Published in Volume XXXIV, Issue 1, 2024, pages 67-87, doi: 10.47743/SACS.2024.1.67

Authors: D. Simovici


We introduce an axiomatization of entropy that generates, as special cases, novel entropy types. These entropies generalize Shannon’s entropy and allow the introduction of entropy for partitions of sets of objects located in metric spaces, and for partitions of sets of vertices in undirected graphs. Corresponding metrics on the sets of partitions are introduced. Also, we hint to applications of these metrics for evaluation of clustering quality.

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  title={Monotonic Entropies},
  author={D. Simovici},
  journal={Scientific Annals of Computer Science},
  organization={Alexandru Ioan Cuza University, Ia\c si, Rom\^ania},
  publisher={Alexandru Ioan Cuza University Press, Ia\c si},