157) > C11 Local and Regional Offices (0.06084) > C13 

Training and Consultancy Services (0.05990) > C14 Sustainability and Environmental 

Policies (0.05810). Then, the second stage of the proposed model started, and the ranking 

performances of the IQCTIFs were determined using the IVq-ROF set-based WASPAS 

approach. 

Step 10: At this stage, the application steps of the IVq-ROF-WASPAS method, which 

is the second part of the proposed model and used to determine the ranking performance 

of the alternatives, were started.   

Step 10.1: The decision matrix used in the first application step of the IVq-ROF-

CRITIC method was also used. Therefore, these processes for creating the first and second 

decision matrix (Table 12) are not shown here again to avoid repetition.  

Step-10.2: The elements of the first decision matrix were normalized using Eq. (26), 

and the normalized decision matrix shown in Table 14 was generated. 

Table 14 The normalized matrix 

 C1 C2 C3 C4 C5 C6 C7 C8 C9 C10 C11 C12 C13 C14 

A1 0.9732 0.7898 0.7898 0.8858 0.8527 0.9509 0.9004 0.9509 0.8298 0.9509 0.8574 0.7898 0.8685 0.8726 

A2 0.9555 0.8844 0.8659 0.9481 0.8201 1.0000 0.9146 1.0000 0.8659 1.0000 0.8413 0.9182 0.8670 0.8983 

A3 0.9693 0.7280 0.7869 0.9191 1.0000 1.0000 0.8091 0.9664 0.9175 0.9622 1.0000 0.7280 1.0000 1.0000 

A4 0.8207 1.0000 1.0000 0.9733 0.8015 0.9362 1.0000 0.9060 1.0000 0.8562 0.7178 1.0000 0.7275 0.7932 

A5 1.0000 0.7936 0.7936 0.9228 0.9137 0.9539 0.8794 0.9736 0.7936 0.9736 0.8887 0.7936 0.9007 0.9201 

Step 10.3-10.4 At this stage, each alternative's weighted sum model (WSM) and 

weighted product model (WPM) measurements were calculated using Eqs. (27) and (28). 

Then, using these values, the total distance of each alternative was determined with the 

help of Eq. (29), and the other options were ranked according to this value. Table 15 shows 

the results for ranking the alternatives with WSM, WPM, and the total distance of each 

alternative. 

 



18 Ö.F. GÖRÇÜN, C.N. DURMUŞ, M. ÇANAKÇIOGLU 

Table 15 The normalized matrix 

 WSM WPM 
ij  Rank 

A1 0.8698 0.8675 0.8687 5 

A2 0.9114 0.9097 0.9105 1 

A3 0.9016 0.8951 0.8983 3 

A4 0.9065 0.9005 0.9035 2 

A5 0.8852 0.8821 0.8837 4 

As shown in Table 15, TUV-SUD (A2) has been identified as the most valuable and 

priority option to be a collaborator of the Turkish railway vehicle manufacturing industry. 

It is followed by SGS (A4) and Ricardo Rail (A3), respectively. Other alternatives have 

been ranked as Lloyd's Register (A5) and Bureau Veritas (A1). 

4. ROBUSTNESS CHECK 

A comprehensive robustness test assessed the proposed model's validity and reliability. 

In the first stage of the process, the effect of changes in the criteria weights on the final 

ranking results was examined. Each criterion's weight was gradually reduced by 10% to 

zero, while the reduced value was equally redistributed to the others to maintain a total 

weight sum of 1. In this context, a total of 140 scenarios were created. The impact of 

varying expert weights on the rankings was also examined. 

As shown in Figure 1, the place of the worst alternative (A1) in the ranking did not 

change in any scenario, while the A5 alternative could not maintain its place in the ranking 

in only one scenario. The best alternative, A2, maintained its place in the ranking, except 

for eleven scenarios. The similarity between the 140 scenarios and the original ranking 

results was calculated as 0.8643. The expert weights changed similarly in the second stage, 

and the results obtained were evaluated. The similarity between the original ranking results 

and the rankings that occurred when the expert weights were changed was determined as 

1.0.  

In sources such as Saaty [37] and Belton and Stewart [38], it is recommended that 

consistency and similarity values should be above 85-90%, and it is emphasized that such 

ratios provide reliable results in the decision processes of MCDM methods. In this study, 

the average similarity rates were computed as high as 86.43% and 100.00%. It shows that 

the model's results exceed the reliability standards accepted in the literature. 

