Distance Measure for Ordinal Data

Abstract

The study considers the problem of construction measures of similarity for ordinal data. The ordinal character of the data required the application of a specific measure of the object’s distance. Walesiak (1993, p. 44–45), gives the proposal of a new measure of an objects similarity, which can be applied in the situation when variables describing objects are measured on the ordinal scale. This measure was used in order to evaluate the similarities of objects, which were based on numbers of relations “equal to”, “greater than”, and “smaller than”. The distance measure takes care of variables with equal weights. We shall describe a slight generalisation of this measure, also covering different weights of variables. The strengths and weaknesses of the proposed distance measure are discussed.