Q-rung Orthopair Fuzzy Research Articles

Innovative q-Rung Orthopair Fuzzy Prioritized Interactive Aggregation Operators to Evaluate Efficient Autonomous Vehicles for Freight Transportation

Innovative q-Rung Orthopair Fuzzy Prioritized Interactive Aggregation Operators to Evaluate Efficient Autonomous Vehicles for Freight Transportation

Golden Cut-Oriented Q-Rung Orthopair Fuzzy Decision-Making Approach to Evaluation of Renewable Energy Alternatives for Microgeneration System Investments

This study aims to find an appropriate system for microgeneration energy investments and identify optimal renewable energy alternatives for the effectiveness of these projects. In this context, a model is constructed by multi stepwise weight assessment ratio analysis (M-SWARA) and technique for order preference by similarity to ideal solution (TOPSIS) with q-rung orthopair fuzzy sets (q-ROFSs) and golden cut. At the first stage, five different systems are weighted for the effectiveness of the microgeneration energy investments. Secondly, four different renewable energy alternatives are ranked regarding the performance of these projects. In addition, a comparative analysis is also implemented with intuitionistic fuzzy sets (IFSs) and Pythagorean fuzzy sets (PFSs). The findings are the same in all different fuzzy sets that demonstrates the reliability of the findings. It is determined that grid-connected with battery backup is the most important system choice. On the other hand, solar energy is the most appropriate alternative for microgeneration system investments. Grid-connected system should be implemented for the performance of the microgeneration projects. Hence, providing a sustainable access to the electricity can be possible. Sufficient amount of electricity may not be obtained from wind and solar energy because of the climate changes. In this process, grid-connected system can handle this problem effectively.

Coalition-oriented strategic selection of renewable energy system alternatives using q-ROF DEMATEL with golden cut

Hybrid energy investment projects help to increase the efficiency in renewable energy production. This situation can be a solution to the high installation cost problem of the clean energy investments. While examining similar studies in the literature, it is determined that there is a need for a new study to identify the optimal combinations of the renewable energy alternatives to increase the effectiveness of the hybrid energy investments. This study aims to identify coalition-oriented strategic selection of renewable energy system alternatives. Several combinations are weighted by q-rung orthopair fuzzy (q-ROF) decision making trial and evaluation laboratory (DEMATEL) with golden cut and coalition game theory. Intuitionistic fuzzy sets (IFSs) and Pythagorean fuzzy sets (PFSs) are also used to check the validity of the findings. Moreover, multi stepwise weight assessment ratio analysis (M-SWARA) methodology is also considered to measure the consistency of the analysis results. It is defined that solar is the most efficient energy alternative for the hybrid energy investments. Solar energy should be prioritized in hybrid investment projects where at least two of the renewable energy alternatives are evaluated together. The usage area of solar energy is wide because it is not necessary to be close to the water source or the city network to install solar panels. Additionally, solar energy systems generally do not require much maintenance that provides a cost advantage compared to others. Owing to these issues, solar energy projects provide the highest contribution in all investment combinations. The novelty of this paper is to provide a unique model by combining the methodology of q-ROF and golden cut properly with the aim of proposing a set of renewable energy system combinations in terms of coalition game theory.

A q-rung orthopair fuzzy decision-making model with new score function and best-worst method for manufacturer selection

Selecting the appropriate manufacturer is important in customized product development because a poor selection may delay the delivery schedule, increase costs, and even affect product quality. This selection task inherently involves ambiguous and imprecise information from decision-makers. The q-rung orthopair fuzzy (q-ROF) sets theory has been proven as a valuable instrument to model human uncertain expressions. However, the existing q-ROF score functions, an essential tool to rank q-ROF values, have some deficiencies, such as generating counterintuitive solutions and antilogarithm or division by zero problems. Furthermore, little research presented the modified best-worst methods (BWM) under q-ROF environments. Nevertheless, these models only generate crisp weights rather than q-ROF weights, which is against the original intention of the q-ROF BWM. To address these problems, this paper first introduces a novel q-ROF score function for measuring q-ROF values. A new q-ROF-BWM is then presented based on the q-ROF preference relations to determine the fuzzy criteria weights. Subsequently, an improved weighted aggregated sum product assessment (WASPAS) with q-ROF settings is presented. Based on them, an integrated q-ROF-BWM-WASPAS model is introduced to rank manufacturers. Additionally, a case study, sensitivity analysis, and several comparisons are conducted to illustrate and validate the usefulness of the developed model.

