# Ontology Modeling Using Fractal and Fuzzy Concepts to Optimize Metadata Management
## 4 Case Study: Mold Assembly
### FFOM Visualization and Analysis
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Step** & **Description** & **OWL Element** & **Example Code** \\ \hline \multirow{4}{*}{\begin{tabular}{c} Class \\ Definition \\ \end{tabular} } & Convert FFOM entities into & & \textless{owl:Class} rdf:about=”Pizza”/\textgreater{} \\  & OWL classes and subclasses, & & \textless{owl:Class} \\  & using \textless{rdfs:subClassOf\textgreater{}} & & rdf:about=”PizzaTopping”\textgreater{} \\  & represent hierarchical & \textless{rdfs:subClassOf\textgreater{}} & \textless{rdfs:subClassOf rdf:resource} \\  & relationships & & \textless{}=”Pizza”/\textgreater{} \\  & & & \textless{}/owl:Class\textgreater{} \\ \hline \multirow{4}{*}{\begin{tabular}{c} Object \\ Property \\ Definition \\ \end{tabular} } & Define relationships between & & \textless{owl:ObjectProperty} \\  & classes as OWL object & & rdf:about=”InsTopping”\textgreater{} \\  & properties. Add annotations & & \textless{rdfs:range} \\  & such as \textless{ruzzy:value\textgreater{}} and & & rdf:resource=”PizzaTopping”\textgreater{} \\  & \textless{fuzzy:timestamp\textgreater{}} to capture & & \textless{ruzzy:value\textgreater{}}0.85\textless{}/fuzzy:value\textgreater{} \\  & fuzzy relationships and & & \textless{}fuzzy:timestamp\textgreater{}2024-04- \\  & temporal dynamics & & 21T12:00:00Z\textless{}/fuzzy:timestamp\textgreater{} \\  & & & \textless{}/owl:ObjectProperty\textgreater{} \\ \hline \multirow{4}{*}{\begin{tabular}{c} Data Property \\ Definition \\ \end{tabular} } & Define attributes of classes & & \textless{owl:DatatypeProperty} \\  & using OWL data properties, & & rdf:about=”PizzaName”\textgreater{} \\  & specifying the domain “class” & & rdf:sd:domain rdf:resource =”Pizza”/\textgreater{} \\  & and range “data type” & & \textless{rdfs:range rdf:resource} \\  & & & \textless{}=”ssd:string”/\textgreater{} \\  & & & \textless{}/owl:DatatypeProperty\textgreater{} \\ \hline \multirow{4}{*}{\begin{tabular}{c} Instance \\ Creation \\ \end{tabular} } & Populate the ontology with & & \textless{owl:NamedIndividual} \\  & specific entities as OWL & & rdf:about=”Margherita-Pizza”\textgreater{} \\  & named individuals, linking & & \textless{rdf:type rdf:resource=”Pizza”/\textgreater{} \\  & them to classes, object & & \textless{}PizzaName\textgreater{}Margherita\textless{}/PizzaName\textgreater{} \\  & properties, and data & & \textless{}hasTopping rdf:resource \\  & properties & & & \textless{}”MushroomTopping”/\textgreater{} \\  & & & & \textless{}/owl:NamedIndividual\textgreater{} \\ \hline \multirow{4}{*}{\
\begin{tabular}{c} Adding \\ Temporal \\ Relationships \\ \end{tabular} } & Represent time-sensitive & & & \textless{owl:ObjectProperty} \\  & changes in relationships by & & rdf:about=”InsTopping”\textgreater{} \\  & updating \textless{ruzzy:value\textgreater{}} and & & \textless{rfuzzy:value\textgreater{}}, & \textless{ruzzy:value\textgreater{}}0.80\textless{}/fuzzy:value\textgreater{} \\  & \textless{ruzzy:timestamp\textgreater{}} & & \textless{ruzzy:timestamp\textgreater{}}2024-05- \\  & annotations in object & & 01T12:00:00Z\textless{}/fuzzy:timestamp\textgreater{} \\  & properties & & \textless{}/owl:ObjectProperty\textgreater{} \\ \hline \multirow{4}{*}{
\begin{tabular}{c} Model \\ Validation \\ \end{tabular} } & Ensure logical consistency and & & & \\  & structural integrity of the & & Validation tools: verify structure in \\  & transformed OWL model & - & Protege, test data retrieval with \\  & using tools like Protege and & & SPARQL \\  & SPARQL queries & & \\ \hline \hline \end{tabular}
\end{table} 
Table 4: _Cont._Figure 9b focuses on one of these subfractals, BaseAssembly (MA-1-1), treating it as an independent fractal. It contains its own subfractals: Drilling (MA-1-1-1) and Bolting (MA-1-1-2), each connected using the same structural pattern and annotated with their own fuzzy values (e.g., (0.80, 0.85, 0.90)) and timestamps (e.g., 2024-01-05T12:00:00Z).