On non-pointwise entropies of coverings: relationship with anti-monotonicity

  • Authors:
  • Daniela Bianucci;Gianpiero Cattaneo

  • Affiliations:
  • Dipartimento di Informatica, Sistemistica e Comunicazione, Università di Milano-Bicocca, Milano, Italia;Dipartimento di Informatica, Sistemistica e Comunicazione, Università di Milano-Bicocca, Milano, Italia

  • Venue:
  • RSKT'08 Proceedings of the 3rd international conference on Rough sets and knowledge technology
  • Year:
  • 2008

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Abstract

Some approaches to the entropy of coverings, generalizing the case of the partition entropy, and some definitions of orderings and quasi-orderings of coverings as extensions to the covering context of various formulations of the standard order on partitions. Unfortunately, we here show that the problem of anti-monotonicity of non-pointwise entropy of coverings is still open. On the other side, we will illustrate an approach to generate a partition from a covering; we will then show how we can indirectly compare the entropies of two coverings, that are in a certain order relation, by comparing the entropies of the induced partitions.