The Method for Solving Multiple Criteria Ill-defined Problems Based on Extenics

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.