因素空间与可拓学的互补性分析及问题处理融合模型

问题智能处理是人工智能领域具有挑战性和交叉性的课题。大数据与人工智能技术背景下，为了给具有较高普遍性的开放性问题求解提供新的理论支撑，对因素空间与可拓学做了对比分析，发现两者具有共同的数学基础，在问题智能处理等研究方向有交叉性和互补性。以面向问题处理的融合模型为例，论证了可拓学与因素空间交叉研究的基本路径及其可行性，提出了两者交叉研究的主要方向，阐明了实际应用的潜在优势及适用范围。该研究将有助于进一步提高问题处理的系统性、智能化水平，提高解决问题从不确定性、偶然性到必然性的程度，并将推动为智能科学服务的智能数学的发展。

A complementary analysis of factor space and extenics and a fusion model for solving problems

Intelligent problem solving is a challenging and cross-cutting subject in the field of artificial intelligence. To theoretically support the method for solving the open problem with high universality under the background of big data and artificial intelligence technology, we conducted a comparative analysis of factor space and extenics, finding that they have a common mathematical basis and are overlapping and complementarity in the research direction of intelligent solving of problems. Taking the fusion model for solving problems as an example, this paper demonstrates the basic path and feasibility of the cross study of extenics and factor space. We presented the main direction of the cross research of extenics and factor space, and we expounded on the potential advantages and application scope of problem solving in practice. This research will help increase the systematic and intelligent level of problem solving, improve the degree of problem solving from uncertainty, contingency to inevitability, and promote the development of intelligent mathematics—a mathematical branch of intelligent science.