# Function-Oriented Applicability Evaluation of Technical Folding Based on Expert Knowledge
## 4 Developing the Central Elements of the EvalTech Method
### Definition of Equations for Similarity Analysis
#### 4.2.2 Calculating the Similarity Between Function Structures  
For detailed determination of the similarity between the hierarchical function structure of the new technical problem and the function structures from the case base 2, two independent similarity equations were defined: The equation of general functional similarity of functions \(\text{sim}_{\text{case2.1}}\) without considering the hierarchical structure and the function of structural similarity of functions considering the hierarchical levels of the functional structure \(\text{sim}_{\text{case2.2}}\). The equation of general functional similarity of functions \(\text{sim}_{\text{case2.1}}\) is calculated as shown below, where FS stands for one _Function Structure_ of case base 2. For each of the n functions of the function structure of the current development task, it is checked to what extent a function used matches functions of the function structures from case 1 of the database. \[\text{sim}_{\text{case 2.1}}=\frac{\sum_{\text{i=1}}^{\text{n}}\text{o}_{\text{i}} }{\text{n}} \begin{cases}\text{o}_{\text{i}}=1,\text{ if the function is part of the compared FS}\\ \text{o}_{\text{i}}=0,\text{ if the function is not part of the compared FS}\end{cases} , \tag{3}\]  
from the subprocess _initially match_, after the functions of the new technical problem have been designed within the process _identify features_. To digitally support the process _initially match_, the MATLAB(r) function _questionnaire.m_ is developed and implemented for the partial automation of the initial evaluation of the technological fit of the subprocess _initially match_. The _EvalTech Questionnaire_ automatically determines the characteristic functions of technical folding systems based on _case base 1_, saves them in an Excel list and uses them for the similarity calculation \(\mathit{sim}_{\text{case 1}}\). The inexperienced product developer uses the _EvalTech Questionnaire_ during concept development before deciding on a solution principle. He answers the _EvalTech Questionnaire_ by comparing the listed characteristic functions with functions of the new technical problem. For each characteristic function listed, the user can select whether this function corresponds exactly (_match_), corresponds analogously (_possible match_), or does not correspond at all (_no match_) to a function of his technical problem, cf. Figure 7.  
Subsequently, the similarity equation \(\mathit{sim}_{\text{case 1}}\) is calculated and its result is visualised as _overall score_, cf. Figure 8. In addition, all matching functions are displayed in a pie chart. Selecting a specific function from the pie chart also shows the significance of the respective function and the user's response. For the subsequent process, _specify features_, the user designs a machine-readable, hierarchical function structure of the new technical problem with the help of the _Hierarchical Function Structure Builder_ (HFSB). The HFSB is implemented as the MATLAB(r) function _fsb.m_, cf. Figure 9. The HFSB supports the user by providing the functions derived from technical folding systems (_function catalogue_) for selection and the option of designing new functions. These functionalities, as well as a general consistency check (_test_) of the function architecture (including unique relationships, use of the subject-verb method), help standardise the designed function structure and ensure high-quality input for the sub-process step _select_. In the subsequent process, _select_, the calculation of similarity between the designed function structure and function structures of _case base 2_ is carried out automatically by the further execution of the MATLAB(r) function _fsa.m_. For this purpose, the similarity equations \(\mathit{sim}_{\text{case 2.1}}\) and \(\mathit{sim}_{\text{case 2.2}}\) are calculated for each successfully applied product from _case base 2_. Within the user interface, the similarity equation \(\mathit{sim}_{\text{case 2.1}}\) is listed for each case from _case base 2_ as \"functional fulfilment in use case\".