Ⅱ-型模糊支持向量机-毕业论文.doc

Classified Index: U.D.C.:  CODE: 10075 NO: A Dissertation for the Degree of M. Science Type-Ⅱ Fuzzy Support Vector Machine Candidate: Huang Jiaying Supervisor: Prof. Ha Minghu Prof. Tian Dazeng Academic Degree Applied for: Master of Science Specialty: Applied Mathematics University: Hebei University Date of Oral Examination: June, 2012 摘 摘  要 要 模糊支持向量机能有效地解决模糊环境下的分类问题，它是支持向量机的一种拓 广。然而，它难以处理客观世界中大量存在的Ⅱ-型模糊环境下的分类问题。Ⅱ-型模糊 集理论作为模糊集理论的一种推广，更能准确描述客观事物的模糊性。基于此，本文讨 论了基于Ⅱ-型模糊样本的支持向量机，将支持向量机所处理数据由实样本拓广到Ⅱ-型 模糊样本。为了解决上述问题，本文采用均值简约方法将Ⅱ-型模糊样本转化为模糊样 本，在可能性理论的基础上，引入模糊事件的广义可信性概念，给出基于Ⅱ-型模糊样 本的强模糊线性可分的定义，分别建立输入、输出为Ⅱ-型模糊样本的支持向量机。应 用实例验证了基于Ⅱ-型模糊样本的支持向量机的有效性。 关键词  支持向量机  Ⅱ-型模糊样本  模糊线性可分  均值简约 I Abstract Abstract Fuzzy support vector machine, which is an extension of support vector machine, can solve the classification problems effectively in fuzzy environment. However, it is difficult to deal with classification problems in type-Ⅱ fuzzy environment. As a generalization of fuzzy set theory, type-Ⅱ fuzzy set theory is more effective for the delineation of existent fuzziness. For this purpose, this paper discusses support vector machine based on type-Ⅱ fuzzy samples which extend real samples to type-Ⅱ fuzzy samples. In order to deal with the problems above, type-Ⅱ fuzzy samples are reduced to ordinary fuzzy samples via the mean reduction method. The credibility of fuzzy event is introduced on the basis of possibility theory, the definition of strong fuzzy linear separable for type-Ⅱ fuzzy samples is given, and the type-Ⅱ fuzzy support vector machine based on input or output type-Ⅱ fuzzy samples is established. Example result shows the efficiency of the type-Ⅱ fuzzy support vector machine. Keywords  Support vector machine  Type-Ⅱ fuzzy samples  Fuzzy linear separable Mean reduction method II 目 目  录 录 第 1 章  绪  论 ........................................................................................................................ 1 1.1 模糊支持向量机的研究