Agglomerative clustering of symbolic objects using the concepts of both similarity and dissimilarity
Pattern Recognition Letters
Computers and Industrial Engineering
Towards general measures of comparison of objects
Fuzzy Sets and Systems - Special issue dedicated to the memory of Professor Arnold Kaufmann
Ordered similarity measures taking into account the rank of documents
Information Processing and Management: an International Journal
A class of rational cardinality-based similarity measures
Journal of Computational and Applied Mathematics
Improved heterogeneous distance functions
Journal of Artificial Intelligence Research
Cluster structures and collections of Galois closed entity subsets
Discrete Applied Mathematics
Hi-index | 7.29 |
The counting measure applies only on countable subsets of the set of real numbers. On the other hand, the Lebesgue measure applies on any countable union of intervals but ignores countable subsets since it assigns to them a null weight indiscriminately. This paper proposes a measure of content which applies on finite unions of intervals and enables to differentiate finite sets. This measure of content is shown to be a Choquet capacity. Furthermore, extension onto the system of all subsets of the real number set is discussed and ideas for generalization to the multidimensional space are presented. A class of content-based measures of comparison is also suggested, along with a discussion of some of their basic properties.