Publication:
A generalization of local divergence measures

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http://www.sciencedirect.com/science/article/pii/S0888613X04001148
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2005-11
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Elsevier Science INC
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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.
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Cibernética matemática
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1207.03 Cibernética
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C. Bertoluzza, I. Bonzani, Su una generalizzazione della nozione di diramativitá in teoria dell'informazione, Stochastica VII (1) (1983) 29–46 (in Italian). C. Bertoluzza, D. Cariolaro, On the measure of a fuzzy set based on continuous t-conorms, Fuzzy Sets Systems (88) (1997) 355–362. J. Kampé de Fériet, B. Forte, P. Benvenuti, Forme générale de l'opération de composition continue d'une information, C. R Acad. Sci. Paris Se´r A-B 269 (1969) 529–534 (in French). D. Dubois, H. Prade, Fuzzy Sets and Systems. Theory and Applications, Academic Press Inc., 1980. B. Forte, N. Pintacuda, Sull'informazione associata alle esperienze incomplete, Ann. Matematica pure e applicata (Ser. IV) Tomo LXXX (1968) 215–234 (in Italian). J. Jiménez, S. Montes, C. Bertoluzza, On the measure of a fuzzy set based on continuous t-conorms, in: Proceedings of EUSFLAT-ESTYLF Joint Conference, Palma de Mallorca (Spain), 1999, pp. 231–234. C.-H. Ling, Representation of associative functions, Publ. Math. Debrecen 12 (1965) 189–212. K. Menger, Statistical metrics, Proc. Nat. Acad. Sci. (28) (1942) 537–537. P. Miranda, E. Torres, P. Gil, Decision making and divergence measures: an application, Belgian J. Oper. Res. Statist. Comput. Sci. 38 (2–3) (1998) 51–66. S. Montes, Particiones y medidas de divergencia en modelos difusos, Ph.D. thesis, University of Oviedo, 1998 (in Spanish).
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https://hdl.handle.net/20.500.14352/50189
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