Different generalizations to the case of coverings of the standard approach to entropy applied to partitions of a finite universe X are explored. In the first approach any covering is represented by an identity resolution of fuzzy sets on X and a corresponding probability distribution with associated entropy is defined. A second approach is based on a probability distribution generated by the covering normalizing the standard counting measure. Finally, the extension to a generic covering of the Liang-Xu approach to entropy is investigated, both from the "global" and the "local" point of view. For each of these three possible entropies the complementary entropy (or co-entropy) is defined showing in particular that the Liang-Xu entropy is a co-entropy.

Bianucci, D., Cattaneo, G., Ciucci, D. (2007). Entropies and co-entropies of coverings with application to incomplete information systems. FUNDAMENTA INFORMATICAE, 75(1-4), 77-105.

Entropies and co-entropies of coverings with application to incomplete information systems

CATTANEO, GIANPIERO;CIUCCI, DAVIDE ELIO
2007

Abstract

Different generalizations to the case of coverings of the standard approach to entropy applied to partitions of a finite universe X are explored. In the first approach any covering is represented by an identity resolution of fuzzy sets on X and a corresponding probability distribution with associated entropy is defined. A second approach is based on a probability distribution generated by the covering normalizing the standard counting measure. Finally, the extension to a generic covering of the Liang-Xu approach to entropy is investigated, both from the "global" and the "local" point of view. For each of these three possible entropies the complementary entropy (or co-entropy) is defined showing in particular that the Liang-Xu entropy is a co-entropy.
Articolo in rivista - Articolo scientifico
Information system, Information entropy, covering
English
gen-2007
75
1-4
77
105
open
Bianucci, D., Cattaneo, G., Ciucci, D. (2007). Entropies and co-entropies of coverings with application to incomplete information systems. FUNDAMENTA INFORMATICAE, 75(1-4), 77-105.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/1423
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