Connectivity and complexity are serious issues in the interconnection of networks. In this chapter, we have discussed various logical operators that are seen as very useful for the interconnection of networks boosting performance, reducing delay, revealing the best paths, high-speed and safe communiqué among processors, and multiple heterogeneous sensing devices. The work presented has the primary goal to build a smart healthcare scheme for a real-time 24 × 7 monitoring system for remote detection and care of various diseases. The system shows the way to improve connectivity problem, with optimal performance and rising reliability rates, among the smart sensors, connectivity layers, and decision-making fog layer. We discuss and analyse the same problem through the study of a perfect difference network using logical operators. The novelty of the proposed work is supported by the experimental results, and the numerical output results justified the performance of our proposal in terms of speed, reliability, delay, latency, sensitivity, and specificity rates.