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International Journal of Approximate Reasoning
Volume 40, Issue 3, November 2005, Pages 127-146
 
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doi:10.1016/j.ijar.2004.10.008    How to Cite or Link Using DOI (Opens New Window)
Copyright © 2004 Elsevier Inc. All rights reserved.

A generalization of local divergence measures

Carlo Bertoluzzaa, E-mail The Corresponding Author, Pedro Mirandab, Corresponding Author Contact Information, E-mail The Corresponding Author and Pedro Gilc, E-mail The Corresponding Author

aDipartimento de Informatica e Sistemistica, INFM Section of Pavia, University of Pavia, Pavia 27100, Italy bDepartamento de Estadística e I.O., Complutense University of Madrid, Plaza de Ciencias, 3, Madrid 28040, Spain cDepartamento de Estadística, I.O. y D.M., University of Oviedo, Oviedo 33007, Spain

Received 1 February 2004; 
accepted 1 October 2004. 
Available online 26 November 2004.

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Abstract

In this paper we propose a generalization of the concept of the local property for divergence measures. These new measures will be called g-local divergence measures, and we study some of their properties. Once this family is defined, a characterization based on Ling’s theorem is given. From this result, we obtain the general form of g-local divergence measures as a function of the divergence in each element of the reference set; this study is divided in three parts according to the cardinality of the reference set: finite, infinite countable or non-countable. Finally, we study the problem of componible divergence measures as a dual concept of g-local divergence measures.

Keywords: Divergence measures; Local property; Ling’s theorem; Componibility


 
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