Application of M-SWARA and TOPSIS Methods in the Evaluation of Investment Alternatives of Microgeneration Energy Technologies

Investments in microgeneration technologies help to boost the usage of clean energy while reducing pollution. However, selecting the appropriate investment remains the most critical phase in developing these technologies. This study aims to design a multi-criteria decision-making method (MCDM) to evaluate investment alternatives for microgeneration energy technologies. The proposed MCDM is based on a Multi Stepwise Weight Assessment Ratio Analysis (M-SWARA), to define the relative importance of the factors. The Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) and q-Rung Orthopair Fuzzy Soft Sets (q-ROFSs) are used to rank investment alternatives. Calculations were also made with Intuitionistic Fuzzy Sets (IFSs) and Pythagorean Fuzzy Sets (PFSs). For analysis, five evaluation criteria were selected based on the literature: frequency of maintenance, ease of installation, environmental adaptation, transmission technologies, and efficiency of cost. Similarly, six alternatives for microgeneration technology investments were selected: ground source heat pumps, micro hydroelectric power, micro combined heat and power, micro bioelectrochemical fuel cell systems, small-scale wind turbines, and photovoltaic systems. The results showed that cost efficiency was the most significant factor in the effectiveness of microgeneration energy investments, and the photovoltaic system was the best alternative to increase microgeneration energy technology investment performance. Furthermore, the results were the same for the analyses made with IFSs and PFSs, demonstrating the reliability of the proposed method. Therefore, investors in microgeneration technologies should prioritize photovoltaic systems. This conclusion is supported by the fact that photovoltaic is a renewable energy source that has witnessed the most technological improvements and cost reductions over the last decade.

RETRACTED ARTICLE: Evaluate the challenges of sustainable supply chain 4.0 implementation under the circular economy concept using new decision making approach

Industry 4.0 has the potential of growing industrialization and, on the other hand, disrupting the sustainability of prevailing manufacturing supply chains through inducing great challenges such as higher resource consumption that, in turn, results in global warming and climate change. As a result, researchers working in the area of sustainable supply chain 4.0 need to make deep evaluations on the challenges arising for manufacturing supply chains contemplating the improvement of their sustainability levels and having a digital transformation toward Industry 4.0. To fill this gap, the current paper designs an innovative framework on the basis of the Stepwise Weight Assessment Ratio Analysis (SWARA) technique and the Complex Proportional Assessment (COPRAS) approach to evaluate the challenges that may arise for supply chain 4.0 in the q-Rung Orthopair Fuzzy Sets (q-ROFSs) setting. The proposed method uses an extended SWARA process to determine the criteria importance degrees considering the experts’ preferences. The performance of the proposed method was assessed by conducting an empirical case study under the q-ROFSs condition. Further, a sensitivity analysis was executed to check whether the proposed method is stable enough to be relied on parameter values. Finally, the results obtained were compared to those of currently used methods to verify the obtained results’ reliability. As revealed by the comparative results, the framework proposed in this article was of higher consistency and strength compared to other prevailing approaches.

INVESTIGATING THE INTERNET-OF-THINGS (IOT) RISKS FOR SUPPLY CHAIN MANAGEMENT USING Q-RUNG ORTHOPAIR FUZZY-SWARA-ARAS FRAMEWORK

Modern “Supply Chains (SCs)” have recently been introduced as value networks of high complexity, and firms have focused on its efficiency as an important support for staying competitive in the market. Firms are currently capable of observing, tracking, and monitoring their products, activities, and processes throughout their value chain networks using new technologies, namely the “Internet of Things (IoT)”. Though, the influencing factors of IoT are highly complex and diverse, which result in the information-intensiveness of the SCs processes. This, in turn, leads to lots of barriers to SCs. In this paper, we evaluate and rank the IoT risks for “Supply Chain Management (SCM)” by utilizing “Stepwise Weight Assessment Ratio Analysis (SWARA)” and “Additive Ratio Assessment (ARAS)” under “q-Rung Orthopair Fuzzy Sets (q-ROFSs)”. A case study is presented for investigating the IoT risks for SCM in the q-ROFSs setting. Moreover, the obtained results were compared to those of some methods currently used in the literature. The outcomes of the study show that the security and privacy risks with a weight value of 0.0572 is the main IoT risk factor for the SCM and the organization-I with the utility degree 0.8208 is the best option with diverse IoT risks for SCM.

