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Fuzzy Least Squares Estimation with New Fuzzy Operations

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Synergies of Soft Computing and Statistics for Intelligent Data Analysis

Part of the book series: Advances in Intelligent Systems and Computing ((AISC,volume 190))

Abstract

This paper deals with fuzzy least squares estimation of the fuzzy linear regression model with fuzzy input-output data that has an error structure. The paper proposes fuzzy least squares estimators (FLSEs) for regression parameters based on a suitable metric, and shows that the estimators are fuzzy-type linear estimators. To find these estimators, we first defined a notion of triangular fuzzy matrices whose elements are given as triangular fuzzy numbers, and also provided some operations among all triangular fuzzy matrices. Simple computational examples of this applications are given.

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Author information

Authors and Affiliations

  1. School of Economics, Yonsei University, Seoul, 120-749, South Korea

    Jin Hee Yoon

  2. School of Liberal Arts and Sciences, Korea Aerospace University, Koyang, 412-791, South Korea

    Seung Hoe Choi

Authors
  1. Jin Hee Yoon
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  2. Seung Hoe Choi
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Corresponding author

Correspondence to Jin Hee Yoon .

Editor information

Editors and Affiliations

  1. Faculty of Computer Science, Otto-von-Guericke University of Magdebur, Geb. 29, Raum 008, Universitätsplatz 2, Magdeburg, 39106, Germany

    Rudolf Kruse

  2. , FB Informatik & Informationswissenschaft, University of Konstanz, Konstanz, 78457, Germany

    Michael R. Berthold

  3. of Magdeburg, Faculty of Computer Science, Otto-von-Guericke University, Geb. 29, Universitätsplatz 2 008, Magdeburg, 39106, Germany

    Christian Moewes

  4. , Department of Statistics and OR, University of Oviedo, C/ Calvo Sotelo, s/n, Oviedo, 33007, Spain

    María Ángeles Gil

  5. Systems Research Institute, Polish Academy of Sciences, Newelska 6, Warsaw, 01-447, Poland

    Przemysław Grzegorzewski

  6. Systems Research Institute, Polish Academy of Sciences, Newelska 6, Warsaw, 01-447, Poland

    Olgierd Hryniewicz

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Yoon, J.H., Choi, S.H. (2013). Fuzzy Least Squares Estimation with New Fuzzy Operations. In: Kruse, R., Berthold, M., Moewes, C., Gil, M., Grzegorzewski, P., Hryniewicz, O. (eds) Synergies of Soft Computing and Statistics for Intelligent Data Analysis. Advances in Intelligent Systems and Computing, vol 190. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-33042-1_21

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  • DOI: https://doi.org/10.1007/978-3-642-33042-1_21

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-33041-4

  • Online ISBN: 978-3-642-33042-1

  • eBook Packages: EngineeringEngineering (R0)

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