A fuzzy multicriteria group decision approach for circular business models prioritization

Paper aims : Presents a new group decision approach for circular business models (CBMs) prioritization based on circular economy (CE) principles and indicators. Originality : It was not found in the literature quantitative approaches to indicate which CBMs can be prioritized towards CE implementation. Research method : Fuzzy AHP is applied to calculate the weights of the CE principles. Fuzzy TOPSIS is used to rank the CBMs. A pilot application demonstrates the applicability of the proposed approach. Main findings : To perform equally on all dimensions of the circularity indicators, recovery by-products have a greater impact on CE implementation. Focusing on economic indicators, Product as a Service and Recovery By-Products should receive priority. Focusing on social indicators, Product as a Service is the most recommended CBM. Implications for theory and practice : It was identified the CBMs that are most suitable for performance improvement regarding CE implementation, according to the organization’s dominant CE principles.

. The business models are the main source of value creation in organizations (Suchek et al., 2021;Ferasso et al., 2020;Richardson, 2008). To be considered circular, a business model should be designed to create, deliver, and capture economic value while simultaneously contributing to environmental and social aspects (Suchek et al., 2021;Lüdeke-Freund et al., 2018). Hence, a circular business model (CBM) is defined as the logic of how an organization creates, delivers and captures value to close and slow loops (Antikainen & Valkokari, 2016;Bocken et al., 2016), and share these values with different stakeholders (Bertassini et al., 2021a).
The transition towards CE depends on the implementation of various CBMs (Husain et al., 2021), and usually the combination of various CBMs. However, there is always one business model that is predominant in the organization (e.g., if an organization has product-as-a-service as its business model, probably it will depend on product life cycle extension and/or recovery to enable the operationalization of the 'main' business model). Thus, the organization needs to choose/prioritize which CBMs will be the predominant in accordance with the organization's main strategies and goals to define the processes, activities, resources, customers, investments, revenues and other factors that are important for the implementation of the CBM. Moreover, the successful implementation of CBMs is directly dependent of the relationship between CE principles and indicators, since companies need to incorporate CE principles in their operations and culture (Bertassini et al., 2021b) and use indicators to measure how well they are performing in the CE transition (Rossi et al., 2020). The use of indicators to measure circularity performance is essential to improve and assess CBMs. However, the measurement and assessment of circularity performance are yet incipient in companies (Sassanelli et al., 2019). To address this issue, Rossi et al. (2020) developed a group of indicators, focused on the three dimensions of sustainability, which are environmental, economic, and social. In this way, to overcome the limitations of conventional indicators, the authors applied these indicators in CBMs to capture the innovations brought by CE, supporting companies to identify areas with high importance and potential for improvement, and thus to increase CE performance. Based on the CE principles and the circularity indicators, organizations may prioritize the most important CBM for its strategical goals. In this direction, only Husain et al., (2021) proposed a model to rank the most important CBMs implementation, however, they have not considerated the relationship between CE principles and circularity indicators in their model.
This relationship can only be assessed by experts with an in-depth knowledge of CE and of the organization in focus. In this direction, Keshavarz Ghorabaee et al. (2017) highlighted that human judgments contain some uncertainty and ambiguity. In this way, Computing with Words (CW) is a necessity when the accessible information is not enought precise to justify the use of numbers and points that CW encompasses a fusion of natural language and computation with fuzzy variables (Zanon et al., 2020;Zadeh, 1965). Therefore, the fuzzy set theory (FST) is one of the most efficient tools to deal with the uncertainty of evaluation processes (Caiado et al., 2021;Tavassoli et al., 2020;Keshavarz Ghorabaee et al., 2017).
In this direction, the combination of multicriteria group decision making (MCGDM) techniques with the fuzzy set theory can bring significant advantages. The fuzzy Analytic Hierarchy Process (AHP) processes pairwise comparative judgments given by the decision makers (Shete et al., 2020;Lima-Junior et al., 2014). These pairwise comparisons are adequate to deal with the subjectiveness during the weights elicitation process (Torkabadi et al., 2018;Dede et al., 2016). Another combination of a MCGDM technique with the fuzzy set theory corresponds to the fuzzy Technique for Order Performance by Similarity to Ideal Solution (TOPSIS) technique (Mahpour, 2018). It ranks alternatives by calculating their mathematical distance both to the positive ideal solution to the negative ideal solution.
There is one study in literature that aims to rank the business models for the successful adoption of CE using fuzzy TOPSIS (Husain et al., 2021). However, to the best of the authors' knowledge, no paper was found proposing to investigate the relations between CE principles and indicators, using fuzzy MCGDM techniques to consider the inherent subjectivity of this context and to reduce research bias. Moreover, no study was found applying these techniques to calculate weights for both the CE principles and indicators, as well as using these techniques to provide recommendations to experts along with CBM feedbacks for the focus organization. Thus, this paper aims to develop a fuzzy multicriteria group decision making model for circular business models prioritization by combining the fuzzy AHP and fuzzy TOPSIS techniques for, respectively, finding the weights of each CE principles considering the specific context of the company under analysis and to build a rank of preference of CBMs according to the organization CE principles. The fuzzy MCGDM techniques were implemented in the Microsoft Excel® software and an illustrative application is presented to exemplify the use of the developed approach in practice.
The paper is organized as follows: section 2 presents the literature review regarding the circular economy construct and fuzzy MCGDM techniques; section 3 presents the proposed model; section 4 brings the results

