Fuzzy Differential Inclusions in Atmospheric and Medical Cybernetics

IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics

Volumn 34, Issue 2, 2004, Pages 877-887

  Majumdar, Kausik Kumar ^a   Majumder, Dwijesh Dutta ^a  

^a INDIAN STATISTICAL INSTITUTE   (India)

Author keywords

Carcinogenesis; Cybernetics; Cyclogenesis; Fuzzy differential inclusions; Fuzzy dynamical systems

Indexed keywords

ALGORITHMS; ARTIFICIAL INTELLIGENCE; CARCINOGENS; COMPUTER SIMULATION; FUZZY CONTROL; MATHEMATICAL MODELS; TUMORS;

CARCINOGENESIS; CYCLOGENESIS; FUZZY DIFFERENTIAL INCLUSIONS (FDI); FUZZY DYNAMICAL SYSTEMS;

CYBERNETICS;

ALGORITHM; ANIMAL; ARTICLE; ATMOSPHERE; BIOLOGICAL MODEL; CELL DIVISION; COMPUTER SIMULATION; CYBERNETICS; DISASTER; EVALUATION; FUZZY LOGIC; HUMAN; METHODOLOGY; NEOPLASM; PATHOLOGY; PATHOPHYSIOLOGY;

ALGORITHMS; ANIMALS; ATMOSPHERE; CELL DIVISION; COMPUTER SIMULATION; CYBERNETICS; FUZZY LOGIC; HUMANS; MODELS, BIOLOGICAL; NATURAL DISASTERS; NEOPLASMS;

EID: 1842430986     PISSN: 10834419     EISSN: None     Source Type: Journal    
DOI: 10.1109/TSMCB.2003.817105     Document Type: Article

References (60)

