## 2 Materials and Methods
### Step 3: The Use of Bayesian Networks  
The database, based on data received in Steps 1 and 2, was installed in order to learn the Bayesian networks (Step 3). The network modelled also used rules designed to illustrate the relationship between the knowledge about AM technology in literature and the state of knowledge in enterprises. The Bayesian network has been a popular method for quantitative and qualitative risk assessment. It is especially useful for modelling rare accidents and forecasting, thanks to the possibility of using expert data, in the case of insufficient historical data. Bayesian network is presented by acyclic graph, which shows dependencies between variables, which is described by the conditional probability collected in tables (CPTs) [74]. It allows knowledge to be gathered and classified by inference, based on premises. Premises can be modified with logical functions, thus creating a network structure described by a set of rules what allow to assess a probability of events, as example--level of knowledge [75; 76; 77]. [PERSON] theorem--Equation (1)--is based on the formula which describe relations between the information or hypothesis and its evidence:  
\[\text{P}(\text{Y}\backslash\text{Z})=[\text{P}(\text{Z}\backslash\text{Y}) \text{P}(\text{Y})]/\text{P}(\text{Z}), \tag{1}\]  
where:  
\(\text{P}(\text{Y}\backslash\text{Z})\)--the 'a posteriori' probability of Y, due to evidence of Z,  
\(\text{P}(\text{Y})\)--the 'a priori' probability of Y, before the evidence Z,  
\(\text{P}(\text{Z}\backslash\text{Y})\)--the probability of the Z evidence, if Y was true,  
\(\text{P}(\text{Z})\)--the probability of the Z evidence. In our previous research work [78] the comparative analysis of classification algorithms was carried out in order to decide to use the Bayesian network to build a research model aimed at clustering knowledge. So, the proposed approach, using BN, aims to present the possibilities of the effective analysis of knowledge based on probability prediction, through the synergistic use of knowledge from the literature and the results of empirical research. Based on elements obtained from Step 1 and Step 2, BN is connected the two independent models with a common node and referred to as \"P\". The value probability for this node, can answer questions in the research problem, what is the probability of identifying recent demand for AM in the context of meeting the needs of companies? Due to this, a network of dependencies was created, based on training sets. It consisted of nodes representing knowledge obtained from the literature named as the \"IF\" network, and empirical research named the \"AM\" network. Relations for knowledge of the BN algorithm can be marked as Bayesian network \(<\) B, \(\Theta\)\(>\), with set of B nodes and set of \(\Theta\) arches, which represents conditional relation. Set B(X\({}_{i}\)), i\(\in\)N was defined [11]. Each element of set B(Xi) has an alternatives x[x\({}_{ij}\)], j\(\in\)N [10]. The training set for Bayesian networks can be described as C\({}_{IF\text{ network}}\) = {C\({}_{1}\), C\({}_{2}\),..., C\({}_{99}\)}, and C\({}_{\text{AM\,network}}\) = {C\({}_{1}\), C\({}_{2}\),..., C\({}_{99}\)}, and their alternatives x\({}_{ij}\). Where, always the \"IF\" network contains elements [10]:  
* X1 \"Type of material\", x \(\in\) {powder; filament},
* X2 \"Lasers\", x\(\in\)[SLM; Nd/Yd:YAG; CO2; High-power diode; Self-development; Hybrid; Fiber],
* X3 \"Materials\": Fe alloy, Ti alloy, Cu alloy, Cr Ni alloy, Ceramic, Al Alloy, Hi speed steel, Stainless steel, Special alloy, Tool steel, Super alloy, YCF101, where x \(\in\) {State0;State1},
* X4-X17 \"Tested properties\": Mechanical properties, Structural properties, Microstructure, Micro-hardness, Hardness, Geometry, Interlayer, Wettability, Morphology, Porosity, Morphology of melt pool, Nano-hardness, Cracking, Modelling, where x \(\in\) {State0;State1},
* X18 \"IF\", impact factor for the analysed articles, x \(\in\) {A; B; C; D; E}.