Interval Regression Analysis with Polynomials and Its Similarity to Rough Sets Concept

  • Authors:

  • Hideo Tanaka;Haekwan Lee

  • Affiliations:

  • (Correspd.) Department of Industrial Engineering, Osaka Prefecture University, Gakuencho 1-1, Sakai, Osaka 599-8531, JAPAN. tanaka@ie.osakafu-u.ac.jp;(Correspd.) Department of Industrial Engineering, Osaka Prefecture University, Gakuencho 1-1, Sakai, Osaka 599-8531, JAPAN. tanaka@ie.osakafu-u.ac.jp

  • Venue:
  • Fundamenta Informaticae
  • Year:
  • 1999

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Abstract

This paper proposes interval regression analysis with polynomials. For data sets with crisp inputs and interval outputs, three estimation models called as an upper, a lower, and a possibility estimation models can be formulated from the concepts of the possibility and necessity measures. Always there exists an upper and a possibility estimation model when a linear system with interval coefficients is considered, but it is not assured to attain a solution for a lower estimation model in an interval linear system. If we can not obtain the lower estimation model, it might be caused by adopting a model not fitting to the given data. Thus we consider polynomials to find a regression model which fits well to the given observations. The possibility model is used to check the existence of the lower model. If we can find a proper lower model, the estimated upper and lower models deserve more credit than the previous models in the former studies. We also introduce the measure of fitness to gauge the degree of approximation of the obtained models to the given data. The upper and lower estimation models in interval regression analysis can be considered as the upper and lower approximations in rough sets. The similarity between the interval estimation models and the rough sets concept is also discussed. In order to illustrate our approach, numerical examples are shown.