1. W. R. Ashby, An Introduction to Cybernetics. London, U.K.: Methuen, 1976.
2. E. Hullermeier, "An approach lo modeling and simulation of uncertain dynamical systems," Int. J. Uncertainty, Fuzzjness, Knowledge-Based Syst., vol. 5, pp. 117-137, 1997.
3. N. Wiener, Cybernetics: Or Control and Communication in the Animal and the Machine. New York: Wiley, 1949.
4. S. S. L. Chang and L. A. Zadeh, "On fuzzy mappings and control," IEEE Trans. Syst. Man, Cybern., vol. SMC-2, pp. 30-34, 1972.
5. P. E. Kloeden, "Fuzzy dynamical systems," Fuzzy Sets Syst., vol. 7, pp. 275-296, 1982.
6. M. de Glas, "Theory of fuzzy systems," Fuzzy Sets Syst., vol. 10, pp. 65-77, 1983.
7. O. Kaleva, "Fuzzy differential equations," Fuzzy Sets Syst., vol. 24, pp. 301-317, 1987.
8. S. Seikkala, "On the fuzzy initial value problem," Fuzzy Sets Syst., vol. 24, pp. 319-330, 1987.
9. K. K. Majumdar, "A fuzzy dynamical system modeling of a disturbance leading to cyclogenesis," J. Intell. Fuzzy Syst., vol. 13, pp. 7-15, 2003.
10. D.D. Majumder and K. K. Majumdar, "Complexity analysis, uncertainty management, and fuzzy dynamical systems: A cybernetic approach with some case studies," Kybernetes. to be published.
11. L. A. Zadeh, "Outline of a new approach to the analysis of complex systems and decision processes," IEEE Trans. Syst. Man, Cybern., vol. SMC-3. pp. 28-44, 1973.
12. E. Hullermeier, "Numerical methods for fuzzy initial value problems," Int. J. Uncertainty, Fuzziness, Knowledge-Based Syst., vol. 7, pp. 1-23, 1999.
13. H. T. Nguyen, "A note on the extension principle for fuzzy sets," J. Math. Anal. Appl., vol. 64, pp. 369-380, 1978.
14. V. F. Dvorak, "Tropical cyclone intensity analysis using satellite data," Satellite Applications Lab., Washington, DC, NOAA Tech. Rep. NESDIS 11, 1984.
15. K. A. Emanuel, "Toward a general theory of hurricanes," Amer Sci., vol. 76, pp. 370-379, 1988.
16. J. C. Mandal, "A semi-implicit multiple-nested grid model for simulation of flow in a tropical storm," Mausam, vol. 47, pp. 1-20, 1996.
17. K. Ooyama, "Numerical simulation of life-cycle of tropical cyclones," J. Atmos. Sci., vol. 26, pp. 3-40, 1969.
18. R. Rotuno and K. A. Emanuel, "An air-sea interaction theory for tropical cyclones. Part II: Evolutionary study using a nonhydrostatic axisymmetric numerical model," J. Atmos. Sci., vol. 44, pp. 542-561.
19. P. Bouthemy and A. Benveniste, "Modeling of atmospheric disturbances in meteorological pictures," IEEE Trans. Patt. Anal. Machine Intell., vol. PAMI-6, pp. 587-600, 1984.
20. R. A. Anthes, "Tropical cyclones: Their evolution, structures, and effects," Amer. Meteorol. Soc., Mono. no. 41, 1982.
21. R. A. Brown, Fluid Mechanics of the Atmosphere. San Diego, CA: Academic, 1991.
22. G. J. Klir and B. Yuan, Fuzzy Sets and Fuzzy Logic: Theory and Applications. New Delhi, India: Prentice-Hall, 1997.
23. A. Kandel, Y. Luo, and Y.-Q. Zhang, "Stability analysis of fuzzy control systems," Fuzzy Sets Syst., vol. 105, pp. 33-48, 1999.
24. D. D. Majumder, "Cybernetics and general systems - A unitary science," Kybernetes, vol. 8, pp. 7-15, 1979.
25. D. D. Majumder and P. K. Roy, "Cancer self-remission and tumor instability - A cybernetic analysis: Toward a fresh paradigm for cancer treatment," Kybernetes, vol. 29, pp. 896-927, 2000.
26. P. Roy, D. D. Majumder, and J. Biswas, "Spontaneous cancer regression: Implications for fluctuation," Ind. J. Phys.,vol. 73-B, pp. 777-883, 1999.
27. W. Horsthemke and R. Lefever, Noise-Induced Transitions: Applications to Physics, Chemistry, and Biology, Berlin: Springer, 1984.
28. P. Glansdorff and I. Prigogine, Thermodynamic Theory of Stability, Structure and Fluctuation. London, U.K.: Wiley, 1971.
29. R. Lefever and W. Horsthemke, "Bistability in fluctuating environments. Implications in tumor immunology," Bull. Math. Biol., vol. 41, pp. 469-490, 1979.
30. R. Lefever and R. P. Garay, "A mathematical model of the immune surveillance against cancer," in Theoretical Immunology, G. I. Bell, A. S. Perelson, and G. H. Pimbley, Eds. New York: Marcel Dekker, 1978.