Literature review
CE has several definitions as presented by Kirchherr et al. (2017). The most know definition of CE points that a circular economy is an industrial system that is restorative or regenerative by intention and design, and seeks to provide multiple value-creation mechanisms which are decoupled from the consumption of finite resources (Ellen MacArthur Foundation, 2012. Considering this definition, the BSI (British Standards Institution, 2017) proposed the six principles that guide the implementation of CE concepts in companies: 1. Systems thinking: a holistic approach to understanding the interactions between individuals and activities within the wider system they are part of; These six principles comprehend, in generic terms; all the aspects that should be covered by a circular system, which can be applied in products/services, processes, business models, value chains, people, and organizational structures. Companies will only achieve a fully circular system when all the six principles are implemented (Agrawal et al., 2021;Bocken et al., 2019). One way to implement the CE principles is through the proposition of CBMs.
CBMs is considered a strategy to achieve sustainability (Geissdoerfer et al., 2017) and can be defined as "[...] the rationale of how an organization creates, delivers, and captures value with slowing, closing, or narrowing flows of the resource loops [...]" (Oghazi & Mostaghel, 2018, p. 3). According to the BSI (British Standards Institution, 2017), there are six types of CBMs: 1. On-demand: produces a product or provides a service only when consumer demand has been quantified and confirmed; 2. Dematerialization: replaces physical infrastructure and assets with digital/virtual services; 3. Product life cycle extension/reuse: products designed to be durable and easy to repair; 4. Recovery of secondary raw materials/by-products: creates products from secondary raw materials/by-products and recycling; 5. Product as service: delivery product performance or defines results rather than the product or service itself; 6. Sharing economy: collaborative consumption amongst users, either individuals or organizations.
According to Rossi et al. (2020) the use of circularity indicators to measure the performance of companies in implementing CE is essential to improve and assess the CBMs. In this way, Rossi et al. (2020) proposed a group of indicators, focused on the three dimensions of sustainability to capture the innovations brought by CE that conventional indicators do not measure. Besides, Rossi et al. (2020) also presented how each CE indicator affects the achievement of each CE principle and how each CBM affects each CE indicator. The intensity levels of the relationships was represented by the linguistic terms strong, median, and weak, as presented in Table 1, Table 2 and  Table 3. These levels of intensity mean that the indicators with strong connections are very efficient to achieve CE. The indicators with median connections could help in the achievement of the requirements but in the proposition of circular solution regarding the product/service or process. The indicators with weak connections could be applied in the initial stages of the CE journey once they are useful to explore the opportunities. The data presented in Table 1. Relationship between CE principles and material indicators proposed.   Table 2 and Table 3 proposed in the research of Rossi et al. (2020) is used in this study as the basis to define the relationship between CE principles and circularity indicators to prioritize the implementation of CBMs.
There are several studies in the recent literature that combines diverse fuzzy techniques considering aspects of MCDM to address CE issues and some of them can be highlighted since they are related to the fuzzy AHP and fuzzy TOPSIS techniques. Tariq et al. (2021) used the fuzzy TOPSIS to evaluate how multiple alternatives for the disposal of diapers can provide sustainable advantages in the Pakistan scenario. Mahpour (2018) applied fuzzy TOPSIS to prioritize the potential barriers to adopt circular economy in construction and demolition waste management from behavioral, technical, and legal perspectives and aggregately. Lee et al. (2021) used fuzzy AHP combined with the fuzzy TOPSIS to propose a comprehensive list of evaluation criteria to rank recycling outlets, and develop an end-of-life tire outlets selection matrix.
Lahane & Kant (2021) proposed a hybrid framework using fuzzy AHP e fuzzy VIKOR to rank solutions for mitigating the risks of circular supply chain implementation. Agrawal et al. (2021)    the fuzzy TOPSIS was combined with DELPHI and Best-worst method to evaluate critical barriers and pathways to implementation of e-waste formalization management systems. Nara et al. (2021) present the application of fuzzy TOPSIS to classify Industry 4.0 technologies based on sustainable development impacts. More studies using MCGDM techniques and fuzzy set theory to solve CE problems is presented in Table 4.  Govindan (2022) Identifies the barriers that exist with the implementation of blockchain technology in the application of the remanufacturing sector. DEMATEL is used to identify the effective and most influential barriers among common barriers.

