A Set Theoretic Framework for Unsupervised Preprocessing and Power Consumption Optimisation in IoT-Enabled Healthcare Systems for Smart Cities

The emergence of the Internet of Things (IoT) has brought about a significant technological shift, coupled with the rise of intelligent computing. IoT integrates various digital and analogue devices with the Internet, enabling advanced communication between devices and humans.The pervasive adoption of IoT has transformed urban infrastructures into interconnected smart cities. Here, we propose a framework that mathematically models and automates power consumption management for IoT devices in smart city environments ranging from residential buildings to healthcare settings. The proposed framework utilises set theoretic association-rule mining and combines unsupervised preprocessing with frequent-item set mining and iterative numerical optimisation to reduce non-critical energy consumption. Readings are first converted into binary transaction matrices; then a modified Apriori algorithm is applied to extract high-confidence usage patterns and association rules. Dimensionality reduction techniques compress these transaction profiles, while the Gauss–Seidel method computes control set points that balance energy efficiency. The resulting rule set is deployed through a web portal that provides real-time device status, remote actuation, and automated billing. These associative rules generate predictive control functions, optimise the response of the framework, and prepare the framework for future events. A web portal is introduced that enables remote control of IoT devices and facilitates power usage monitoring, as well as automated billing.