1982 Volume 18 Issue 4 Pages 377-384
This paper proposes a new method of constructing interval scales from numerical data obtained by paired comparisons. This method is based on band function model.
Band function model has been suggested by Kobayashi and Shibata to construct a reasonable interval scale. However, Kobayashi-Shibata's iterative algorithm gives only one scale of various scales which should be given as solutions, and the accuracy is affected by the choice of initial value.
First, the authors explain that information contained in paired comparisons data can be transformed reasonably into simultaneous homogeneous linear inequalities.
Next, effective algorithm is introduced to solve the inequalities to obtain interval scales.
The solution domain is given as a set of inner points of a polyhedral convex cone, and expressed with a set of edge vectors. As the extent of the solution domain indicates the fuzziness, further discussion on precision has become able to be done.
This method is compared with Kobayashi-Shibata's method, and the solution of the latter method is shown to be located a step inside of the boundary of this method's solution domain.
Finally, the proposed method is applied to the experimental data obtained from subjective comparisons of weights. The obtained interval scale shows good agreement with the real weighing scale.
