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Fuzzy Information and Engineering Volume 2 pp 797–808Cite as

Principal Component Analysis of Triangular Fuzzy Number Data

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Part of the book series: Advances in Intelligent and Soft Computing ((AINSC,volume 62))

Abstract

Principal component analysis (PCA) is a well-known tool often used for the exploratory analysis of a data set, which can be used to reduce the data dimensionality and also to decrease the dependency among features. The traditional PCA algorithms are designed aiming at numerical data instead of non-numerical data. In this article we propose a generalized PCA algorithm which tackles a problem where data is linguistic variable represented by triangular fuzzy number. Using the information provided by the centroid and fuzzy boundary of triangular fuzzy number, the proposed method starts with translating triangular fuzzy numbers into real numbers, then PCA is carried out on high-dimensional real number data set. Finally, the application of the proposed algorithm to a triangular fuzzy number data set is described.

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Author information

Authors and Affiliations

  1. Department of Mathematics, Dalian Maritime University, Dalian, 116026, China

    Na-xin Chen & Yun-jie Zhang

Authors
  1. Na-xin Chen
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  2. Yun-jie Zhang
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Editor information

Editors and Affiliations

  1. Guangzhou University, China

    Bingyuan Cao

  2. Chongqing University of Science and Technology, Chongqing, PR China

    Tai-Fu Li

  3. Hainan Normal University, Hainan, PR China

    Cheng-Yi Zhang

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© 2009 Springer-Verlag Berlin Heidelberg

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Chen, Nx., Zhang, Yj. (2009). Principal Component Analysis of Triangular Fuzzy Number Data. In: Cao, B., Li, TF., Zhang, CY. (eds) Fuzzy Information and Engineering Volume 2. Advances in Intelligent and Soft Computing, vol 62. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-03664-4_87

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  • DOI: https://doi.org/10.1007/978-3-642-03664-4_87

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-03663-7

  • Online ISBN: 978-3-642-03664-4

  • eBook Packages: EngineeringEngineering (R0)

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