Analysis of Maclaurin Symmetric Mean Operators for Managing Complex Interval-Valued q-Rung Orthopair Fuzzy Setting and Their Applications

Risk is demonstrated as unknowns that have measurable possibilities, while complication requires unknown with no significant possibilities of the outcome. These notions are associated but are not identical. Ambiguity and risk are closely concerned notions in decisionmaking strategies using fuzzy set theory. Similarly, Maclaurin symmetric mean (MSM) is also massive beneficial and valuable for using to accumulate the family of attributes into a singleton set. To enhance the superiority of the research work, in this scenario, we used the informative idea of a complex interval-valued q-rung orthopair fuzzy (CIVq-ROF) setting and took a valuable tool of MSM to present the CIVq-ROF MSM (CIVq-ROFMSM), CIVq-ROF-weighted MSM (CIVq-ROFWMSM), CIVq-ROF dual MSM (CIVq-ROFDMSM), and CIVq-ROF-weighted dual MSM (CIVq-ROFWDMSM) operators. To verify the supremacy of the invented works for the different values of parameters, several specific cases are also explored. Finally, with the help of multi-attribute decision-making (MADM) skills, we identified a beneficial optimal in the presence of the source of descriptions in the form of invented operators using the decision making process. Comparison of the invented approaches with many existing scenarios is also simplified at the end of this analysis, which shows the dominancy and competency of the diagnosed approaches.

A new integrated multi-attribute decision-making approach for mobile medical app evaluation under q-rung orthopair fuzzy environment

Mobile medical app evaluation can be modelled as a multi-attribute decision-making (MADM) problem with multiple assessment attributes. Due to the increasing complexity and high uncertainty of decision environments, numerical numbers and/or traditional fuzzy sets may not be appropriate to model attribute information of mobile medical apps. In addition, heterogeneous relationships are often observed among different attributes in various practical decision situations. To deal with these issues, a q-rung orthopair fuzzy (q-ROF) MADM approach, which is a very powerful tool for describing vague information occurring in real decision circumstances, is proposed to handle decision-making problems in medical app evaluation. In particular, q-rung orthopair fuzzy numbers (q-ROFNs) are first applied to better express the preference information and expert assessment information. Then, q-ROFNs are extended by combining with Zhenyuan integral, resulting in the q-ROF Zhenyuan integral (q-ROFZI). This integral can capture complementary, redundant and/or independent characteristics among the attributes and is superior to existing operators on q-ROFNs. Next, based on the best-worst method (BWM) and Shapley value, two optimization models are constructed to objectively identify optimal fuzzy measures on the attribute set. Finally, a novel integrated q-ROF MADM approach is proposed and its computation procedure is presented and illustrated with its application to the problem of mobile medical app evaluation. A comparative analysis is carried out to demonstrate the validity, rationality, robustness and superiority of the developed method.

A q-Rung Orthopair Fuzzy FUCOM Double Normalization-Based Multi-Aggregation Method for Healthcare Waste Treatment Method Selection

Healthcare waste (HCW) management is an intricate issue upon which numerous factors, such as technical, economic, environmental, and social factors, have an impact. A determination on the best treatment method for HCW management can be viewed as a challenging multi-criteria decision-making (MCDM) problem in which various options and evaluation criteria are considered. One critical concern when assessing HCW treatment (HCWT) methods is the representation and treatment of dubious data. In this paper, we present a q-rung orthopair fuzzy full consistency method double normalization-based multi-aggregation methodology called q-ROF-FUCOM-DNMA to solve MCDM problems with q-rung orthopair fuzzy information (q-ROFI). In the proposed approach, criteria weights are estimated through the full consistency method (FUCOM) and a ranking of the alternatives is obtained through the double-normalization-based multi-aggregation (DNMA) method with q-ROFI. A HCWT method assessment issue was considered in order to clarify the relevance of the proposed approach. Five HCWT methods, including chemical disinfection, microwave disinfection, incineration, autoclaving (steam sterilization), and reverse polymerization, were considered as alternatives. The results show that autoclaving (steam sterilization) is the most efficient HCWT method. Furthermore, we performed a sensitivity analysis to determine the stability of the proposed approach. Additionally, we compared the presented approach with existing methods.

