Revista Integración, temas de matemáticas.

Revista Integración, temas de matemáticas

Vol. 30 Núm. 1 (2012): Revista Integración, temas de matemáticas
Artículos científicos

Una aproximación a los conjuntos alcanzables de una inclusión diferencial difusa

PDF
  • William González Calderón
William González Calderón
Universidad Autónoma de Bucaramanga, Departamento de Matemáticas y Ciencias Naturales, A.A. 1642, Bucaramanga, Colombia.

Publicado 2012-08-21

Palabras clave

  • inclusiones diferenciales difusas,
  • técnicas de aproximación,
  • con-juntos alcanzables difusos

Cómo citar

González Calderón, W. (2012). Una aproximación a los conjuntos alcanzables de una inclusión diferencial difusa. Revista Integración, Temas De matemáticas, 30(1), 57–74. Recuperado a partir de https://revistas.uis.edu.co/index.php/revistaintegracion/article/view/2702

Resumen

Se estudian los sistemas dinámicos difusos a partir de la noción de inclusión diferencial difusa introducida en [24]. Se analizan algunas técnicas utilizadas para resolver inclusiones diferenciales difusas asociadas a problemas de valor inicial, y se introduce una nueva forma de aproximación a los conjuntos alcanzables difusos, la cual permite resolver de manera más natural una inclusión diferencial difusa.

PDF

Descargas

Los datos de descargas todavía no están disponibles.