DEMATEL CE barriers
Shahidzadeh & Shokouhyar (2022) Conceptual model of sustainability was proposed, discussed and analyzed to determine the relationship between reverse logistics performance and sustainability.  A theoretical framework that identifies and evaluates drivers and sub-drivers that are needed for the adoption of circular principles in product-service system business model.   (2020) Evaluate the key strategies to accomplish CE and to develop a causal relationship among these strategies.

DEMATEL CE strategies
Mahpour (2018) Prioritize the potential barriers to adopt circular economy in construction and demolition waste management from behavioral, technical, and legal perspectives and aggregately. Based on the review of previous studies we identified that just one study (from our set of publications) did a proposition to rank CBMs (Husain et al., 2021). However, in this study the authors defined some successful criteria to rank the CBMs (Partnership, Activities, Resources, Value proposition, Customer relationships, Distribution Channels, Client segments, Cost structure, Revenue flows) instead of using the relationship between CE principles and circularity indicators as we are proposing in the present research. The novelty of this study remains in the adoption of CE principles and circularity indicators to prioritize CBMs. Performance indicators are essential to show how well an organization is performing in CE and what could be improved. In this sense, use the circularity indicators to prioritize CBMs may help companies set the parameters such as technologies, resources, people, cultural aspects, legislations and others things that are needed for the implementation of CE in the specific context for the organization.

Fuzzy sets
Initially proposed by Zadeh (1965), the theories based on fuzzy sets stand out due to their ability to be combined with several multi-criteria techniques in the proposition of decision-making models that address data imprecision and uncertainty in human judgement (Deng et al., 2021;Zanon et al., 2020;Malviya et al., 2018;Kahraman et al., 2015). Linguistic variables and fuzzy numbers are used to represent decision makers' subjective assessments of the alternatives' performance and criteria weights considered in a problem (Abdullah, 2013). The linguistic variables are represented qualitatively using linguistic terms and quantitatively translated by fuzzy sets in a discourse universe using pertinence functions (Klir & Yuan, 1995).
According to Dubois (1980), for a given universe X → 0,1     , a fuzzy set A  can be defined as: , then x partially belongs to the fuzzy set A  . The triangular membership function is one of the most common shapes used to represent a fuzzy number (Klir and Yuan, 1995). Let , l m and u, be real numbers with l m u < < , in which m represents the point of maximum membership degree, and outside the range , l u     , the degree of membership is null, then the triangular membership , , Z l m u =  be two triangular fuzzy numbers (TFN) with 1 0 l ≥ , 2 0 l ≥ , and K  be a real number, then the euclidian distance ( ( ) , d Y Z   ) between two TFN is described as in Equation 2 (Wan et al., 2013).
To deal with hierarchical evaluations and the operations of scoring, weighting, and aggregating judgments under a fuzzy environment, the fuzzy weighted average is widely applied in several studies (Chang & Hung, 2005;Guh et al., 2008).
 be a set of fuzzy numbers that represent the rates given to some alternatives

