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Boscovich Fuzzy Regression Line

Author

Listed:
  • Pavel Škrabánek

    (Institute of Automation and Computer Science, Brno University of Technology, Technická 2896/2, 616 69 Brno, Czech Republic)

  • Jaroslav Marek

    (Department of Mathematics and Physics, University of Pardubice, Studentská 95, 532 10 Pardubice, Czech Republic)

  • Alena Pozdílková

    (Department of Mathematics and Physics, University of Pardubice, Studentská 95, 532 10 Pardubice, Czech Republic)

Abstract

We introduce a new fuzzy linear regression method. The method is capable of approximating fuzzy relationships between an independent and a dependent variable. The independent and dependent variables are expected to be a real value and triangular fuzzy numbers, respectively. We demonstrate on twenty datasets that the method is reliable, and it is less sensitive to outliers, compare with possibilistic-based fuzzy regression methods. Unlike other commonly used fuzzy regression methods, the presented method is simple for implementation and it has linear time-complexity. The method guarantees non-negativity of model parameter spreads.

Suggested Citation

  • Pavel Škrabánek & Jaroslav Marek & Alena Pozdílková, 2021. "Boscovich Fuzzy Regression Line," Mathematics, MDPI, vol. 9(6), pages 1-14, March.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:6:p:685-:d:522357
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    References listed on IDEAS

    as
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    2. Hojati, Mehran & Bector, C. R. & Smimou, Kamal, 2005. "A simple method for computation of fuzzy linear regression," European Journal of Operational Research, Elsevier, vol. 166(1), pages 172-184, October.
    3. Kao, Chiang & Chyu, Chin-Lu, 2003. "Least-squares estimates in fuzzy regression analysis," European Journal of Operational Research, Elsevier, vol. 148(2), pages 426-435, July.
    4. Tanaka, Hideo & Hayashi, Isao & Watada, Junzo, 1989. "Possibilistic linear regression analysis for fuzzy data," European Journal of Operational Research, Elsevier, vol. 40(3), pages 389-396, June.
    5. D'Urso, Pierpaolo & Gastaldi, Tommaso, 2000. "A least-squares approach to fuzzy linear regression analysis," Computational Statistics & Data Analysis, Elsevier, vol. 34(4), pages 427-440, October.
    6. Kim, Kwang Jae & Moskowitz, Herbert & Koksalan, Murat, 1996. "Fuzzy versus statistical linear regression," European Journal of Operational Research, Elsevier, vol. 92(2), pages 417-434, July.
    Full references (including those not matched with items on IDEAS)

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