In business, managers may use the association information among products to define promotion and competitive strategies. The mining of high-utility association rules (HARs) from high-utility itemsets enables users to select their own weights for rules, based either on the utility or confidence values. This approach also provides more information, which can help managers to make better decisions. Some efficient methods for mining HARs have been developed in recent years. However, in some decision-support systems, users only need to mine a smallest set of HARs for efficient use. Therefore, this paper proposes a method for the efficient mining of non-redundant high-utility association rules (NR-HARs). We first build a semi-lattice of mined high-utility itemsets, and then identify closed and generator itemsets within this. Following this, an efficient algorithm is developed for generating rules from the built lattice. This new approach was verified on different types of datasets to demonstrate that it has a faster runtime and does not require more memory than existing methods. The proposed algorithm can be integrated with a variety of applications and would combine well with external systems, such as the Internet of Things (IoT) and distributed computer systems. Many companies have been applying IoT and such computing systems into their business activities, monitoring data or decision-making. The data can be sent into the system continuously through the IoT or any other information system. Selecting an appropriate and fast approach helps management to visualize customer needs as well as make more timely decisions on business strategy.