## 3 Integrated User-Oriented Framework
### End-User Application
#### 3.3.1 Helping User to Select the Printing Material  
Given that a variety of recycled material will be used and that the user is not a material expert, the key to the success of the framework lies in the user being able to choose the most suitable material to print under specified properties. Material selection is very important in the design and manufacture of parts, defining their properties, performance and reliability [70]. The difficulty is increased when using recycled materials, as their properties are compromised even by the recycling cycles they have undergone. [71]. The proposed architecture takes this into account through a recommendation system that allows the user to select the most suitable material for the manufacturing of a part. The choice of one material or another is generally made based on its mechanical behaviour and the performance expected in the application. The choice of material is approached as Multi-Criteria Decision-Making (MCDM), where an alternative (material) is selected based on certain criteria (properties) that it must have to meet its requirements, as is stated in [72]. Among the MCDM algorithms, the TOPSIS (Technique for Order Preference by Similarity to an Ideal Solution) method is proposed for its simplicity and good computational efficiency [73], as the intention is for it to be run repeatedly so that the user can test different combinations of requirements. The TOPSIS method enables the selection of alternatives based on the idea of establishing a ranking between them. This ranking is carried out using the idea of the distance between both ideal and non-ideal alternatives [74]. The service provider determines the evaluation criteria based on which one of the alternatives (materials) is selected. These criteria are commonly defined by technical terms for materials, such as yield strength or surface roughness. This terminology can be confusing for a non-expert user, so these properties could be renamed on the basis of more common characteristics, such as \"strength\", \"finish\", etc. The method used for this purpose (TOPSIS) comprises the following steps [75]:  
Step 1: Construction of the decision matrix and weight allocation (Table 4). Each of the \(m\) alternatives \(A_{i}\), with \(i=1,2\ldots m\), is evaluated for each of the \(n\) criteria \(\mathrm{C}_{j}\), with \(j=1,2\ldots n\). Each criterion's weights are set by the user specifying how much it is estimated that the final part should have that property. Figure 5: IDEF0 of the slicing process from user decisions to final part. Step 2: Decision matrix normalisation. As the elements of the decision matrix may not be in the same domain (as the criteria can be evaluated in different units of measurement), they are normalised. Likewise, the weights are normalised so that the sum equals unity. \[n_{ij}=\frac{x_{ij}}{\sqrt{\sum_{j=1}^{m}x_{ij}^{2}}} \tag{1}\]  
\[w_{j}=\frac{W_{j}}{\sum_{j=1}^{n}W_{j}} \tag{2}\]  
Step 3: Construction of weighted normalised decision matrix. The normalised elements of the decision matrix are weighted. \[v_{ij}=w_{j}n_{ij} \tag{3}\]  
Step 4: Obtaining of the ideal positive and negative solution. This would be equivalent to finding the best and the worst material for each criterion. \[A^{+}=\big{\{}v_{1}^{+},\dots,v_{n}^{+}\big{\}}=\big{\{}\big{(}max_{i}\big{(}v _{ij}\big{)},\,j\in J\big{)}\big{(}min_{i}\big{(}v_{ij}\big{)},\,j\in J^{ \prime}\big{)}\big{\}} \tag{4}\]  
\[A^{-}=\big{\{}v_{1}^{-},\dots,v_{n}^{-}\big{\}}=\big{\{}\big{(}min_{i}\big{(} v_{ij}\big{)},\,j\in J\big{)}\big{(}max\big{(}v_{ij}\big{)},\,j\in J^{ \prime}\big{)}\big{\}} \tag{5}\]  
where \(J\) is linked to benefit criteria (more is better) and \(J^{\prime}\) to cost criteria (less is better). Step 5: Computing the Euclidean distance of each alternative to the ideal and anti-ideal solution.