Tri-reference point method for [formula omitted]-rung orthopair fuzzy multiple attribute decision making by considering the interaction of attributes with Bayesian network

As an irrational behavior theory, the tri-reference point (TRP) method proposed by combining multiple reference points and practical scenarios can consider more complex and realistic scenarios. In order to explore the application of TRP under q-rung orthopair fuzzy (q-ROF) environment, we construct a new TRP model and solve the multi-attribute decision making (MADM) problem with Bayesian network (BN). More specifically, considering that BN can automatically learn the relationship of attributes from both the direction of influence and the degree of interaction, we firstly introduce the BN into q-ROF environment to depict the interaction between attributes in a MADM. BN can deduce posterior probability according to the prior knowledge, so it can calculate the probabilities of attributes for a MADM problem under q-ROF environment. Based on their probabilities, we further propose an improved Borda score method to calculate the attributes weights. Then, inspired by prospect theory, we develop a new TRP model by utilizing the double-S shape of TRP. Meanwhile, a novel comparison method for two q-rung orthopair fuzzy numbers (q-ROFNs) is presented which combines possibility degree method and score function. Finally, we give an example of land investment project selection of rural cooperative to elaborate and verify our proposed method.

Complex Interval-Valued q-Rung Orthopair Fuzzy Hamy Mean Operators and Their Application in Decision-Making Strategy

This paper deals with uncertainty, asymmetric information, and risk modelling in a complex power system. The uncertainty is managed by using probability and decision theory methods. Multi-attribute decision-making (MADM) technique is a very effective and well-known tool to investigate fuzzy information more effectively. However, the selection of houses cannot be carried out by utilizing symmetry information, because enterprises does not have complete information, so asymmetric information should be used when selecting enterprises. Hamy mean (HM) operator is a feasible tool to handle strategic decision-making problems because it can capture the order between the finite input terms. Additionally, the complex interval-valued q-rung orthopair fuzzy (CIVq-ROF) setting is a broadly flexible and massively dominant technique to operate problematic and awkward data in actual life problems. The major contribution of this analysis is how to aggregate the collection of alternatives into a singleton set, for this we analyzed the technique of CIVq-ROF Hamy mean (CIVq-ROFHM) operator and CIVq-ROF weighted Hamy mean (Cq-ROFWHM) operator and some well-known results are deliberated. Keeping the advantages of the parameters in HM operators, we discussed the specific cases of the invented operators. To investigate the decision-making problems based on CIVq-ROF information, we suggested the following multi-attribute decision-making (MADM) technique to determine the beneficial term from the finite group of alternatives with the help of evaluating several examples. This manuscript showed how to make decisions when there is asymmetric information about enterprises. Finally, based on the evaluating examples, we try to discover the sensitive analysis and supremacy of the invented operators to find the flexibility and dominancy of the diagnosed approaches.

Multiple attribute dynamic decision making method based on some complex aggregation functions in CQROF setting

The q-rung Orthopair fuzzy set (QROFS) is one of the fuzzy structures which can introduce more fuzzy information than other fuzzy frames proposed by Ronald R. Yager. In this article, the dynamic multiple attribute decision making (DMADM) approach with complex q-rung Orthopair fuzzy (CQROF) information has been introduced. The ideas of CQROF variable and uncertain CQROF variables are defined and introduced new dynamic weighted averaging (DWA) operators called dynamic complex q-rung Orthopair fuzzy weighted average (DCQROFWA) operator and uncertain dynamic complex q-rung Orthopair fuzzy weighted average (UDCQROFWA) operator. For the moment, a procedure has been developed based on DCQROFWA and CQROFWA operator to solve DMADM problems where all attribute information are used in complex q-rung Orthopair fuzzy numbers (CQROFNs) collected at distinct periods, and another procedure is developed based on UDCQROFWA and CIVQROFWA operators to solve uncertain DMADM problems for interval uncertainty in which all attribute information takes in the form of complex interval-valued q-rung Orthopair fuzzy numbers (CIVQROFNs) collected at distinct periods. Finally, a comprehensive comparative analysis has been made for the proposed approach for testing its applicability and efficiency by considering a numerical example.

