区间数多维标度分析及其应用

摘要

多维标度法（multidimensional scaling,MDS）是一种利用客体间的相似性去揭示其空间关系的统计分析方法.为了将普通的多维标度分析扩展到数据为区间数的多维标度分析,首先对多维标度理论、区间分析理论及其应用进行了概括,其次给出了多维标度的相关概念及区间数的相关定义及性质,最后依据给出的三个区间距离和相似度将普通的多维标度分析扩展到区间数多维标度分析,并用区间多维标度法对2009-2010年河南省15个品种小麦产量进行分析,用SPSS软件分析得到Stress-K压力指数和RSQ值来说明拟合效果,通过空间感知图来揭示各品种产量的空间关系并对结果进行解释.%Multidimensional scaling （multidimensional scaling, MDS） is a method of using objectSimilarity to reveal the spatial relationship of the statistieal analysis method. In order to extended the ordinary multidimensional scaling analysis is to the data is interval of multidimensional scaling analysis. In this paper, Firstly, the theory of multidimensional scaling, interval analysis theory and its application is generalized. Then gives the related concepts and related definitions and properties of multidimensional scaling and interval numbers. Finally the given Three interval distance and similarity of the multidimensional scaling analysis is extended the ordinary multidimensional sealing analysis to the interval number of multidimensional scaling analysis and interval Muhidimensional sealing method for 2009--2010 in He Nan Province in 15 varieties of wheat yield were analyzed, using SPSS software analysis to Stress - K pressure index and the value of RSQ to illustrate the fitting effect and by spatial perceptual map to reveal all varieties yield Spatial relations and interpretation of results.