Current mainstream deep learning models, due to insufficient interpretability, struggle to meet the demands for decision transparency and controllability in risk-sensitive domains such as healthcare, justice, and finance. To address the limitation that existing supervised learning methods focus on classification prediction while neglecting the transformability of sample features, this research introduces Extenics theory and proposes a basic-element transformation algorithm based on decision trees. The algorithm first clarifies the essential differences between classification and transformation problems and establishes a formal mathematical model for the transformation problem. It then defines a transformation distance to quantify the difficulty of transforming between different feature values. On this basis, a general transformation mechanism is designed which can be embedded into arbitrary decision-tree models, enabling quantitative derivation of feature-level transformation paths. Experimental results demonstrate that the proposed algorithm can effectively mine samples in the positive extension domain and improve the overall compliance rate in personalized healthcare scenarios, verifying the effectiveness and generalizability of the method.

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.

With the rapid advancement of the Internet, the Internet of Things, and artificial intelligence technologies, information is experiencing exponential growth. The widespread adoption of data services has significantly increased the complexity, uncertainty, and dynamism of internal and external environments. This paper builds upon the solution methods for Single-goal Ill-defined Problems, and defines Multiple Criteria Ill-defined Problems as those in which the objectives and domains are relatively well-defined, but due to uncertain or insufficient environmental resources, conditional boundaries, or constraints, conflicts arise among the goals, making it difficult or impossible to achieve them simultaneously. To address such challenges, an initial extension model construction method is proposed for Multiple Criteria Ill-defined Problems. By integrating extensible analysis methods, extension transformation methods, and superiority evaluation methods, the approach seeks to derive optimal or near-optimal strategies for achieving the intended goals. A general procedural framework for solving Multiple Criteria Ill-defined Problems is developed, along with a flowchart that outlines the key steps. Finally, a case study is presented to demonstrate the feasibility and effectiveness of the proposed method. The solution approach is characterized by formalization, modeling, and quantification. It provides a foundational methodology for the intelligent resolution of ill-defined problems, and further extends the application scope of Extenics in addressing goal conflicts and complex decision-making scenarios.

Ill-defined problems, with relatively defined goals and problem domains but expandable boundary conditions, are ubiquitous in life. It is of significant importance to provide directions for the intelligent expansion of knowledge under theoretical guidance, there by forming a comprehensive knowledge network for solving such open-ended problems. This research identifies three primary knowledge categories that constitute the foundation of complete knowledge network: descriptive knowledge of strategy generation materials, domain knowledge that delineates the initial goals and conditions of the problems, and methodological knowledge suitable for the tools employed in strategy generation. The completeness of knowledge network is validated through the achievement of the initial objectives. Finally, the feasibility of the proposed approach is demonstrated through a case study on the design of the ergonomic office chair. By adopting a hybrid approach that integrates formalization and quantification within the extension innovation methodology system, this research offers a novel pathway for establishing a comprehensive knowledge network for solving open-ended problems in an artificial intelligence context.