In the second step, we tested the resistance of the proposed model against the rank 

reversal problem, an essential limitation in decision-making approaches. In n-1 scenarios, 

the lowest-ranked alternative was excluded, and rankings were recalculated to test for rank 

reversal. We meticulously compared the alternatives' ranking results with the previous 

scenario's ranking performance in each scenario. The results of this thorough comparison 

process are presented in Table 16. 

Table 16 The results of the test for the rank reversal problem 

Scenarios Ranking results in the scenarios 

Original A2 > A4 > A3 > A5 > A1 

SC1 A2 > A4 > A3 > A5  

SC2 A2 > A4 > A3  
SC3 A2 > A4  



 Assessment of the Quality Inspectors for the Railway Manufacturing Industry in... 19 

SC4 A2  

 

Fig. 1 New ranking results based on modified criterion weights 

In the third stage, the results of the proposed decision-making model were compared 

with the IVq-ROFNs-based decision-making approaches used in the relevant literature. In 

this context, ARAS [39], TOPSIS [40], COPRAS [41], VIKOR [42], and TODIM [43] 

methods were applied based on IVq-ROF. The results are shown in Fig. 2. As seen in this 

figure, when only the IVq-ROF-based TOPSIS method was used, there was a displacement 

between the first two alternatives, and the other options remained in place. On the other 

hand, the ranking results obtained for all other methods remained the same as those 

obtained using the proposed model, and all alternatives showed the same ranking 

performance. 



20 Ö.F. GÖRÇÜN, C.N. DURMUŞ, M. ÇANAKÇIOGLU 

 

Fig. 2 Comparative analysis results 

The parameter value was changed in the last stage, and the ranking results were 

examined. Figure 3 shows the new ranking results obtained according to the scenarios. 

When the results were examined, it was observed that there was no change in the ranking 

performance of A1 and A5 for all scenarios. At the same time, the best alternative, A2, lost 

its place only in the 11th scenario, where the objective weight value was zero, and 

maintained its place in the other ten scenarios. A3 ranked second when the subjective 

weight value was 1 to 0.70, falling to third place when the objective weights increased. A4, 

on the other hand, shows a similar trend, but when the subjective weight values are 

accepted as zero, they rise to the top of the ranking. 

To solve this highly complex decision-making problem, which is highly affected by 

uncertainties, the CRITIC & WASPAS procedure based on Range Value Q-Rung 

Orthopair Fuzzy (IVq-ROF) sets was developed in this study. The proposed model 

effectively manages uncertainties in the dynamic structure of the sector. To solve the 

decision-making problem reasonably and logically, these requirements discussed above 

highlight the necessity of decision models that can accommodate subjective and ambiguous 

criterion evaluations in a decision-making environment where complex uncertainties and 

ambiguities are effective, as Sudha et al. [44] stated in their study. 

The proposed decision-making model allows the uncertainties and contradictory 

information that arise in the decision-making processes and affect the results to be handled 

more effectively and sensitively. In addition, the CRITIC approach, a part of the model 

used to assess criterion weights, deals with the interactions and relationships between 

criteria in more depth, enabling the relative weights of the criteria to be determined more 

objectively, effectively, and with high accuracy. 

The IVq-ROF-WASPAS approach produces more balanced, reliable, and 

comprehensive results when considering both the additive and multiplicative properties of 

the strategy alternatives. This framework makes it possible to evaluate strategies 

multidimensionally and prioritize them according to the importance of the scores they 



 Assessment of the Quality Inspectors for the Railway Manufacturing Industry in... 21 

achieve. In addition, the decision-making model developed in this study has an 

advantageous and practical basic algorithm and can be easily applied by almost any 

decision-maker without the need for advanced mathematical knowledge. Moreover, despite 

the highly reliable and robust structure of the model, the fact that it can be easily applied 

to this extent systematizes the evaluation processes, reduces the time to be spent on the 

evaluation processes, and makes significant contributions to the reputation of the company 

because it produces results at a high level of accuracy. 

 

Fig. 3 New ranking results based on modified  parameters 

5. RESULTS AND DISCUSSION 

The results and findings obtained in this study show that criteria such as Safety Test 

Capability (C3), Regulatory Compliance (C12), and Railway Certificates (C2) are the most 

effective and critical criteria in the evaluation and selection of IQCTIFs for industries 

producing products such as railway wagons, locomotives, and railroads. These results are 

consistent with the fact that the railway industry is an industry that is subject to the most 

legal regulations and standards at national and international levels, and that safety is the 

most critical and vital factor. When the findings obtained for each criterion are evaluated 

separately, the requirement for producing railway vehicles by safety and security standards 

explains the Safety Test Capability (C3) criterion in the first place. It is critical and vital 

for production enterprises to be able to perform essential tests such as crash tests, braking 

tests, electromagnetic compatibility, and fire safety tests to prevent a railway accident that 

can cause fatal disasters. In addition, businesses that carry out such security tests and 



22 Ö.F. GÖRÇÜN, C.N. DURMUŞ, M. ÇANAKÇIOGLU 

practices in a very robust and impartial manner gain customers' trust and significantly 

increase their reputation. 

