Communications of the Korean Mathematical Society (대한수학회논문집)

Korean Mathematical Society (대한수학회)
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FUZZY REGRESSION MODEL WITH MONOTONIC RESPONSE FUNCTION

  • Choi, Seung Hoe (School of Liberal Arts and Science Korea Aerospace University) ;
  • Jung, Hye-Young (Faculty of Liberal Education Seoul National University) ;
  • Lee, Woo-Joo (Department of Mathematics Yonsei University) ;
  • Yoon, Jin Hee (School of Mathematics and Statistics Sejong University)
  • Received : 2017.03.02
  • Accepted : 2018.05.18
  • Published : 2018.07.31
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Abstract

Fuzzy linear regression model has been widely studied with many successful applications but there have been only a few studies on the fuzzy regression model with monotonic response function as a generalization of the linear response function. In this paper, we propose the fuzzy regression model with the monotonic response function and the algorithm to construct the proposed model by using ${\alpha}-level$ set of fuzzy number and the resolution identity theorem. To estimate parameters of the proposed model, the least squares (LS) method and the least absolute deviation (LAD) method have been used in this paper. In addition, to evaluate the performance of the proposed model, two performance measures of goodness of fit are introduced. The numerical examples indicate that the fuzzy regression model with the monotonic response function is preferable to the fuzzy linear regression model when the fuzzy data represent the non-linear pattern.

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References

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