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.
The author’s work has been supported by MIUR\(\backslash\)PRIN project “Automata and Formal languages: mathematical and application driven studies”and by “Funds of Sovvenzione Globale INGENIO allocated by Fondo Sociale Europeo, Ministero del Lavoro e della Previdenza Sociale, and Regione Lombardia”.
For lack of space, this is an extended abstract of a forthcoming larger version.
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References
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Bianucci, D., Cattaneo, G. (2008). On Non–pointwise Entropies of Coverings: Relationship with Anti–monotonicity . In: Wang, G., Li, T., Grzymala-Busse, J.W., Miao, D., Skowron, A., Yao, Y. (eds) Rough Sets and Knowledge Technology. RSKT 2008. Lecture Notes in Computer Science(), vol 5009. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-79721-0_54
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DOI: https://doi.org/10.1007/978-3-540-79721-0_54
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