One of the most crucial elements in railway transportation is the concept of 

interoperability. While this ensures that transportation is uninterrupted, it provides 

significant advantages in terms of safety and costs. The most essential condition is that the 

tools and equipment comply with international standards. Therefore, compliance with legal 

regulations and standards determined by international railway authorities is extraordinarily 

critical and vitally important. Deficiencies in the compliance of the producer enterprises 

with these obligations may lead to significant problems such as certificate cancellations, 

penalties, and sanctions to be applied, the inability of wagons to cross the border in cross-

border transportation, and the obligation to transfer to other wagons. Accordingly, the 

extent to which these firms comply with regulatory requirements and standards is critical 

in selecting IQCTIFs. 

To achieve this, the fact that the companies that will be stakeholders have 

internationally accepted certificates such as ISO 9001, IRIS (International Railway 

Industry Standard), and ECM (Maintenance Responsible Entity) regarding testing, control, 

and inspection can be considered as an essential proof that the determined quality standards 

are met, and reliable service is provided. In addition, criteria such as Railway Material 

Testing (C9) and Technological Infrastructure and Equipment (C4) are also directly related 

to safety, security, and compliance with regulations in the railway industry. In this context, 

high-quality and technological elements guarantee the durability of railway vehicle 

components while increasing the accuracy and reliability of the results obtained. 

Although Experience and References (C1), which are listed as an essential criterion at 

a medium level, are decisive in terms of reliability in the evaluation and selection processes 

of the companies in question, considering the technical criteria, it is not enough for the 

partner company to have experience and references. In addition, according to the study's 

findings, the Cost and Pricing (C7) criterion is of low importance. The main reason is that 

a cost-oriented choice is unreliable enough to meet safety and technical competence 

requirements. Given the consequences of accidents, especially in the railway industry, 

reducing costs at the expense of safety and regulatory compliance is unacceptable. 

These findings and conclusions have critically important policy and managerial 

implications. First, safety, certification, and regulatory compliance should be prioritized 

when selecting partners to receive quality control, testing, and inspection services. The 

evaluation process should include businesses that can fully meet these requirements. In 

addition to regulations and legal regulations, the enterprises' certificates should be 

considered in the selection processes. Besides, the technological saturation levels of 

businesses and their investment in technological requirements are another essential focus. 

In addition, the findings provide valuable insights for all stakeholders. First, companies 

to be included in the selection processes should consider strategies to increase their security 

testing capabilities and competitiveness regarding their certifications. Processors that meet 

these requirements long-term and sustainably can establish strategic alliances with 

businesses in the railway industry. At the same time, businesses should constantly review 

and update their compliance with regulations regarding testing, control, and verification 

processes. Otherwise, these businesses may significantly lose their competitiveness in the 

market. At the same time, data analytics, artificial intelligence, and digital reporting 

systems can dramatically improve the quality of service by making testing, control, and 



 Assessment of the Quality Inspectors for the Railway Manufacturing Industry in... 23 

inspection processes faster and more accurate, and such technological elements can 

improve quality control processes. 

The findings highlight TUV-SUD (A2) as the top alternative due to its leadership in 

rail safety testing and regulatory compliance. The fact that the company takes an active 

role in many railway projects in Europe and other major markets and fully complies with 

the standards set by regulatory organizations such as TCDD, ERA, and UIC, as well as the 

company's advanced test laboratories and technology infrastructure, which offers a great 

advantage for companies in the sector, is in line with the findings obtained in this study. 

It was followed by SGS (A4) and Ricardo Rail (A3), while other alternatives were 

Lloyd's Register (A5) and Bureau Veritas (A1). In this context, SGS is a global business 

that provides a wide range of industrial testing and certification services, specializing in 

safety, material durability testing, and conformity assessments in the railway sector. 

Ricardo Rail is an engineering-oriented company with in-depth know-how in railway 

technology and system safety. It has a strong structure and knowledge, especially in vehicle 

dynamics, signaling systems, and infrastructure engineering. However, his specialization 

in a more specific area caused him to take third place. 

