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A goal programming approach to fuzzy linear regression with fuzzy input–output data

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Abstract

Fuzzy linear regression is an active area of research. In the literature, fuzziness is considered in outputs and/or in inputs. This paper focuses on both fuzzy inputs and fuzzy outputs. First, some approximations for multiplication of two triangular fuzzy numbers are introduced. Then, to evaluate the fuzzy linear regression, the best approximation is selected to minimize a suitable function via goal programming. An important feature of the proposed model is that it takes into account the centers of fuzzy data as well as their spreads. Moreover, it is flexible to deal with both symmetric and non-symmetric data. Furthermore, it can handle the crisp inputs and trapezoidal fuzzy outputs easily. To show the efficiency of the proposed model, some numerical examples are solved and compared with some earlier methods.

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Acknowledgments

The authors would like to express their gratitude to the two anonymous referees for their comments and suggestions on the first version of this paper. Also, partial support by the Fuzzy Systems and Applications Center of Excellence at Shahid Bahonar University of Kerman is gratefully acknowledged.

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Authors and Affiliations

  1. Department of Mathematics, University of Birjand, Birjand, Islamic Republic of Iran

    H. Hassanpour

  2. Faculty of Basic Sciences, Shiraz University of Technology, Shiraz, Islamic Republic of Iran

    H. R. Maleki

  3. Department of Mathematics, Faculty of Mathematics and Computer, Shahid Bahonar University of Kerman, Kerman, Islamic Republic of Iran

    M. A. Yaghoobi

Authors
  1. H. Hassanpour
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  2. H. R. Maleki
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  3. M. A. Yaghoobi
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Correspondence to H. Hassanpour.

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Hassanpour, H., Maleki, H.R. & Yaghoobi, M.A. A goal programming approach to fuzzy linear regression with fuzzy input–output data. Soft Comput 15, 1569–1580 (2011). https://doi.org/10.1007/s00500-010-0688-6

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