Fuzzy AHP
The Analytic Hierarchy Process (AHP) was proposed by Saaty (1980) and it is a MCDM that have been widely applied in several research areas, such as: engineering, business, decision sciences, environmental sciences, social sciences, economics, among others (Vieira et al., 2017;Zyoud & Fuchs-Hanusch, 2017),. The AHP is one of the most important MCDM to support decision-making problems (Wang et al., 2020;Ikram et al., 2020). In this way, the AHP can aim the experts to obtain the relative importance of a set of alternatives or criteria. However, the AHP is not fully appropriated to deal with the subjectiveness judgments of decision makers (Sultana et al., 2015). Chang (1996) proposed the fuzzy AHP, which is a technique adequate to capture the ambiguities and uncertainty present in decision makers judgments (Lima-Junior et al., 2014;Keshavarz Ghorabaee et al., 2017).
The fuzzy AHP expresses comparative judgments given by the decision makers through the use of linguistic variables (Lima-Junior et al., 2014 a goal set. According to Chang (1996), each object must be analyzed for each goal, producing m extend the analysis for each object as shown in where all the j gi M are TFNs. The value of fuzzy synthetic extent related to i th object is computed with Equation 5: The can be computed with the following Equation 7: Next, is necessary to calculate the degree of possibility of ( ) ( ) Next, the degree of possibility for a convex fuzzy number be greater than k convex fuzzy numbers ( ) Which can be normalized and next to be represented by Equation 13: where W is a crisp number.
To check the consistency of the expert's judgments, after the pairwise comparisons, the consistency ratio (CR) must be calculated. For that, firstly it is necessary to defuzzify the matrix with the graded mean integration, given by Equation 14.
Next, only for the calculation of the CR reasons, consider j w as the normalized weight of the alternative j by applying Equation 15, proposed by Saaty (2008), and the ij a as the all the pairwise comparations between the alternatives, which was defuzzyfied by applying Equation 14. The i ϑ must be calculated for each alternative with Equation 16.
where, n RI is a random index, which can be obtained in Table 5, according to the number n of alternatives. If CR < 0.1, the matrix can be considered consistent. Otherwise, the matrix is not consistent and the expert evaluations should be revised.

Fuzzy TOPSIS
The TOPSIS (Technique for Order Performance by Similarity to Ideal Solution) is a widely applied technique to solve MCDM problems that aim to rank the alternatives and select the best solution based on criteria and using a simple and intuitive algorithm (Montanari et al., 2021;Yadav et al., 2018;Onat et al., 2016;Wanke et al., 2015). The development of the TOPSIS algorithm is based on the idea to achieve a solution that is both as close as possible to the positive ideal solution and as far as possible from the negative ideal solution Raut et al., 2017;Shukla et al., 2017). Since its proposition by Hwang & Yoon (1981), the TOPSIS technique has become one of the most used MCDM methods with the development of different extension proposals (Çelikbilek & Tüysüz, 2020). To deal with different experts' subjective judgments, which can be imprecise and uncertain, Chen (2000) proposed the fuzzy TOPSIS. The fuzzy TOPSIS also became a very popular and successfully applied technique in several current real-world challenges from many research fields (Palczewski & Sałabun, 2019).
In the fuzzy TOPSIS, linguistic variables are used by the decision-makers to evaluate the alternatives. These linguistic variables are represented by fuzzy numbers that are used in the following steps of the TOPSIS algorithm (Nădăban et al., 2016).
Step 1:aggregate the linguistic variables provided by the decision-makers on the performance of each alternative and the weight of the criteria through Equations 20 and 21.
Where k ij x  is a fuzzy element that represents the judgment of decision-maker ( ) for the performance of the alternative i = (1, 2, …, n) related to the criterion ( ) 1, 2, , j m = … . k j w  is the fuzzy element that represents the judgment of decision-maker k for the weight of the criterion j .
Step 2: create a decision matrix D  to represent all the performances ( ) Step 3: normalize the matrix D  using a linear transformation scale represented by the Equations 24 to 26 to get the matrix R  .
Step 4: multiply the elements ij r in matrix R  by the weights j w  to obtain the matrix V  as shown in Equations 27 and 28.
Step 5 Step 6: Calculate de distance i S + between the values of FPIS (F + ) and the scores of the alternative i A in the V  matrix using Equations 31 and 32. The same procedure should be performed for the calculus of the distance i S − between the values of FNIS (F − ) and the scores of the V  matrix. For this purpose, the Euclidian distance between two triangular fuzzy numbers presented in Equation 2 is used.
Step 7: Compute the closeness coefficient i CC for each alternative i A using Equation 33. Then, based on the i CC results, a ranking of the alternatives i A is created in decreasing order. The closer the coefficient is to 1, the better is the overall performance of the alternative. The proposed model uses the hybridization of fuzzy AHP and fuzzy TOPSIS techniques, since both techniques are necessary for different purposes. The fuzzy AHP is commonly used to determine the relative weights of decision criteria, as can be seen in several studies (Büyüközkan & Güler, 2021;Ortiz-Barrios & Alfaro-Saiz, 2020;. In addition, the fuzzy TOPSIS is an adequate technique to find an alternative's priority rank (Montanari et al., 2021). Despite of fuzzy AHP is also often used to rank alternatives, it was not appropriate to use it to rank the alternatives, since the available inputs of relationship between CE indicator and CBM (Table 1, Table 2 and Table 3) are not pairwise comparisons.
As can be seen in Figure 1, the proposed decision making model is composed of four steps.
Step 1 consists of the parametrization of the fuzzy numbers as detailed in section 3 and the selection of the CE principles. In this way, it is necessary to define the linguistic terms and the correspondent fuzzy sets to the judgments