31. R. P. Garey and R. Lefever, "A kinetic approach to the immunology of cancer: Stationary state properties of effector-target cell reactions," J. Theoretical Biol., vol. 73, pp. 417-438, 1978.
32. L. E. Dickson, New First Course in the Theory of Equations. New York: Wiley, 1947.
33. T. Kapitaniak and S. R. Bishop. The Illustrated Dictionary of Nonlinear Dynamics and Chaos. Chichester, U.K.: Wiley, 1999.
34. H. Haken, "Transition phenomena in nonlinear systems," in Stochastic Nonlinear Systems in Physics, Chemistry, and Biology. L. Arnold and R. Lefever, Eds, Berlin, Germany: Springer-Verlag, 1981.
35. V. Krivan and G. Colombo, "A nonstochastic approach for modeling uncertainty in population dynamics," Bull. Math. Biol., vol. 60, pp. 721-751, 1998.
36. J.-P. Aubin, "Fuzzy differential inclusions," Probl. Cont. Inform. Theory, vol. 19, pp. 55-57, 1990.
37. K. K. Majumdar, "A mathematical model of the nascent cyclone," IEEE Int. Geosci. Remote Sensing, vol. 41, pp. 1118-1122, 2003.
38. L. V. Bertalanffy, General System Theory. New York: George Brazillier, 1968.
39. P. Diamond, "Time-dependent differential inclusions, cocycle attractors and fuzzy differential equations," IEEE Trans. Fuzzy Syst., vol. 7, pp. 734-740, Dec. 1999.
40. _, "Stability and periodicity in fuzzy differential equations," IEEE Trans. Fuzzy Syst., vol. 8, pp. 583-590, Oct. 2000.
41. P. Antonelli and V. Krivan, "Fuzzy differential inclusions as substitutes for stochastic differential equations in population biology," in Volterra-Hamillon Models in the Ecology and Evolution of Colonial Organisms. ser. Series in Mathematical Biology and Medicine. P. L. Antonelli and R. H. Bradbury, Eds. Singapore: World Scientific, 1996, vol. 2.
42. K.-P. Adlassnig, "Fuzzy set theory in medical diagnosis," IEEE Trans. Syst. Man, Cybern, vol. SMC-16, pp. 260-265, 1986.
43. M. L. Tsetlin, Automaton Theory and Modeling of Biological Systems. New York: Academic, 1973.
44. L. V. Fausett, Applied Numerical Analysis Using MATLAB. Englewood Cliffs, NJ: Prentice-Hall, 1999.
45. B. B. Mandelbrot, The Fractal Geometry of Nature. New York: W.H. Freeman, 1982.
46. A. Mees and C. Sparrow, "Some tools for analyzing chaos," Proc. IEEE, vol. 75, pp. 1058-1070, 1987.
47. E. Ott, C. Orebogi, and J. A. York, "Controlling chaos," Phys. Rev. Lett., vol. 64, pp. 1196-1199, 1990.
48. P. Diamond, "Chaos and fuzzy representations of dynamical systems," in Proc. 2nd Int. Conf. Fuzzy Logic Neural Networks, Iizuka, Japan. July 17-22, 1992, pp. 51-58.
49. H.-N. Teodorescu, "Chaos in fuzzy systems and signals," in Proc. 2nd Int. Conf. Fuzzy Logic Neural Networks, Iizuka, Japan, July 17-22, 1992, pp. 21-50.
50. P. E. Kloeden, "Chaotic iteration of fuzzy sets," Fuzzy Sets Syst., vol. 42, pp. 37-42, 1991.
51. J. J. Buckley and Y. Hayashi, "Applications of fuzzy chaos to fuzzy simulation," Fuzzy Sets Syst., vol. 99, pp. 151-157, 1998.
52. R. L. Devaney, An Introduction to Chaotic Dynamical Systems. Redwood City, CA: Addison-Wesley, 1989.
53. M. F. Barnsley, Fractals Everywhere. San Diego, CA: Academic, 1988.
54. C. A. Cabrelli, B. Forte, U. M. Molter, and E. R. Vrscay, "Iterated fuzzy sets systems: A new approach to the inverse problem for fractals and other sets," J. Math. Anal. Appl., vol. 171, pp. 79-100, 1992.
55. K. K. Majumdar, "Some studies on uncertainty management in dynamical systems by fuzzy techniques with applications," Ph.D. dissertation, Indian Statist. Inst., Calcutta, India, Mar. 2003. submitted.
56. "Bulletin Section," Fuzzy Sets Syst., vol. 24, 1987.
57. G. A. Edgar. Measure, Topology, and Fractal Geometry. New York: Springer-Verlag, 1990.
58. A. Kandel, Y. Lou, and Y.-Q. Zhang, "Stability analysis of fuzzy control systems," Fuzzyy Sets Syst., vol. 105, pp. 33-48, 1999.
59. K. S. Ray and D. D. Majumder, "Application of circle criteria for stability analysis of linear SISO and MIMO systems associated with fuzzy logic controllers," IEEE Trans. Syst. Man, Cybern., vol. SMC-14, pp. 345-349, 1984.
60. K. K. Majumdar, "Fuzzy fractals and fuzzy turbulence," IEEE Trans. Syst., Man, Cybern. B, to be published.