Safe E-scooter operation alternative prioritization using a q-rung orthopair Fuzzy Einstein based WASPAS approach

E-scooters globally have proven an increasingly popular form of dockless micro-mobility, while also contributing to sustainable urban transportation forms. However, some safety issues arise with e-scooter use in the cities. This study aims to propose a decision-making model based on q-rung orthopair fuzzy sets for prioritizing the safe e-scooter operation alternative. The proposed model consists of two stages: weighting the criteria and ranking the alternatives. First, a fuzzy logarithmic additive assessment of the weight coefficients methodology and fuzzy Einstein weighted averaging operator were applied to define the reference relationships between the criteria and determine their weights. Second, a q-rung orthopair fuzzy sets based decision-making model integrating q-rung orthopair fuzzy Einstein average and q-rung orthopair fuzzy Hamacher geometric mean operator was used to rank the alternatives. A fictional case study is presented to show the practicality of the proposed model. The contribution of the work is as a decision-support system for evaluating safe e-scooter strategies, including infrastructure placement, user behavior and how e-scooters interact with other transportation means, showing that applicability of the proposed model to real-world problems.

Confidence levels under complex q-rung orthopair fuzzy aggregation operators and their applications

The major contribution of this analysis is to analyze the confidence complex q-rung orthopair fuzzy weighted averaging (CCQROFWA) operator, confidence complex q-rung orthopair fuzzy ordered weighted averaging (CCQROFOWA) operator, confidence complex q-rung orthopair fuzzy weighted geometric (CCQROFWG) operator, and confidence complex q-rung orthopair fuzzy ordered weighted geometric (CCQROFOWG) operator and invented their feasible properties and related results. Future more, under the invented operators, we diagnosed the best crystalline solid from the family of crystalline solids with the help of the opinion of different experts in the environment of decision-making strategy. Finally, to demonstrate the feasibility and flexibility of the invented works, we explored the sensitivity analysis and graphically shown of the initiated works.

Evaluation of circular supply chains barriers in the era of Industry 4.0 transition using an extended decision-making approach

PurposeThe poor leadership style is a key obstacle to the effective implementation of Industry 4.0 technologies. To successfully apply the Industry 4.0 technologies, which can enhance the sustainability of firms, senior management needs to be inspiring and transformational. On the other hand, numerous factors can hinder the Industry 4.0 transition and “Circular Supply Chain (CSC)” transformation. Therefore, the main purpose of this study is to evaluate the related barriers of CSCs in the era of Industry 4.0 transition.Design/methodology/approachThe current study developed an innovative decision-making approach with the help of the “Combined Compromise Solution (CoCoSo)” method and “Criteria Importance Through Intercriteria Correlation (CRITIC)” method on the “q-Rung Orthopair Fuzzy Sets (q-ROFSs).” CRITIC in this combined method was used to predict the importance or weighting degrees of the CSCs barriers in the age of Industry 4.0 transition.FindingsThe results of this study found that the absence of knowledge about the Industry 4.0 technologies and circular approaches was the first barrier followed by the problems associated with data security in relationship management in circular flows, the deficiency of knowledge regarding the data management among stakeholders and the lack of awareness about the potential benefits of autonomous systems in labor-oriented “End-of-Life (EOL)” activities for CSCs in the era of Industry 4.0 transition.Research limitations/implicationsA limitation may be that despite the generalizability of the proposed framework, the results may differ when it is implemented in different sectors. By emphasizing the obstacles to sustainable operations of supply chains (SCs) in the context of circular economy (CE) and Industry 4.0, researchers working in the same domain may be encouraged to find ways to remove such obstacles in different settings. As suggested in this study, the priority of various barriers helps researchers suggest effective strategies for the sustainable development of companies within the current dynamic business atmosphere.Practical implicationsThe findings of this paper can aid industry practitioners in fixing their attention on the digitization or automation of their systems in the context of sustainability or resource circularity. Note that within the current context of CE, one of the crucial issues is how to conserve the existing resources; the answer to this question can save the environment.Originality/valueThe current paper proposed a new multi-criteria decision-making method using q-ROFSs to analyze, rank and evaluate the CSC barriers in the age of Industry 4.0 transition. To this end, a new decision-making approach with the help of CRITIC and CoCoSo methods on q-ROFSs called q-ROF-CRITIC-CoCoSo was introduced to evaluate the CSCs barriers in the era of Industry 4.0 transition.

