粗糙回归模型与算法研究

项目名称： 粗糙回归模型与算法研究

项目编号： No.61502335

项目类型： 青年科学基金项目

立项/批准年度： 2016

项目学科： 其他

项目作者： 石红

作者单位： 天津大学

项目金额： 20万元

中文摘要： 回归分析在自然科学领域和社会领域有着广泛的应用，传统的回归方法较少关注混合多变量数据多粒度建模的要求。本项目提出粗糙回归建模方法，即基于粒化思想和近似逼近的混合数据非参数回归建模策略。.利用邻域粗糙集和模糊粗糙集理论，研究多粒度回归模型与算法：通过定义不同尺度的决策邻域和特征空间邻域，实现对样本回归变量与输入变量的粒化，建立邻域粗糙回归模型与算法；基于模糊粗糙模型，将回归量视为模糊决策变量，构建由模糊粒度信息来近似模糊决策类的回归模型与算法；针对模型噪声敏感问题，通过改进上下近似构造鲁棒的粗糙回归模型，开发快速、鲁棒、适用于复杂数据易理解的回归分析算法，并将提出的方法应用于风力发电中的短期电功率预报。.本项目提出系统地研究基于粗糙集的回归建模方法，拓展了粗糙集的应用范围，也为混合数据的多粒度分析提供了新的框架。

中文关键词： 粗糙集；邻域粗糙回归；模糊粗糙回归

英文摘要： Regression analysis has a wide range of applications in both fields of natural science and social science. Traditional regression methods pay less attention to the requirements of multi-granularity modeling with heterogenous and multivariable data. This project proposes a rough regression modeling method, which is a nonparametric regression strategy for heterogenous and multivariable data based on granulation and approximation. .Multi granularity regression models and algorithms are investigated using neighborhood rough set and fuzzy rough set theories. Neighborhood rough regression model is built based on granulations of the regression variables and the input variables of a sample set, and granulations is achieved according to defining various neighborhoods with different scales in decision space and feature space. Based on the fuzzy rough models, decision variables are extended to fuzzy ones and fuzzy granulation information is used to approximate fuzzy decision. In addition, this project also devote to build rubost rough regression model to deal with noise sensitive problems by means of improving the definition of lower and upper approximation, and develop fast, robust and understandable regression analysis algorithms to process complex data. Finally, the proposed methods are applied to wind power short-term prediction..This project makes a systematic study on rough set based regression modeling methods, which greatly expands the application fields of rough set, and also provides a new framework for multi-granularity analysis with heterogenous data.

英文关键词： Rough Sets;Neighborhood Rough Regression;Fuzzy Rough Regression