In
Step 2, the experts should evaluate the preference relations between the CE principles, presented in section 2, using the linguistic terms defined in Step 1. Note that, since the experts' assessments are independent, the consistency ratio (CR) should be checked for each one of them. Therefore, it is necessary to apply Equations 14 to 19 to calculate the CR of each decision maker set of assessments. If CR < 0.1, the assessments are considered consistent, otherwise, the decision makers with a CR ≥ 0.1 must review their assessments. Then, the expert's assessments can be aggregated using the arithmetic mean (Lima-Junior et al., 2014): Following the fuzzy AHP procedure, it is necessary to compute the values of the fuzzy synthetic extent, by applying Equations 5 and 7. Next, the degrees of possibility of the fuzzy values must be calculated with Equations 9 and 10. Finally, the CE principles weight vector ' W can be calculated using Equation 12, which should be normalized. To begin Step 3, firstly it is necessary to select the adequate CE indicators for the organization since not all of them can be applied for all organizations. Next, is necessary to calculate the weights of the CE indicators, by using the fuzzy weighted averaging (FWA) aggregation operator, to aggregate the intensity level of the relationship of each CE principle for all CE indicators. Therefore, by applying Equation 3, using the weights of the CE principles, computed in Step 2, and the level of the relationship between the CE principles and the CE indicators, the CE indicators weights can be calculated. Note that the intensity level of the relationship of each CE principle for all CE indicators should be assessed by the DMs.
Finally, with fuzzy TOPSIS technique, it is possible to prioritize the mentioned CBMs in Section 2. In this way, Step 4 uses the CE indicators weights, calculated in Step 3, and the intensity level of the relationship between the CE indicators and the CBMs, which also have to be assessed by the DMs. The ij p  index, from Equation 20, is composed by the level of the intensity of the relationship between the CE indicators and the CBMs. The  j K value corresponds to the normalized CE indicators weights, which can be computed by defuzzifying the CE indicators weights computed in Step 3 with Equation 14 and normalizing them.
Following the fuzzy TOPSIS procedure, the intensity level of the relationship between the CE indicators and the CBMs converted in TFNs. Next, the decision matrix must be normalized with Equations 24 to 26. Using Equation 28, the normalized decision matrix has to be multiplied using the CE indicators weights.

Results
In order to illustrate the step-by-step of the model proposed in section 4, a manufacturer from the automotive industry supply chain was chosen for an illustrative application. This organization aims to implement CE to related to the pairwise comparisons between the preference orders of the CE principles. In addition, it is necessary to define the fuzzy sets related to the linguistic term which represents the intensity level of the relationship between the CE principles, the CE indicators, and CBM. An example of linguistic terms and the correspondent fuzzy sets can be seen in Table 6 and 7. Table 7. Fuzzy linguistic terms to represent the intensity level of the relationship. (5,9,9) Medium (1, 5, 9)