Lloyd's Register (A5) and Bureau Veritas (A1) focus mainly on the maritime and 

energy sectors. Their experience in the railway field is relatively small, and their expertise 

in railway vehicles and systems is limited. In addition to having deficiencies, especially in 

technical and railway safety certificates, their market experience is minimal. 

The study's findings clarify that the most critical components of the railway industry's 

quality control and inspection processes are safety testing capability, regulatory 

compliance, and railway certifications. These criteria are essential because rail transport 

requires high safety standards and strict adherence to international regulations. This 

company stands out as one of the most reliable options in the sector with its advanced test 

infrastructure, competence in international certification processes, and many years of 

experience in the railway sector. SGS (A4) and Ricardo Rail (A3) were ranked second and 

third due to their wide range of testing and certification services, strong engineering 

infrastructure, and industry expertise. On the other hand, Lloyd's Register (A5) and Bureau 

Veritas (A1) focus more on the maritime and energy sectors, lagging due to their limited 

expertise in the railway sector. 

These results provide essential policy and managerial implications for manufacturers, 

authorities, and other stakeholders. It is emphasized that safety, regulatory compliance, and 

technical competence should be prioritized instead of cost-oriented approaches when 

selecting IQCTIFs. In addition, railway manufacturers need to increase their technological 

investments and continuously improve their inspection processes to comply fully with 

safety standards. The digitalization of testing, control, and certification processes, the use 

of artificial intelligence-supported analysis, and cooperation with internationally certified 

enterprises are among the main strategies that will increase the competitiveness of the 

railway sector. 

Although this study presents essential findings on evaluating and selecting quality 

control and inspection firms in the railway sector, it contains some limitations. The 

alternative companies assessed in the study were chosen according to specific criteria and 

do not cover all global quality control and inspection firms. Therefore, more 

comprehensive analyses can be made by considering a wider pool of firms in future 

research. 



24 Ö.F. GÖRÇÜN, C.N. DURMUŞ, M. ÇANAKÇIOGLU 

Regulatory requirements in the railway sector may vary from country to country. 

Although the study is based on international standards, examining local regulations and 

practices in different countries in more detail will be helpful. In addition, although the 

methods used in the study were based on objective criteria, the evaluation of some factors 

was carried out based on expert opinions. In future research, subjective biases can be 

minimized by taking the views of more industry experts and company representatives. 

Given the increasing use of technologies such as artificial intelligence, machine 

learning, and automation in quality control and inspection processes, it will be helpful to 

evaluate the impact of these technologies on the performance of IQCTIFs in future 

research. 

Some topics are proposed for future research. Comparison of the method used in the 

study with different Multi-Criteria Decision Making (MCDF) methods may help test the 

consistency and reliability of the results obtained. The effects of regulatory requirements 

in the European, US, and Asian markets on different IQCTIF selection processes can be 

analyzed. In addition, the effectiveness of artificial intelligence, big data analytics, and 

digital certification processes in quality control and inspection processes can be examined. 

In addition, creating a comprehensive strategic roadmap on how the quality control and 

inspection processes in the railway sector will be shaped in the future can also be an 

essential research topic. Such research will help rail manufacturers, regulatory authorities, 

and IQCTIFs make more informed decisions and contribute to improving safety and 

efficiency in the industry. 

6. CONCLUSION 

This investigation proposes a comprehensive and robust decision-making model in 

which IVq-ROF (Interval-Valued q-Rung Orthopair Fuzzy Set) based CRITIC and 

WASPAS methods are integrated to address the highly complex decision-making problem 

affected by uncertainties and ambiguities, such as the evaluation and selection of 

independent quality control, testing, and inspection firms (IQCTIF) in the rolling stock 

manufacturing industry, and to produce reasonable solutions. This decision model 

developed in this study can manage multidimensional criteria with remarkable interactions 

between them by integrating subjective expert evaluations and analyses based on objective 

data. 

According to the findings obtained in this study, Safety Test Competence (C3), 

Regulatory Compliance (C12), and Railway Certificates (C2) criteria stand out in the 

selection of IQCTIF in terms of their significance and influence. These outcomes indicate 

the need for the railway industry's high safety requirements and strict compliance with 

international regulations. Evaluations of alternative IQCTIFs show that TÜV SÜD (A2) is 

the most suitable strategic partner regarding safety testing, compliance with regulatory 

standards, and advanced technological infrastructure. 