An Integrated Decision-Making Approach Based on q-Rung Orthopair Fuzzy Sets in Service Industry

This study defines key issues for sustainable healthcare policy in COVID-19 period. For this purpose, 9 different criteria that affect vaccine hesitancy are selected with the help of a detailed literature evaluation. A novel hybrid fuzzy decision-making model is developed using DEMATEL and TOPSIS based on q-Rung orthopair fuzzy sets. A comparative evaluation has also been performed using IF DEMATEL and PF DEMATEL. The results of all different methods are almost the same that indicates the reliability and coherency of the proposed model. The findings demonstrate that religion is the most critical factor that causes vaccine hesitancy. It is also defined that active population in daily life is the most important alternative. Developing countries should mainly focus on the actions regarding the religious issues to have sustainable healthcare policies in COVID-19 period. In this context, religious leaders can be released to the media and give information that the vaccine is not against religious rules. This has a significant contribution to convince people who are against the vaccine. Furthermore, these countries should also give priorities to the active population in daily life. Because this group supports the workforce in the country very seriously, it can be possible to increase the workforce in the country by completing the vaccination of this group that helps to boost economic development.

Multicriteria q-Rung orthopair fuzzy decision analysis: a novel approach based on Archimedean aggregation operators with the confidence levels

The confidence levels can reduce the influence of the unreasonable evaluation value that was given by the decision-maker on the decision-making results. The Archimedean t-norm and t-conorm (ATS) also have many advantages for the processing of uncertain data. Under this environment, the confidence q-rung orthopair fuzzy aggregation operator based on ATS is one of the most successful extensions of confidence q-rung orthopair fuzzy numbers in which we decrease the deviation caused by the subjective perspective of the decision-maker in the multicriteria group decision-making problems. In this paper, we propose weighted, ordered weighted averaging aggregation operators and weighted, ordered weighted geometric aggregation operators based on ATS, respectively. Moreover, the properties and four specific forms associated with aggregation operators are also investigated. In this study, a novel MCGDM approach is introduced by using the proposed operator. A reasonable example is proposed and compared the results that are obtained by our operators and that in the existing literature, so as to verify the rationality and flexible of our method. From the study, we concluded that the proposed method can reduce the impact of extreme data, and make decision-making results more reasonable by considering the attitudes of decision-makers.

An Extended QUALIFLEX Method with Comprehensive Weight for Green Supplier Selection in Normal q-Rung Orthopair Fuzzy Environment

An Extended QUALIFLEX Method with Comprehensive Weight for Green Supplier Selection in Normal q-Rung Orthopair Fuzzy Environment

Multiple attribute group decision making based on multigranulation probabilistic models, MULTIMOORA and TPOP in incomplete q-rung orthopair fuzzy information systems

The concept of q-rung orthopair fuzzy sets (q-ROFSs) severs as an extended form of orthopair fuzzy sets, which excels in flexibly depicting imprecise information existed in multiple attribute group decision making (MAGDM) via allowing a greater space in terms of membership degrees (MD) and non-membership degrees (ND). Moreover, incomplete information systems play a significant role in depicting incomplete information existed in MAGDM. In this paper, for the sake of exploring MAGDM with imprecise and incomplete information, a new MAGDM method based on multigranulation probabilistic models, MULTIMOORA (Multi-Objective Optimization by Ratio Analysis plus the full MULTIplicative form) and the technique of precise order preference (TPOP) method in incomplete q-rung orthopair fuzzy (q-ROF) information systems is systematically investigated. First, the concept of multigranulation (MG) incomplete q-ROF information systems is established. Then, a completion technique is put forward to obtain MG q-ROF information systems via patching lost values. Moreover, three versions of MG q-ROF probabilistic rough sets (PRSs) are put forward in light of MG q-ROF information systems. Afterwards, a new MAGDM method is constructed by means of MG q-ROF PRSs, MULTIMOORA and the TPOP method. At last, two experimental studies from open datasets are performed to present the applicability of the constructed MAGDM method, and corresponding sensitivity analysis and comparative analysis are further conducted to demonstrate the validity of the presented methodology.