Fuzzy Linguistic Terms Triangular Fuzzy Number
Extremely more important (EI) (7,9,9) Much more important (MMI) (3, 5, 7) More important (MI) (1, 3, 5) A little more important (LMI) (1, 1, 3) Equally important (EI) (1, 1, 1) become more sustainable. However, to initiate the transition towards CE, the organization needs to decide which CBM is more suitable for its context and is more valuable to put resources. Therefore, to select the most suitable CBM based on the CE principles, four organization's specialists in sustainability and CE were selected to judge the relative importance of the CE principles. In Step 1, all the CE principles were selected, Table 6 and Table 7 show the fuzzy linguistic terms and the TFNs for the pairwise comparisons and to represent the intensity level of the relationship, respectively. Note that the linguistic terms used to represent the intensity level of the relationship between the CE principles, the CE indicators, and the CBM, were defined based on the study of Rossi et al. (2020), as can be seen in the Table 1, Table 2 and Table 3. Following Step 2 of the proposed model, the linguistic pairwise comparisons between the CE principles of each DM were converted to TFN and the CR of each DM matrix, computed with Equations 14 to 19, are shown in Table 8. The DMs pairwise comparisons converted to TFN and their respective CR can be seen in the Supplementary Material (Table S1). Since, the CR's of DM1, DM2, DM3 and DM4 are respectively, 0.070, 0.083, 0.077 and 0.067, all the CR are lower than 0.1, and therefore, the decisions matrices can be aggregated with arithmetic mean, considering that all DMs have the same weight. The aggregated decision matrix is presented in Table 9.
For example, the indicator reduction of raw materials has a strong relationship with the principle systems thinking, a weak relationship with innovation, a strong relationship with stewardship, a median relationship with collaboration, a strong relationship with value optimization, and a median relationship with transparency. The TFN associated with these intensity levels of relationship, shown in Table S3 (from the supplementary material), were multiplied with their related principle weight. Therefore, the weight  j K of the reduction of raw materials, the indicator is given by: 132 * 5, 9, 9 0.132 * 1,1 , 5 0.135 * 5, 9, 9 0.169 * 1, 5, 9 0.187 * 5, 9, 9 0.245 * 1, 5, 9 2.81, 6.29, 8.47 The weights of all CE indicators are presented in the supplementary material (Table S3). Next, the CE indicators weights were defuzzyfied with Equation 21, for example:   Table 7 presents the performance of the CBMs and the respective ranking considering the influence of all the three dimensions of indicators. The main purpose of this ranking is to show that to achieve greater performance in the proposed circularity indicators, CBMs should be prioritized as the presented classification. The best CBM ranked indicated that Recovery by-products is the most suitable CBM for improving the circularity of an organization when all the indicators of the three dimensions (economic, social, and material) are selected. Product life extension was classified as the second and Product as a service as the third. These three CBMs are closely related to each other.
Recovery by-products means that other products will be created from secondary raw materials and/or end-oflife materials (British Standards Institution, 2017;Ellen MacArthur Foundation, 2012). A lot of organizations emerged to apply this business model to deal with the existing waste. Applying this kind of CBM means that resources in the product remain available for consumption and that no virgin materials need to be mined (Prosman & Sacchi, 2018;Vegter et al., 2020). Moreover, the performance objective is to recover a product, so that is available for subsequent consumption, making it possible to use less materials, water, and energy (Vegter et al., 2020). Recovery by-products helps in the extension of product life and in closing the loop when Product as a Service CBM is applied (Arponen et al., 2018).
Product life extension seeks to design products to be more durable and to circulate in the system aiming to keep value. Product life extension is the key to reducing rapid and excessive consumption of Product as a service . It is also the main purpose to create durable products to slow material and energy flows (Milios, 2021). For companies and stakeholders, it is important to create and capture value via extending The defuzzyfied values and the normalized CE indicators weights are also shown in the supplementary material (Table S3). Likewise in Step 3, the DMs agreed to consider the intensity level of the relationship between the CE indicators and the CBMs presented in Table 1, Table 2 and Table 3, which were converted to TFNs (Table S4). For example, the relationship between the indicator Reduction of Raw materials and the CBM Product as service is strong. Therefore, the respective TFN for this relationship is (5,9,9). Following Equation 24 and Equation 25, the decision matrix was normalized considering 9 j u + = . For instance, (5,9,9) is normalized to (0.555, 1.000, 1.000).
The normalized values of the intensity level of the relationship between the CE indicators and CBMs can be found in the supplementary material (Table S5). With Equation 28, the normalized decision matrix was multiplied by the CE indicators weights, obtained in Step 3. Therefore, following the same example of the relationship between the indicator Reduction of Raw materials and the CBM Product as service:  (Table S7,  Table S8 and Table S9). product lifetime in their business models (Hopkinson et al., 2020). Recovery by-products and Product life extension are directly connected to Product as a service, since the first two CBM are essential for the planning and implementation of successful Product as a service system. Product as a service is based on the idea of a performance economy, where ownership-based business models are replaced with pay-per-use models to reduce production and fulfill CE requirements (British Standards Institution, 2017;Chen et al., 2020). Product as a service incorporates strategies such as leasing, renting, and pay-per-use which help manufacturers and product owners handle the whole life cycle of products and decide when they should be repaired, recycled, or remanufactured (Arponen et al., 2018;British Standards Institution, 2017;Chen et al., 2020).
Those CBM were classified as the third that most impacts on the achievement of a good circular performance because they incorporates the majority of the specific indicators of the three dimensions of CE indicators. Those CBM when correctly implemented in the automobile sector have the potential to reduce operating expenses, make companies participate in secondary sales, increase gross profits, generate and increase revenue, and reduce input material costs (Arponen et al., 2018).

