A Fuzzy Regression Technique Through Same-Points in Fuzzy Geometry

  • Debdas GhoshEmail author
  • Ravi Raushan
  • Gaurav Somani
Conference paper
Part of the Communications in Computer and Information Science book series (CCIS, volume 834)


In this short article, a method to obtain a fuzzy regression curve for a set of imprecise locations is proposed. The given imprecise locations are presented by fuzzy points. The studied fuzzy regression curve is obtained with the help of a smooth regression technique for a set of precise locations. We observe the given imprecise points as a bunch of same points with varied membership values. For a set of same points, we obtain a smooth regression curve. The union of all these smooth regression curves, with different membership values, for the same points yields the proposed fuzzy regression curve. The method is demonstrated with a numerical example.


Fuzzy points Same points Fuzzy curves Smooth regression Fuzzy regression 



The first author gratefully acknowledges the financial support through Early Career Research Award (ECR/2015/000467), Science & Engineering Research Board, Government of India.


  1. 1.
    Geoffrey, S.W.: Smooth regression analysis, Sankhya, Series A (1961–2002), vol. 26, no. 4, pp. 359–372, December 1964Google Scholar
  2. 2.
    Chakraborty, D., Ghosh, D.: Analytical fuzzy plane geometry II. Fuzzy Sets Syst. 243, 84–110 (2014)MathSciNetCrossRefGoogle Scholar
  3. 3.
    Ghosh, D., Chakraborty, D.: Analytical fuzzy plane geometry I. Fuzzy Sets Syst. 209, 66–83 (2012)MathSciNetCrossRefGoogle Scholar
  4. 4.
    Ghosh, D., Chakraborty, D.: Analytical fuzzy plane geometry III. Fuzzy Sets Syst. 283, 83–107 (2016)MathSciNetCrossRefGoogle Scholar
  5. 5.
    Ghosh, D., Chakraborty, D.: On general form of fuzzy lines and its application in fuzzy line fitting. J. Intell. Fuzzy Syst. 29, 659–671 (2015)MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer Nature Singapore Pte Ltd. 2018

Authors and Affiliations

  1. 1.Department of Mathematical SciencesIndian Institute of Technology (BHU) VaranasiVaranasiIndia

Personalised recommendations