## 3 Methodology
### Digital Twin Architecture Evaluation Using Modified AHP  
As shown in Figure 4, the individual physical operation of a physical farm would have a corresponding logical object in the virtual farm based on the digital twin concept. A logical object (digital twin) is a virtualization of a physical object consisting of a sensor to capture data and a wireless communication end system to send data to a fog, an end, or a cloud system for further fish or environment status detection. The logical object also uses a prediction model to make a decision that enables an action sequence to control the machinery and bring benefits to the farmer. For example, as seen in Figure 4, our logical object for smart feeding scheduling uses multiple logical sub-objects to predict the amount of fish food for daily feeding. Thus, the smart fish-feeding digital twin might contain several sub-objects to prevent the fish from over-feeding or underfeeding. To achieve the goal of intelligent fish farming, this study analyzes the user requirements of the cloud-based information system, comprising six sub-systems to manage the sensors, aquaculture machinery and fish ponds, end system management, live data monitoring, production planning, and value-added services. These sub-systems form the first-tier key factors of the analytic hierarchy. As mentioned in the previous sub-section, we use the digital twins to implement each sub-system. The resulting analytic hierarchy is thus of two tiers, as shown in Figure 5. Although all the sub-systems should be included to address the issues of intelligent fish farming, the digital twins supporting individual fish farms could be very different due to the limitation of resource investment. Figure 3: The reinforcement learning-based digital twin for controlling the smart feeding machine to minimize the usage of fish food. Consequently, the analytic hierarchy process (AHP) could be adopted to locate each digital twin's important weight (priority) in the AIoT information system. The hierarchical network also represents the decision problem of our intelligent fish farming. The overall objective, with the details defined by the next two lower levels, represents the criteria and sub-criteria. With comparative judgments, users are requested to set up a comparison matrix at each hierarchy by comparing pairs of criteria or sub-criteria. Generally, AHP uses a scale of values ranging from 1 (indifference) to 9 (extreme preference) to express the user's preference. Finally, in the synthesis of the priority stage, each comparison matrix is solved by an eigenvector method for determining the criteria importance. In this study, the AHP should be modified for two reasons. First, the number of the second-tier criteria is often larger than 9; thus, it exceeds the limits of the AHP. Second, it is difficult to construct the comparison matrices using questionnaire surveys since real-world fish farm managers have very few experiences operating an intelligent fish farming  
Figure 4: User requirement analysis of intelligent fish farming using digital twins [9]. Figure 5: Hierarchy of digital twin architecture related to the AIoT system for intelligent fish farm management. management system. To deal with these two difficulties, in this study, we use the importance and easiness indexes defined in Equations (1) and (2), respectively, to synthesize the importance and easiness of all the criteria of the analytic hierarchy. Figure 6 shows the workflow of the AIoT system for intelligent fish farming. The first step is the design of the fish production environment, such as an indoor fish pond, outdoor fish pond, or offshore cage, which might also be equipped with devices for quality improvement. Next, the sensors set in the aquaculture environment captures sensor data which are then automatically uploaded to the cloud system for storage using a data networking end system.