On Perturbation Measure for Binary Vectors

Abstract

The paper is about remoteness of objects described by the nominal-valued attributes. Nominal values of the attributes are replaced by respective binary vectors. A new measure of remoteness between sets, based on binary attributes' values, is introduced. The new measure is called a measure of perturbation of one binary vector by another binary vector and can be treated as a binary version of developed by the authors sets' perturbation measure. Values of the newly developed measure range between 0 and 1, and the perturbation measure of one binary vector by another is not the same as the perturbation of the second binary vector by the first one-it means that the measure is not symmetric in general.