Regarding the managerial and practical implications
This paper is relevant for practitioners since, based on the analysis and tests conducted, it was possible to identify the CBMs that are most suitable for the improvement of performance regarding CE implementation. The ranking of the CBMs concerning the CE principles and the circularity indicators indicate that organizations have some paths to follow in the transition towards CE. The choice will depend on the main strategic goals of the organization. If the organization aims to have equal performance on the three dimensions of circularity indicators, it should choose Recovery by-products as its initial CBM. If the focus is on economic indicators, the organization could choose between Products as a Service or Recovery by-products. If the focus is on social indicators the decision is to implement Product as a service. In case of the intention is to improve the material indicators, the decision is to implement Recovery by-products. Hence, this research contributes to managers and practitioners by operationalizing forms to connect CBMs ans CE indicators systematically.
It is worth saying that a combination of different CBMs could be used to make the business stronger and to fulfill some aspects of the value proposition that sometimes could not be fulfilled using only one CBM. Also, it should be highlighted that the choice of the CE indicators can vary depending on the organizational context. Therefore, the model must be applied selecting only the relevant CE indicators, and then, the company can obtain the appropriate CBM ranking.

Regarding contributions to theory
CE can support organizations to develop sustainable solutions, maximizing the collaboration between stakeholders to create positive social and environmental impacts. The CBMs are strategies used to achieve sustainability. However, it was not found in the literature quantitative approaches to indicate which CBMs can be prioritized towards CE implementation.
In contrast with similar papers, and in a wide search through the literature, to the best of our knowledge, just the study of Husain et al. (2021) similarly addresses CBMs, as it can be seen in Table 5. However, Husain et al. (2021) do not analyze the relationship between CE principles and circularity indicators as we propose in the present research. The authors only seek to rank the CBMs with pre-defined criteria. Hence, the use of CE principles and circularity indicators to rank CBMs remains innovative in this study. Performance indicators are critical for determining how well a business is performing in CE and where improvements may be made. In this regard, using circularity indicators to prioritize CBMs may assist firms in establishing the parameters like as technology, resources, people, cultural elements, regulations, and other things that are required for CE implementation.

