Generalized Minkowski metrics for mixed features

Abstract This paper presents simple and convenient generalized Minkowski metrics on multidimensional feature space in which each coordinate axis is associated not only with a quantitative feature, but also a qualitative feature. The metrics are defined on a new mathematical model ( U ( d ), +, × constructed by the authors called simply the Cartesian space model. In this model, U ( d ) is the feature space, + is the Cartesian join operator which abstracts a generalized description from two given descriptions on U ( d ) , and × is the Cartesian meet which extracts a common description from two given descriptions on U ( d ) . In our approach, intervals and finite sets are also permitted as possible feature values. Two simple numerical examples are presented to illustrate the usefulness of our metrics.