A generalization of local divergence measures

  • Authors:

  • Carlo Bertoluzza;Pedro Miranda;Pedro Gil

  • Affiliations:

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

  • Venue:
  • International Journal of Approximate Reasoning
  • Year:
  • 2005

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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.