Proximity measures in symbolic data analysis

Abstract

The Authors consider the general problem of similarity and dissimilarity measures in Symbolic Data Analysis. First of all they examine the classical definitions of elementary event, assertion object, hierarchical dependences and logical dependences. Then they consider some well-known measures of similarity and dissimilarity between two objects (Sokal-Michener, Roger-Tanimoto, Sokal-Sneath, Dice-Czekanowski-Sorenson, Russel-Rao). For resemblance measures based on aggregation functions, the authors consider the proposal of Gowda-Diday, De Baets et al., Malerba et al., Vladutu et al., and Ichino-Iyaghuchi. A paragraph is dedicated to the general algebraic structure; particularly to intervals and vector lattices in Banach space.