...
  • 主题
高级搜索  >
历史搜索 清空历史
首页> 外文期刊>Fuzzy sets and systems >Interval regression by tolerance analysis approach
【24h】

Interval regression by tolerance analysis approach

机译：公差分析法进行区间回归

获取原文
获取原文并翻译 | 示例
           
页面导航
  • 摘要
  • 著录项
  • 相似文献
  • 相关主题

摘要

In interval linear regression analysis, we are given crisp or interval data and we are to determine appropriate interval regression parameters. There are various methods for interval regression; many of them possess the property that while some of the resulting interval regression parameters are very wide, the other parameters are crisp. This drawback is the main limiting factor for such methods and much effort has been devoted to overcoming it. We propose a method motivated by tolerance analysis in linear systems. Our method yields intervals for regression parameters the widths of which are proportional to an in-advance given vector of parameters. Moreover, the method is computationally very cheap, and provides a natural measure of quality of a model. First we formulate the method for the basic model of crisp input-crisp output data and then extend it to crisp input-interval output and interval input-interval output models. For the interval-valued cases we study several formulations of the solution concept: possibility, strong possibility, weak possibility, necessity. Here, strong possibility is a new concept proposed as a natural counterpart to the remaining ones. We prove that the method provides optimal interval parameters meeting centrality and proportionality requirements. We also show that the method provides interval regression parameters satisfying various versions of Tanaka-Lee's inclusion property. We also derive a form of a complementarity theorem for the weak possibility and necessity solution concepts. Since practical problems may be affected by outlying observations we show that our approach is easily adapted to deal with them. We illustrate the theory by examples.
机译：在区间线性回归分析中，我们将获得清晰的或区间数据，并确定适当的区间回归参数。区间回归的方法多种多样。它们中的许多具有以下特性：尽管某些结果区间回归参数非常宽，但其他参数却很清晰。该缺点是这种方法的主要限制因素，并且已经致力于解决该问题。我们提出了一种基于线性系统公差分析的方法。我们的方法为回归参数产生间隔，该间隔的宽度与预先给定的参数向量成比例。而且，该方法在计算上非常便宜，并且提供了模型质量的自然度量。首先，我们为清晰输入-酥脆输出数据的基本模型制定了方法，然后将其扩展到清晰输入-间隔输出和间隔输入-间隔输出模型。对于区间值情况，我们研究了解决方案概念的几种表述：可能性，强可能性，弱可能性，必要性。在这里，很可能提出一种新的概念，作为与其余概念的自然对应。我们证明该方法提供了满足中心性和比例性要求的最佳间隔参数。我们还表明，该方法提供了满足Tanaka-Lee包含属性的各种版本的区间回归参数。我们还针对弱可能性和必要性解决方案概念推导了互补性定理的一种形式。由于实际问题可能会受到外围观察的影响，因此我们证明了我们的方法很容易适应这些问题。我们通过实例说明该理论。

著录项

  • 来源
    《Fuzzy sets and systems》 |2012年第2012期|p.85-107|共23页
  • 作者

    Milan Hladik; Michal Cerny;

  • 作者单位

    Charles University, Faculty of Mathematics and Physics, Department of Applied Mathematics, Malostranske num. 25, 11800 Prague, Czech Republic;

    University of Economics, Faculty of Computer Science and Statistics, nam. W. Churchilla 4, 13067 Prague. Czech Republic;

  • 收录信息 美国《科学引文索引》(SCI);美国《工程索引》(EI);
  • 原文格式 PDF
  • 正文语种 eng
  • 中图分类
  • 关键词

    possibilistic regression; fuzzy linear regression; interval linear regression;

    机译：可能性回归;模糊线性回归区间线性回归;

相似文献

  • 外文文献
  • 中文文献
  • 专利
获取原文

客服邮箱：kefu@zhangqiaokeyan.com

京公网安备：11010802029741号 ICP备案号：京ICP备15016152号-6 六维联合信息科技 (北京) 有限公司©版权所有

  • 客服微信

  • 服务号