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Least Squares Method with Interactive Fuzzy Coefficient: Application on Longitudinal Data

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Book cover Fuzzy Information Processing (NAFIPS 2018)

Part of the book series: Communications in Computer and Information Science ((CCIS,volume 831))

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Abstract

This work focus on the least square method to fit a fuzzy function to longitudinal data given by fuzzy numbers. In order to consider the intrinsic correlation of longitudinal data, we assume that there exits a linear relation among the involved fuzzy numbers that arises from the concept of a joint possibility distribution. We propose a numerical method to solve a fuzzy least square problem taking into account this linear correlation. To this end, we extend the classical least square method by means of the \(\sup \)-J extension principle, which consists of a generalization of Zadeh’s extension principle. Finally, we use our proposal method to fit a longitudinal dataset.

N. J. B. Pinto—Grantee CAPES 1691227.

V. F. Wasques—Grantee CNPq 142414/2017-4.

E. Esmi—Grantee FAPESP 2016/26040-7.

L. C. Barros—Grantee CNPq 306546/2017-5.

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Authors and Affiliations

  1. Institute of Mathematics, Statistics and Scientific Computing, State University of Campinas, Campinas, São Paulo, 13081-970, Brazil

    Nilmara J. B. Pinto, Vinícius F. Wasques, Estevão Esmi & Laécio C. Barros

Authors
  1. Nilmara J. B. Pinto
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  2. Vinícius F. Wasques
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  3. Estevão Esmi
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  4. Laécio C. Barros
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Corresponding authors

Correspondence to Nilmara J. B. Pinto or Vinícius F. Wasques .

Editor information

Editors and Affiliations

  1. Department of Teleinformatics Engineering, Federal University of Ceará, Fortaleza, Ceará, Brazil

    Guilherme A. Barreto

  2. Department of Statistics & Applied Mathematics, Federal University of Ceará, Fortaleza, Ceará, Brazil

    Ricardo Coelho

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Pinto, N.J.B., Wasques, V.F., Esmi, E., Barros, L.C. (2018). Least Squares Method with Interactive Fuzzy Coefficient: Application on Longitudinal Data. In: Barreto, G., Coelho, R. (eds) Fuzzy Information Processing. NAFIPS 2018. Communications in Computer and Information Science, vol 831. Springer, Cham. https://doi.org/10.1007/978-3-319-95312-0_12

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  • DOI: https://doi.org/10.1007/978-3-319-95312-0_12

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-95311-3

  • Online ISBN: 978-3-319-95312-0

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