Least-squares approach to regression modeling in full interval-valued fuzzy environment

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• 作者：Mohammad Reza Rabiei (1)
  Nasser Reza Arghami (1)
  S. Mahmoud Taheri (2) (3)
  Bahram Sadeghpour Gildeh (1)
  
• 关键词：Interval ; valued fuzzy number ; Fuzzy regression ; Least ; squares method ; Cross validation ; Goodness of fit
• 刊名：Soft Computing - A Fusion of Foundations, Methodologies and Applications
• 出版年：2014
• 出版时间：October 2014
• 年：2014
• 卷：18
• 期：10
• 页码：2043-2059
• 全文大小：785 KB
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• 作者单位：Mohammad Reza Rabiei (1)
  Nasser Reza Arghami (1)
  S. Mahmoud Taheri (2) (3)
  Bahram Sadeghpour Gildeh (1)
  
  1. Department of Statistics, School of Mathematical Sciences, Ferdowsi University of Mashhad, Mashhad, 91775, Iran
  2. Department of Engineering Science, College of Engineering, University of Tehran, Tehran, Iran
  3. Department of Mathematical Sciences, Isfahan University of Technology, Isfahan, 84156-83111, Iran
  
• ISSN：1433-7479

文摘

A regression procedure is introduced when the observations of the response and the independent variables, as well as the coefficients that are to be estimated, are triangular interval-valued fuzzy numbers (IVFNs). The coefficients of the model are obtained by least square method, using a distance that we define on the space of IVFNs. Three real data sets, on soil sciences and hydrology engineering are used to test the applicability of the proposed method. The predictive performance of the models thus obtained are examined by cross-validation. To check the overall performance of the proposed method, two measures of goodness of fit are introduced and employed.