中文摘要：

泥石流危险性评价是对研究区域泥石流危险因子的综合分析评价。泥石流灾害成因和评价因子的复杂性给泥石流灾害危险性评价造成了一定的困难。在现今科学研究和工程实践中，各种数学模型在分析数据、解决实际问题方面的作用日益突出，成为继理论分析、实验之后又一种重要的研究方法。介绍了层次分析法、灰色关联分析法、模糊综合评判法和BP神经网络等数学模型及其在泥石流危险性评价中的应用。各种数学模型的发展成熟，进一步完善和丰富了泥石流危险性评价的方法体系。

英文摘要：

The hazard factors are analyzed comprehensively in assessment for debris flow hazard degree in the research area. But the data about hazard factors are scarce in most cases. The mathematical models are superior to data analysis and settlement of practical problems. The mathematical models become another research method following theoretical analyses and experiments. This paper shows the mathematical models for the multivariate analysis in the debris flow hazard degree. They include Analytical Hierarchy Process, Grey Relational Analysis, Fuzzy Comprehensive Evaluation Method and BP Artificial Neural Network. The development of these mathematical models has improved the assessment system for debris flow hazard degree.