Artículos científicos
Publicado 2009-03-05
Palabras clave
- Métrica de Hausdorff,
- conjunto difuso compacto,
- conjunto difuso cerrado
Cómo citar
Chalco-Cano, Y., & Jiménez-Gamero, M. D. (2009). Una generalización de la métrica de Hausdorff sobre C(Rn). Revista Integración, Temas De matemáticas, 27(1), 59–67. Recuperado a partir de https://revistas.uis.edu.co/index.php/revistaintegracion/article/view/501
Resumen
En este trabajo hacemos una extensión de la métrica de Hausdorff sobre C(Rn), el espacio de todos los conjuntos difusos cerrados en Rn, obteniendo una familia de métricas Df . Estudiamos algunas propiedades topológicas del espacio métrico C(Rn),Df.
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Referencias
[1] J.P. Aubin and A. Cellina. Differential Inclusions, Springer- Verleg, New york Tokyo, 1984.
[2] C. Bertoluzza, N. Corral, A. Salas. “On new class of distances between fuzzy numbers”, Mathware Soft Computing, 2 (1995) 71-84.
[3] S. Barro and R. Marín. Fuzzy Logic in Medicine, Heidelberg: Physica-Verlag, 2002.
[4] Y. Chalco-Cano and H. Román-Flores. “On the new solution of fuzzy differential equations”, Chaos, Solitons & Fractals, 38 (2008) 112-119.
[5] D.P. Datta. “The Golden mean, scale free extension of real number system, fuzzy sets and 1/f spectrum in physics and biology”, Chaos, Solitons& Fractals, 17 (2003) 781-788.
[6] P. Diamond and P. Kloeden. Metric Space of Fuzzy Sets:Theory and Application, Singapure World Scientific, 1994.
[7] M. Hanss. Applied Fuzzy Arithmetic: An Introduction with Engineering Applications, Springer Verlag, Berlin, 2005.
[8] F. Hiai. “Strong laws of large numbers for multivalued random variables, Multifunctions and Integrands” (G. Salinetti, ed.), Lecture Notes in Math., vol. 1091, SpringerBerlag, (1984) 160-172.
[9] F. Hiai. “Convergence of conditional expectations and strong laws of large numbers for multivalued random variables”, Trans. Amer. Math. Soc., 291 (1985) 613-627.
[10] C. Hess. “The distribution of Unbounded Random Sets and the Multivalued Strong Law of Large Numbers in Nonreflexive Banach Spaces”, J. Convex Anal., 6 (1999) 163-182.
[11] S.P. Moshokoa. “The Hausdorff metric and its extensions”, Demostratio Mathematica, Vol XXXV,No 2 (2002) 233-241.
[12] E.P. Klement, M.L. Puri and D.A. Ralescu. “Limit theorems for fuzzy random variables”, Proc. R. Soc. Lond., A-407 (1986) 171-182.
[13] V. Kratschmer. “Some complete metrics on spaces of fuzzy subsets”, Fuzzy Sets and Systems, 130 (2002) 357-365.
[14] M.L. Puri, D.A. Ralescu. “Fuzzy random variables”, J. Math. Anal. Appl. 114 (1986) 409-422.
[15] W. Trutschnig, G. González-Rodríguez, A. Colubi, M.A. Gil. “A new family of metrics for compact, convex (fuzzy) sets based on a generalized concept of mid and spread”, Infromation Sciences (2009).
[2] C. Bertoluzza, N. Corral, A. Salas. “On new class of distances between fuzzy numbers”, Mathware Soft Computing, 2 (1995) 71-84.
[3] S. Barro and R. Marín. Fuzzy Logic in Medicine, Heidelberg: Physica-Verlag, 2002.
[4] Y. Chalco-Cano and H. Román-Flores. “On the new solution of fuzzy differential equations”, Chaos, Solitons & Fractals, 38 (2008) 112-119.
[5] D.P. Datta. “The Golden mean, scale free extension of real number system, fuzzy sets and 1/f spectrum in physics and biology”, Chaos, Solitons& Fractals, 17 (2003) 781-788.
[6] P. Diamond and P. Kloeden. Metric Space of Fuzzy Sets:Theory and Application, Singapure World Scientific, 1994.
[7] M. Hanss. Applied Fuzzy Arithmetic: An Introduction with Engineering Applications, Springer Verlag, Berlin, 2005.
[8] F. Hiai. “Strong laws of large numbers for multivalued random variables, Multifunctions and Integrands” (G. Salinetti, ed.), Lecture Notes in Math., vol. 1091, SpringerBerlag, (1984) 160-172.
[9] F. Hiai. “Convergence of conditional expectations and strong laws of large numbers for multivalued random variables”, Trans. Amer. Math. Soc., 291 (1985) 613-627.
[10] C. Hess. “The distribution of Unbounded Random Sets and the Multivalued Strong Law of Large Numbers in Nonreflexive Banach Spaces”, J. Convex Anal., 6 (1999) 163-182.
[11] S.P. Moshokoa. “The Hausdorff metric and its extensions”, Demostratio Mathematica, Vol XXXV,No 2 (2002) 233-241.
[12] E.P. Klement, M.L. Puri and D.A. Ralescu. “Limit theorems for fuzzy random variables”, Proc. R. Soc. Lond., A-407 (1986) 171-182.
[13] V. Kratschmer. “Some complete metrics on spaces of fuzzy subsets”, Fuzzy Sets and Systems, 130 (2002) 357-365.
[14] M.L. Puri, D.A. Ralescu. “Fuzzy random variables”, J. Math. Anal. Appl. 114 (1986) 409-422.
[15] W. Trutschnig, G. González-Rodríguez, A. Colubi, M.A. Gil. “A new family of metrics for compact, convex (fuzzy) sets based on a generalized concept of mid and spread”, Infromation Sciences (2009).