Closed frequent itemsets (CFIs) play a crucial role in frequent pattern mining by providing a compact and complete representation of all frequent itemsets (FIs). This study systematically explores the theoretical properties of CFIs by revisiting closure operators and their fundamental definitions. A series of formal properties and rigorous proofs are presented to improve the theoretical understanding of CFIs. Furthermore, we propose confidence interval-based closed frequent itemsets (CICFIs) by integrating frequent pattern mining with probability theory. To evaluate the stability, three classical confidence interval (CI) estimation methods of relative support (rsup) based on the Wald CI, the Wilson CI, and the Clopper–Pearson CI are introduced. Extensive experiments on both an illustrative example and two real datasets are conducted to validate the theoretical properties. The results demonstrate that CICFIs effectively enhance the robustness and interpretability of frequent pattern mining under uncertainty. These contributions not only reinforce the solid theoretical foundation of CFIs but also provide practical insights for the development of more efficient algorithms in frequent pattern mining.

Under the background of the rapid development of new economy characterized by new technology, new business form, new industry and new model, China's engineering education urgently needs to cultivate diversified and innovative scientific and technological talents. New engineering research has increasingly become the mainstream of the innovation and reform of engineering education. This paper focuses on the practical innovation of “artificial intelligence + X” new engineering cross integration, focuses on cultivating engineering and technical talents to meet social needs, carries out interdisciplinary cross integration engineering practice research, and investigates the cross integration practice of “artificial intelligence + X” new engineering from five aspects: multi-dimensional curriculum system, teaching mode, training platform, training environment and diversified teaching evaluation mechanism, Understanding the employment needs of enterprises, highlighting the characteristic teaching of interdisciplinary cross integration, giving full play to the role of interdisciplinary cross integration in discipline research and practical innovation, and helping the deep integration and efficient iterative development of new engineering education and artificial intelligence technology are of great significance for the construction of new engineering and improving the training quality of engineering and technical talents.

Data interpolation and principal component transformation (PCT) were used to compute the discarding points of a frying oil by measuring the physicochemical parameters—acid value, carbonyl value, and total polar compounds. Herein, the discarding point refers to the time point (associated with the value of each physicochemical parameter) at which the frying oil should be discarded. First, a primary visual analysis was performed for the obtained data by using line charts. Second, a curve interpolation method was used to compute the discarding points for each parameter and thus determine the discarding points for the frying oil. At 190, 205, and 220°C, the frying oil reached the discarding points at 22.1, 17.7, and 13 hr, respectively. The discarding area was also visualized on the corresponding surfaces for the originally obtained data and the interpolated data to investigate the discarding points. Third, the PCT was conducted for the three parameters at each temperature; the discarding point estimation for the three parameters could be reduced to the estimation from the first principal component (FPC), thereby simplifying this process. At 190, 205, and 220°C, the frying oil reached the discarding points when the FPCs were 10.4524, 6.2881, and −1.7629 at the time points 22.1, 17.7, and 13 hr, respectively. Finally, a verification experiment revealed that the correlation between the results obtained by our interpolation method or PCT and the verified data was higher than 0.98, which demonstrates the effectiveness of our method.

High average-utility itemset mining is a significant research direction in data mining. The traditional average-utility (AU) measure employs itemset length as the normalization benchmark, which mitigates the bias toward long itemsets; however, it does not adequately account for the discrepancies between unit profit and actual sales volume. This paper introduces two novel measures: the weighted average utility based on external utility (E_WAU) and that based on internal utility (I_WAU), and examines the theoretical relationships among AU, E_WAU, and I_WAU. Subsequently, we establish a three-dimensional evaluation framework, namely, “category average–profit conversion–unit profitability”. Based on this framework, we develop classification decision matrices for pairwise comparisons of AU, E_WAU, and I_WAU. Within these matrices, products are grouped according to combinations of any two measures, yielding distinct product classifications that support customized marketing strategies. This approach further underscores the practical value of E_WAU and I_WAU in facilitating real-world decision-making. Finally, we conduct empirical validation and analysis on three real-world datasets. Experimental results demonstrate that, compared with using AU alone, the combined use of E_WAU and I_WAU is more effective in identifying product categories and devising appropriate sales strategies.