A new pseudometric on a subclass of Riesz spaces based on similarity measures

Abstract

The Bunke–Shearer metric is one of many distance measures used in data analysis for studying similarities between finite sets. In this work, we generalize it to a new pseudometric for a certain subclass of Riesz spaces. We exemplify some particular cases of this general pseudometric in the contexts of measure spaces, Euclidean spaces, and fuzzy sets.