*2.2. Sustainability-Related Metrics*

In the present study, sustainability is understood as a matter of trade-offs among environmental, economic, and circular economy aspects. Therefore, to implement the proposed approach, both the environmental impact and costs of the whole lifecycle of the investigated components need to be assessed and integrated into the MCDM-based tool introduced in Section 2.3. Hence, lifecycle metrics linked to the environment and costs are accounted for; to this end, Life Cycle Assessment (LCA) and Life Cycle Costing (LCC) data were gathered from the relevant literature to calculate the said impact of the components. The tool also integrates a circular economy indicator which has been linked to the technological performance of the investigated components. For the sake of the current study, this is expressed through a specific property of the components, namely, specific stiffness.

Environmental impact has been linked to the emitted greenhouse gases (GHG) associated with the whole lifecycle of the components, namely raw material production, manufacturing, use phase, and recycling. GHG emissions represent the most widely reported environmental impact metric across industry and academia [11]. The economic impact of the components has been related to the costs associated with the energy requirements for the production, manufacturing, and recycling of the components or the fuel price when assessing the use phase impact of the components. The relevant environmental and economic impact results associated with production, manufacturing, and recycling are given in kgCO2eq per specific component mass or in euros per component mass, respectively. LCA starts with the production of the primary material, i.e., carbon fibers (PAN) and epoxy resin [11,26–29]. The autoclave molding process has been chosen as the relevant manufacturing process of the virgin CFRP aviation component. For the manufacturing of recycled components, the compression molding process has been considered [30]. The environmental impact and costs of upgrade technologies of recycled carbon fibers (e.g., sizing, alignment) were not accounted for due to a lack of relevant literature data. The chosen recycling process of the CFRPs has been the fluidized bed process (FBP), as being a promising method for recovering fibers of mechanical properties comparable to these of the virgin ones [6,26]. Compared to other promising recycling methods, which are currently at a low technology readiness level (TRL) (e.g., solvolysis [31]), the FBP method is at a TRL of 6 and is found at the pilot phase. In order to calculate the process-related energy costs, the non-household price of kWh in Germany has been accounted for [32].

For the assessment of the impact of the components' mass variation on emissions and costs linked to the use phase, the type of fuel is accounted for, where fuel consumption is assumed to be proportional to the component mass [11,33]. Hence, the components have been considered a load that must be carried by aircraft during flight. In this context, the environmental and economic impact results are given in a service function unit, namely, per component mass per km, which represents a wider approach for all aircraft types and classes and types regardless of the split between passengers and cargo payloads [34]. Four types of fuels were considered, i.e., kerosene, conventionally produced liquid hydrogen, liquid hydrogen from a wind source, and liquid hydrogen from a geothermal source, where the respective environmental and cost metrics relating to these fuels have been taken from [34]. The assessment of the overall impact of the use phase was conducted considering that the average lifetime distance of Airbus A320 was approximated based on the number of flying hours for which it was designed, i.e., 60,000 flying hours over a lifespan of 25 years, and the average cruising speed, i.e., 840 km/h [35,36].

For achieving the transition towards a CE, indicators and metrics for measuring CE progress are required. Up to now, various interpretations have been proposed, e.g., [37,38]. However, said interpretations lead to a variety of metrics and indicators in both content and form [39], while many of them focus on materials preservation [40,41]. In the aviation sector, the prevailing interpretation of circularity refers to the percentage of the aircraft mass which can be recycled or reused at the End-of-Life (EoL) of the aircraft [42]. However, in the above interpretation, the performance features of the recycled products are undermined, which in our view, represent an essential parameter when using a recycled product for an aviation application. Hence, considering that the quality of the recycled material represents a decisive factor towards CE goals as quality is linked to the durability of a material, a CE metric is introduced in the present study, which is linked to a quality feature of the component under study, i.e., a mechanical property. In the context of this study, the latter is expressed through the specific stiffness of the investigated components. For the focus on an aviation application, the choice of the specific stiffness is well justified as, in most applications, the allowable design of an aircraft structure does not exceed the linear elastic region of the stress-strain curve; in the case of CFRPs, this region remains almost linear up to failure. Considering the absence of standardized circular economy indicators in the aviation sector, future studies could focus on developing more specific circular economy indicators. However, this task is beyond the scope of the present work.

#### *2.3. Structure of the Hybrid MCDM Tool and Sensitivity Analysis*

The MCDM-based tool implemented herein has been introduced by the authors in [22] as a material selection tool for the aviation sector. The said tool combines the AHP and a WSM, whose output is a weighted sum of the normalized individual indicators. The advantage of integrating the WSM into the proposed hybrid tool is that it offers a proportional linear transformation of the raw data; namely, it maintains the relative order of magnitude of the standardized scores. The latter allows for a more effective and comprehensible interpretation of the final ranking obtained, as well as for distinguishing the impact of each term on the final output. The tool integrates environmental and economic metrics related to the component under study, as well as a suitable CE indicator, as introduced in Section 2.2. Based on the definitions of Section 2.2, the WSM equation, as it has been introduced in the previous work of the authors [22], is given as:

$$\mathbf{S}\_{\bar{i}} = \mathbf{K}\_{\text{CEI}} \cdot \mathbf{C} \mathbf{E} \mathbf{I}\_{\text{Q}\_i} + \mathbf{K}\_{\text{C}} \cdot \mathbf{C}\_{\text{i}} + \mathbf{K}\_{\text{E}} \cdot \mathbf{E}\_{\text{i}} \tag{2}$$

where Si is the final output value of the i component and can be considered a metric of overall sustainability and emerges as a matter of trade-off between environmental impact, costs, and circularity performance. Ei and Ci are the inversed normalized environmental and cost indicators of the i component, respectively. The inversed values have been considered due to the fact that environmental impact and costs have a negative impact on the overall sustainability index and, hence, the smaller these factors are, the higher the sustainability index becomes. CEIQi is the normalized quality-related CEI of the i component, expressed through the specific stiffness of the considered components. KCEI, KC, and KE stand for dimensionless weight factors and reflect the importance attributed to each term of the overall index value.

### 2.3.1. Factors' Weights Determination

Determination of the criteria weights is a frequent issue in many MCDM techniques. Hence, the selection of a proper weighting method is crucial in solving a multi-criteria decision problem as the weighting procedure followed may significantly influence the result; in this context, a variety of different weighting methods exist, with AHP receiving high popularity [43]. So as to define the weight factors of the above criteria, the AHP [44] was applied in [22], which is considered one of the most widely employed established decision-making methodologies [45]. AHP is based on pairwise comparisons; namely, it evaluates relationships between pairs when making group comparisons to judge which of each alternative is preferred. The main strength of AHP lies in its capability to combine it with other MCDM methodologies to obtain a flexible and tailored solution approach. The determination of the weight factors (KCEI, KC, KE) is subjective, reflecting the priority criteria of the user for a specific application. The final ranking among the alternative components occurs through the application of the WSM. However, one of the main concerns regards the inconsistency of decision makers in pairwise comparisons owing to the large number of comparisons needed to obtain the weights [46]. In 2015, another pairwise comparison-based method, namely the best-worst method (BWM), was introduced as an appropriate alternative to AHP in MCDM problems, demonstrating some advantages over AHP, such as fewer pairwise comparisons required and hence, better consistency. The BWM determines the pairwise relative comparisons, i.e., the preference between only the best and the worst criterion over all other criteria [47,48]. For both AHP and BWM, a similar linguistic terminology is being used, i.e., the importance of the criteria is defined on the same scale, i.e., 1–9, where 1 means that two criteria are of equal importance, while 9 means that the selected criterion is extremely more important compared to another criterion, as presented in Table 2. Therefore, a direct comparison can be made under the same level of reference so as the effect of the utilized weighting method can be clearly determined.


**Table 2.** The AHP Scale [44].

Although in the current work, the AHP was considered for the determination of the weight factors, BWM can be considered an effective alternative to the AHP method. However, the number of criteria (3) considered in the current study does not lead to different results as the number of pairwise comparisons as well as the system to be solved are identical for the two techniques. Yet, the sensitivity of the weighting procedure when more than three criteria (terms) are considered, and hence, a larger number of comparisons are made remains something to be investigated.

#### 2.3.2. Assessment of the Tool Sensitivity to the Applied Normalization Technique

Normalization is a critical step in any decision-making process as it transforms heterogeneous data into data that share a common scale. In the literature, a variety of normalization techniques have been proposed, including the min-max method, the z-score, the ranking normalization, the distance to target normalization, and the proportionate normalization, which are considered the five most widely employed ones [49]. In order to obtain the normalized indicators in [22], the min-max method was implemented to rescale the range of the individual indicators between 0 and 1. The general equation of the min-max technique [49] is given as:

$$\mathbf{x}' = \frac{\mathbf{x} - \min(\mathbf{x})}{\max(\mathbf{x}) - \min(\mathbf{x})} \tag{3}$$

where x is the normalized value, x is the original value, min(x) and max(x) are the minimum and maximum values of each individual indicator, respectively. In this study, to assess the sensitivity of the results to the normalization technique utilized, two alternative normalization methods were implemented, namely z-score and proportionate normalization. Z-score normalization is a typical methodology widely used in statistics. A z-score describes the position of a raw score in terms of its distance from the mean when measured in standard deviation units. On the other hand, proportionate normalization has the advantage that each value of a dataset is divided by the total sum; in this way, the normalized values maintain proportionality, reflecting the percentage of the sum of the total indicator's values. Dividing by the sum ensures that even the smallest value, which is greater than zero, is attributed a positive normalized value, while the differences among the normalized values become narrow. Alternative normalization techniques, such as ranking normalization and distance to target normalization, were considered inappropriate for this case study. More specifically, ranking normalization is a qualitative method; therefore, a quantitative assessment of the differences among the considered alternatives is not feasible. Finally, distance to target normalization requires the definition of a desired target (deriving mainly from policy targets), which in our case, is not a straightforward one.
