Dependent functions serve as a quantitative mathematical tool, playing a key role in the generation and evaluation of extension sets and extension strategies. They characterize the degree to which an object possesses a given property within a universe of discourse. This paper proposes an easily-to-operate construction method for high-dimensional simple dependent functions and provides rigorous proofs of their key mathematical properties. Numerical simulations and case analyses demonstrate the applicability and superiority of this method in multi-dimensional evaluation scenarios, with comparative analyses conducted across various case types. The results indicate that the proposed method maintains high operability and theoretical feasibility even in high-dimensional situations, while more accurately characterizing the coupling relationships among multiple evaluation features. This work provides a practical theoretical and methodological tool for superiority evaluation and can further improve the quantitative assessment of contradictory problems.

Traditional classification algorithms typically assume that the labels of training samples are static and deterministic, ignoring the dynamic characteristics of sample labels that may change with conditions in real-world scenarios. In response to this issue, this paper proposes a new learning problem setting—the Extended Classification Problem, which simultaneously gives the class labels and label variability states of samples in the training data, which to characterize the class transition potential of samples under the influence of change mechanisms. Based on this setting, a multi-label learning framework was designed, an extension classification algorithm for label variability using support vector machine was constructed, to achieve collaborative optimization of category discrimination and label variability prediction. The experimental section validated the effectiveness of the proposed algorithm on both synthetic and real datasets. This paper provides a new modeling approach for label dynamic learning problems, which has good application prospects.