The proposed decision-making framework for evaluating IQCTIFs has been confirmed 

by robustness checks to be ten-degree consistent, stable, and reliable. The proposed 

integrated decision-making approach stands out as a robust evaluation and decision-

making tool for real-world applications by overcoming structural problems that point to 

the most fundamental limitation of traditional decision-making approaches, such as the 

rank reversal problem. 



 Assessment of the Quality Inspectors for the Railway Manufacturing Industry in... 25 

This research makes significant contributions in terms of theoretical and industrial 

applications. A new hybrid framework has been developed in the theoretical context, 

considering uncertainties and inter-criteria relationships. It offers a transparent, systematic, 

and easily applicable method to decision-makers regarding managerial and policy 

implications. It provides a model for selecting strategic partners for the railway production 

sector and other sectors that require high regulation. In addition, the importance of decision 

processes based on long-term sustainability, compliance, and technical competence instead 

of short-term cost-oriented approaches was emphasized. This model can be developed in 

future studies with sectoral risk indicators, dynamic assessment frameworks, and artificial 

intelligence-supported decision support systems, and tested with wider applications in 

different sectors. 

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APPENDICES 

Appendix Table A: Linguistics assessments of the professionals for the experts 

  F1 F2 F3 F4 F5 F6 F7 

DM PR1 PR2 PR3 PR1 PR2 PR3 PR1 PR2 PR3 PR1 PR2 PR3 PR1 PR2 PR3 PR1 PR2 PR3 PR1 PR2 PR3 

1 VVH VH VH EH VH VH EH H VVH EH H VH EH VVH VVH VVH VH VH EH VH VVH 

2 VH H H VVH H H VVH H VH VVH H H H H H VVH VH VH VH H VH 

3 H EH VH VH EH H H VVH H VH EH VH EH EH VVH VVH VVH VH H H H 

4 MH VVH H H VVH MH MH VH MH H VVH H EH EH VVH VH VVH VH MH MH MH 
5 M H MH MH H MH H H H MH H VH VH VH VH H VH VVH H H H 

Appendix Table B: Linguistics assessments of the experts for the alternatives 

  C1 C2 C3 C4 C5 C6 C7 C8 C9 C10 C11 C12 C13 C14 

A1 DM1 EH MH MH VH H VVH VVH VVH MH VVH VH MH VH VVH 

A1 DM2 VVH H H H H VH VH VH H VH H H H VH 

A1 DM3 VVH MH MH H VH VH VH VH H VH VH MH VH VH 

A1 DM4 VVH MH MH H VH VH VH VH H VH VH MH H VH 

A1 DM5 H MH MH H H VH VH VH MH VH H MH VH MH 

A2 DM1 VVH H H VH H VVH VH VVH H VVH H H H VH 

A2 DM2 VVH VH VH VH H VVH VH VVH VH VVH H VH H VH 

A2 DM3 VVH H MH VH H VVH VH VVH MH VVH VH VVH VH VVH 

A2 DM4 VVH H H VH H VVH VH VVH H VVH VH H VH VVH 

A2 DM5 H H H VH H VVH VH VVH H VVH H H VH H 

A3 DM1 VH MH MH VVH VVH VVH EH VH MH VH EH MH VVH EH 

A3 DM2 VH MH MH VH VVH VVH VVH VH MH H VVH MH VVH VVH 

A3 DM3 VVH M VH H EH VVH EH VH EH VVH EH M EH EH 

A3 DM4 VVH M M H EH VVH EH VH EH VVH EH M EH EH 

A3 DM5 EH M M H EH VVH EH EH M VVH EH M EH EH 

A4 DM1 H VH VH H MH VH H H VH H MH VH MH H 

A4 DM2 H VVH VVH VH H VH H VH VVH H MH VVH MH H 

A4 DM3 H VVH VVH VVH H VH H VH VVH H MH VVH MH H 

A4 DM4 H VVH VVH VVH H VH H VH VVH H MH VVH MH H 

A4 DM5 MH VVH VVH VVH H VH H H VVH H MH VVH MH MH 

A5 DM1 EH H H VVH VVH VVH EH EH H EH VVH H VVH EH 

A5 DM2 EH H H VH VVH VVH VVH VVH H VVH VH H VH VVH 

A5 DM3 EH MH MH VH VVH VVH VVH VVH MH VVH VVH MH VVH VVH 

A5 DM4 EH MH MH VH VVH VVH VVH VVH MH VVH VVH MH VVH VVH 

A5 DM5 VVH MH MH VH VVH VVH VVH VVH MH VVH VVH MH VVH VVH