Referencias

  1. Abbasbandy S., Nieto J.J. and Alavic M., “Tuning of reachable set in one dimensional fuzzy differential inclusions”, Chaos Solitions Fractals 26 (2005), no. 5, 1337–1341.
  2. Aubin J.P., “Fuzzy differential inclusions”, Problems Control Inform. Theory/Problemy Upravlen. Teor. Inform. 19 (1990), no. 1, 55–67.
  3. Aubin J.P. and Cellina A., Differential inclusions. Set-valued maps and viability theory, Springer-Verlag, Berlin, 1984.
  4. Aubin J.P. and Frankowska H., Set-Valued Analysis, Birkhäuser Boston, Inc., Boston, MA, 1990.
  5. Baidosov V.A., “Differential inclusions with fuzzy right-hand side”, Soviet Math. Dokl. 40 (1990), no. 3, 567–569.
  6. Baidosov V.A., “Fuzzy differential inclusions”, J. Appl. Math. Mech. 54 (1990), no. 1, 8–13.
  7. Barros L.C., Bassanezi R.C. and de Oliveira R.Z.G., “Epidemiological Models with Fuzzy Differential Inclusion”, Proceedings of the Third Brazilian Symposium on Mathematical and
  8. Computational Biology, vol. II, R. Mondaini (editor), E-Papers Serviços Editoriais, Ltda.,Rio de Janeiro, (2004).
  9. Bede B. and Gal S.G., “Almost periodic fuzzy-number-valued functions”, Fuzzy Sets and System 147 (2004), no. 3, 385–403.
  10. Bede B. and Gal S.G., “Generalizations of the differentiability of fuzzy-number-valued functions with applications to fuzzy differential equations”, Fuzzy Sets and Systems 151 (2005), no. 3, 581–599.
  11. Bencsik A., Bede B., Tar J. and Fodor J., Fuzzy differential equations in modeling hydraulic differential servo cylinders, Third Romanian-Hungarian joint symposium on applied computational
  12. intelligence (SACI), Timisoara, Romania, 2006.
  13. Bothe D., “Multivalued differential equations on graphs”, Nonlinear Anal. 18 (1992), no. 3, 245–252.
  14. Cellina A., “Approximation of set valued functions and fixed point theorems”, Ann. Mat. Pura Appl. 4 (1969), no. 82, 17–24.
  15. Chalco-Cano Y. and Román-Flores H., “Comparation between some approaches to solve fuzzy differential equations”, Fuzzy Sets and Systems 160 (2009), no. 11, 1517–1527.
  16. Chalco-Cano Y., Rojas-Medar M.A. and Román-Flores H., “Fuzzy differential equations with generalized derivate”, Proc. 27 th NAFIPS Internat. Conf. IEEE, (2008).
  17. Chalco-Cano Y., Rojas-Medar M.A. and Román-Flores H., “Sobre ecuaciones diferenciales difusas”, Bol. Soc. Esp. Mat. Apl. S�eMA 41 (2007), 91–99.
  18. Chen M., Li D. and Xue X., “Periodic problems of first order uncertain dynamical systems”,Fuzzy Sets and Systems 162 (2011), 67–78.
  19. Diamond P., “Time-dependent differential inclusions, cocycle attractors and fuzzy differential equations”, IEEE Trans. Fuzzy System 7 (1999), no. 6, 734–740.
  20. Diamond P., “Stability and periodicity in fuzzy differential equations”, IEEE Trans. Fuzzy System 8 (2000), no. 8, 583–590.
  21. Diamond P. and Watson P., “Regularity of solution sets for differential inclusions quasiconcave in a parameter”, Appl. Math. Lett. 13 (2000), no. 1, 31–35.
  22. Fernández-Cara E., Rojas-Medar M.A. y Brandão A.J.V., “Inclusiones Diferenciales, Matemática Difusa y Aplicaciones”, Bol. Soc. Esp. Mat. Apl. SeMA 24 (2003), 31–62.
  23. Guo M. and Li R., “Impulsive functional differential inclusions and fuzzy populations models”, Fuzzy Sets and Systems 138 (2003), no. 3, 601–615.
  24. Guo M., Xue X. and Li R., “The oscillation of delay differential inclusions and fuzzy biodynamics models”, Math. Comput. Modelling 37 (2003), no. 7-8, 651–658.
  25. Hüllermeier E., A fuzzy simulation method, International Symposium on Soft Computing, 1996.
  26. Hüllermeier E., “An approach to modeling and simulation of uncertain dynamical systems”,International Journal of Uncertainty, Fuziness and Knowledge-Bases Systems 5 (1997), no. 2, 117–137.
  27. Hüllermeier E., “Numerical methods for fuzzy initial value problems”, International Journal of Uncertainty, Fuziness and Knowledge-Bases Systems 7 (1999), no. 5, 439-461.
  28. Kaleva O., “Fuzzy differential equations”, Fuzzy Sets and Systems 24 (1987), no. 3, 301–317.
  29. Kaleva O., “A note on fuzzy differential equations”, Nonlinear Anal. 64 (2006), no. 5, 895-900.
  30. Kaleva O., “The Cauchy problem for fuzzy differential equations”, Fuzzy Sets and Systems 35 (1990), no. 3, 389–396.
  31. Kandel A. and Byatt W.J., “Fuzzy differential equations”, Proceedings of the International Conference on Cybernetics and Society, Tokyo, November 1978, 1213–1216.
  32. Kisielewicz M., Differential inclusions and optimal control, Mathematics and its Applications (East European Series), Warsaw, 1991.
  33. Kloeden P.E., “Remarks on peano-like theorems for fuzzy differential equations”, Fuzzy Sets and Systems 44 (1991), no. 1, 161–163.
  34. Colombo G., “A non-stochastic approach for modelling uncertainty in population dinamic”, Bull. Math. Biology 60 (1998), 721–751.
  35. Majumdar K.K., “A fuzzy dynamical system modelling of a disturbance leading to cyclogenesis”, Journal of Intelligent and Fuzzy Systems 13 (2002), 7–15.
  36. Majumdar K.K. and Majumder D.D., “Fuzzy differential inclusions in atmospheric and medical cybernetics”, IEEE Transactions on Systems, Man, and Cybernetics, Part-B: Cybernetics
  37. (2004), no. 2, 877–887.
  38. Nieto J.J. and Rodriguez-López R., “Bounded solutions for fuzzy differential and integral equations”, Chaos Solitons Fractals 27 (2006), no. 5, 1376–1386.
  39. Nieto J.J., “The Cauchy problem for continuous fuzzy differential equations”, Fuzzy Sets and Systems 102 (1999), no. 2, 259–262.
  40. Oberguggenberger M. and Pittschmann S., “Differential equations with fuzzy parameters”, Mathematical and Computer Modelling of Dynamical Systems 5 (1999), no. 3, 181–202.
  41. Puri M.L. and Ralescu D.A., “Differential and fuzzy functions”, J. Math. Anal. Appl. 91 (1983), no. 2, 552–558.
  42. Puri M.L. and Ralescu D.A., “Fuzzy random variables”, J. Math. Anal. Appl. 114 (1986), no. 2, 409–422.
  43. Rojas-Medar M.A., Notas de Análisis Fuzzy Multívoco, Universidad Estadual de Campinas, 2003.
  44. Seikkala S., “On the fuzzy initial value problem”, Fuzzy Sets and Systems 24 (1987), no. 3,
  45. –330.
  46. Song S. and Wu C., “Existence and uniqueness of solutions to Cauchy problem of fuzzy diferential equations”, Fuzzy Sets and Systems 110 (2000), no. 1, 55–67.
  47. Villamizar-Roa E.J. and González-Calderón W., “A note on the Cauchy problem of fuzzy differential equations”, Rev. Acad. Colombiana Cienc. Exact. Fís. Natur. 34 (2010), no. 133, 541–552.
  48. Zhu Y. and Rao L., “Differential inclusions for fuzzy maps”, Fuzzy Sets and Systems 112(2000), no. 2, 257–261.