## 3 Problem Definition
### Interoperability Challenges  
Devices within IoT, when used in a variety of sectors including traffic management, environment observation, and parking management, generate information with many formats and schemas. With such diversity, integration and analysis of information between edge servers become a big challenge. Centralized architectures can achieve standardization through collecting all information in a single storehouse, but such an approach is not feasible for real-time use cases due to increased communications costs, added latency, and even privacy concerns. Consequently, semantic interoperability in a decentralized system, in which edge servers run in an autonomous manner, is a key challenge that must be considered.  
Interoperability in Industrial IoT (IIoT) is a critical factor due to the vast heterogeneity of devices, protocols, and data formats used in industrial environments [32]. Unlike consumer IoT, where standardization efforts are more mature, IIoT systems must integrate diverse components such as programmable logic controllers (PLCs), supervisory control and data acquisition (SCADA) systems, industrial gateways, smart sensors, and real-time monitoring platforms. These components often come from different manufacturers and operate on varying communication protocols (e.g., OPC UA, MQTT, Modbus, Profibus). The lack of seamless interoperability leads to data silos, inefficient decision making, and increased integration costs. To address these challenges, ontology-based data standardization plays a vital role by enabling a unified semantic representation of heterogeneous data sources. This ensures that edge servers, federated learning models, and decision-makingsystems can process data in a structured and meaningful way, facilitating real-time analytics, predictive maintenance, and automation in industrial applications. By incorporating ontology-driven standardization into IIoT, the objective is to ensure scalability, adaptability, and cross-platform compatibility, making industrial environments with complex and evolving infrastructures more manageable.  
Communication networks in IoT rely on various protocols to ensure efficient data transmission between devices, edge servers, and cloud systems. Commonly used protocols include HTTPS (Hypertext Transfer Protocol Secure) for secure web communication, TCP/IP (Transmission Control Protocol/Internet Protocol) for reliable packet-based networking, and Modbus for industrial automation. Additionally, message-based protocols like MQTT (Message Queuing Telemetry Transport) and CoAP (Constrained Application Protocol) are widely adopted in resource-constrained IoT environments. MQTT is a lightweight publish-subscribe protocol optimized for low-bandwidth and high-latency networks, commonly used in smart cities, industrial IoT, and remote monitoring. CoAP, designed for constrained devices, follows a client-server architecture and is optimized for low-power wireless communication, making it suitable for sensor networks and smart home automation.  
**Formal definition**: Given \(m\) edge servers \(E=\{E_{1},E_{2},\ldots,E_{m}\}\) and \(n\) IoT devices \(D=\{D_{1},D_{2},\ldots,D_{n}\}\), each device \(D_{i}\) produces data \(x_{i}\) with its own schema \(S_{i}\). The goal is to transform and align all schemas \(S=\{S_{1},S_{2},\ldots,S_{n}\}\) to a unified ontology \(O\), enabling consistent data representation across edge servers as follows:  
\[M:S_{i}\to O,\quad\forall i\in\{1,2,\ldots,n\} \tag{1}\]