Sensitivity analysis
Sensitivity analysis is usually performed to check the robustness of the current search structure by considering the sources of uncertainty within a multi-criteria analysis (Maliene et al., 2018). In the application of the Fuzzy TOPSIS technique, sensitivity analysis contributes to understanding the influence of varying input data on the final ranking of alternatives (Kumar & Barman, 2021). Thus, several studies dealing with a variety of criteria and applying Fuzzy TOPSIS seek to change the weights of the decision-making criteria to assess their influence on the final solution (Awasthi et al., 2011;Dwivedi et al., 2018;Kumar & Barman, 2021).
In this way tests were conducted to understand the influence of the indicators' weights on the prioritization of the CBMs according to each dimension of indicators. To perform these tests, each dimension of indicator had its weight considered as integral while the other dimensions of indicators had their weights set to zero. Table 11 presents the performance of the CBMs and the respective ranking for each test carried out. The best CBM ranked according to each dimension of indicators indicates that Product as a service is the most suitable CBM in the economic and social dimension and Recovery by-products is the most suitable CBM for the material and economic dimension. Both CBM are complementary to each other since Recovery by-product is part of the Product as a service (Arponen et al., 2018). Moreover, Recovery by-products has a major focus on value optimization of materials while Product as a service has its major focus in creates new kinds of business structures.
In order to understand the influence of the principles' weights on the prioritization of the CBMs, tests were conducted by setting each principle with its weight considered as integral while the other principles had their weights set to zero. Table 12 presents the performance of the CBMs and the respective resulting ranking.
It's relevant to note that although some variations in the rankings could be noted from the changes in the weights, the order of the CBMs remains unaltered. This happens because all CE indicators were selected in the performed test, which makes them all assume similar weights. This indicates the robustness of the proposed decision model and consistency in the execution of the soft computing techniques.
As it can also be observed in Table 12, the ranking of CBM consists of the Recovery by-products first, followed by Product life extension, Product as a service, sharing economy, and On-demand. In this direction, it should be emphasized that, in real case applications, each organization should select only the principles that apply to its reality, as commented in section 4. The company of the illustrative application did not especified which indicator's dimension should be focused, which justifies the rank obtained in Table 10.

Conclusions
This paper presented a new approach to support CBMs prioritization based on fuzzy multicriteria group decision making. The proposed model combines the fuzzy AHP technique for weighting the CE principles, which is used to find the weights of the CE indicators, with the fuzzy TOPSIS technique to find the priority order of the CBMs. An illustrative application was conducted to evaluate the CBM prioritization of a manufacturer of the automotive industry supply chain, according to four organization's experts in sustainability and CE.
This paper brings a novelty in the analysis of the CBMs that should be applied to foster the transition towards the CE in combination with the use of circularity indicators to measure organizational performance. To the best of the authors' knowledge, no previous article proposes such analysis using fuzzy techniques. Thus, this paper brings new insights for the research field proposing a more analytical way to look at the CBMs and showing the importance of the implementation of CBMs combined with circularity indicators.
A major contribution of the presented work is the proposal of the first approach to CBM prioritization, which was developed based on two of the main elements of the CE: CE principles and CE indicators. Therefore, this article can be used to a guide future research on the proposition of other approaches to CBM prioritization. For further researches, it is suggested to explore other group decision making approaches, such as consensus reaching process techniques. Also, since this paper presented an illustrative application, it is suggested to compare the results of the proposed model application in real-world companies from different sectors.
As a suggestion for future studies, it can be cited the consideration of the interretaltions between CBMs to obtain the final ranking. The adoption of CE is possible through a combination of different CBMs (Husain et al., 2021), being that always will be a predominant one and other CBMs that are complementar. In this sense, it is important to identify how the different CBMs are related and complementar to each other. For this purpose, different techniques can be used, such as the DEMATEL and the Fuzzy Cognitive Maps.
Another suggestion for future studies is the use of more advanced linguistic representations of fuzzy sets. For instance, Hesitant Fuzzy Sets, Dual Hesitant Fuzzy Sets and Double Hierarchy Hesitant Fuzzy Linguistic Terms Sets are fuzzy generalizations that allow to collect more complex evaluations composed of sentences of judgments. In this way, such generalizations are able to handle higher levels of imprecision and hesitation in the decision makers' evaluations. As a final direction for future research, other MCDM techiniques, such as combined compromise solution (CoCoSo) and Complex Proportional Assessment (COPRAS) which can be applied to prioritize CBMs.

Supplementary Material
Supplementary material accompanies this paper. Table S1. Expert's pairwise comparisons between CE principles converted in TFN and their CR. Table S2. Intensity level of relationship between CE principles and indicator converted in TFN. Table S3. CE indicators weights, defuzzyfied weights and normalized weights. Table S4. Intensity level of relationship between the CE indicators and CBMs converted in TFNs. Table S5. Normalized intensity level of relationship between the CE indicators and CBMs. Table S6. Weighted intensity level of relationship between the CE indicators and CBMs. This material is available as part of the online article from https://www.scielo.br/j/prod