【作者】 王丽；

【导师】 陈明浩；

【作者基本信息】 哈尔滨工业大学 ， 运筹学与控制论， 2014， 硕士

【摘要】 本篇论文建立了一个新的模糊度量空间(Y,N,*),在该空间上证明模糊压缩映射不动点定理和间断时间的模糊压缩映射不动点定理。本篇论文主要分为三部分：首先,介绍了模糊集合的发展与现实意义,以及近年来它在国内外的研究现状和实际生活中的应用,许多学者对已有的模糊度量空间进行修正优化。其次,在参考目前已有的模糊度量空间的基础上,给出一种比较新的模糊度量空间(Y,N,*),同时给出(Y,N,*)上的N-Cauchy列,P-Cauchy列的基本定义以及建立N-完备模糊度量空间,在此空间上建立新的模糊压缩映射,运用迭代的基本方法,证明(Y,N,*)上的模糊压缩映射不动点的存在性与唯一性,给出在N-完备模糊度量空间模糊压缩序列具有唯一的不动点的必要条件。并举例验证其可行性。最后,在给出模糊度量空间(Y,N,*)上的模糊压缩映射不动点定理后,引入无限乘积,定义出关键的收敛性条件,将连续时间改为间断时间下的模糊压缩映射不动点定理进行进一步证明,举例进行验证。然后简单介绍了该定理在彩色图像处理中的应用,即模糊度量图像滤波技术。通过比较在不同方法下彩色图像处理的结果,进一步说明模糊度量在彩色图像处理中是一种非常好的手段。本篇论文的主要目的是研究不同方向下的模糊度量空间的Banach压缩映射不动点定理。更多还原

【Abstract】 This paper mainly establishes a fuzzy metric spaces (Y, N,*),based on this new fuzzy metric spaces proof fuzzy contraction fixed point theory and interrupted time fuzzy contraction fixed point theory.This paper mainly have three parts:Firstly,it will introduce the new development of fuzzy sets and practical significance,research status and the application of fuzzy metric spaces in recent years,Many scholars have been corrected fuzzy metric space optimization.Secondly, in the many different views of currently available in fuzzy metric spaces, give a relatively new concept fuzzy metric spaces (Y,N,*),in the same time this paper gives the basic definition of N-Cauchy and P-Cauchy in fuzzy metric spaces (Y, N,*), and establishes a N-completeness of fuzzy metric spaces.In fuzzy metric spaces creates a new fuzzy contraction mapping.This paper uses the basic of iterative method,In fuzzy metric spaces proof fuzzy contraction mapping fixed-point existence and uniqueness. This paper give fuzzy contraction sequences necessary conditions for a unique fixed point in the N-completeness fuzzy metric spaces. And give an example to verify its feasibility.Finally,ti is when the proof of the following fuzzy metric space (YN,*) contraction mapping fixed point theorem,using the infinite product,defining the critical conditions for convergence.When the continuou time condition changed interrupted time proof fuzzy contraction mapping fixed-point theorey.And give an example to verify its feasibility.Then a brief introduction to the application of the theorem in the color image processing, image filtering technique that fuzzy metric. By comparing the results of different methods under color image processing, and further described in the color image processing fuzzy metric is a very good tool.The aim of this paper is to extend the Banach fixed-point theorem to contractive mappings on complete fuzzy metric spaces in several senses.更多还原