Fuzzy stochastic differential equations of decreasing fuzziness: Approximate solutions

Journal of Intelligent and Fuzzy Systems

Volumn 29, Issue 3, 2015, Pages 1087-1107

  Malinowski, Marek T ^a  

^a CRACOW UNIVERSITY OF TECHNOLOGY   (Poland)

Author keywords

approximate solutions; Fuzzy stochastic differential equation; fuzzy stochastic process; set valued stochastic differential equation; solution of decreasing fuzziness; uncertainty

Indexed keywords

DIFFERENTIAL EQUATIONS; FUZZY SET THEORY; FUZZY SYSTEMS; RANDOM PROCESSES;

APPROXIMATE SOLUTION; CLOSED FORM; EXISTENCE AND UNIQUENESS OF SOLUTION; FUZZY STOCHASTIC PROCESS; METHODS OF CONSTRUCTIONS; RATES OF CONVERGENCE; STOCHASTIC DIFFERENTIAL EQUATIONS; UNCERTAINTY;

STOCHASTIC SYSTEMS;

EID: 84944609051     PISSN: 10641246     EISSN: 18758967     Source Type: Journal    
DOI: 10.3233/IFS-151725     Document Type: Article

References (46)

1. L. Arnold, Stochastic Differential Equations: Theory, and Applications, John Wiley & Sons, New York, 1974
2. D.R. Bell, and S.E.A. Mohammed, On the solution of stochastic ordinary differential equations via small delays, Stoch Stoch Rep 29 (1989), 293-299
3. Y.T. Chang, S.J. Ho, and B.S. Chen, Robust stabilization design of nonlinear stochastic partial differential systems: Fuzzy approach, Fuzzy Sets Syst 248 (2014), 61-85
4. B.S. Chen, B. Lee, and L. Guo, Optimal tracking design for stochastic fuzzy systems, IEEE Trans Fuzzy Syst 11 (2003), 796-813
5. L. Chen, R. Wu, and D. Pan, Mean square exponential stability of impulsive stochastic fuzzy cellular neural networks with distributed delays, Expert Syst Appl 38 (2011), 6294-6299
6. Y. Feng, Mean-square integral, and differential of fuzzy stochastic processes, Fuzzy Sets Syst 102 (1999), 271-280
7. Q. Gan, Exponential synchronization of stochastic fuzzy cellular neural networks with reaction-diffusion terms via periodically intermittent control, Neural Process Lett 37 (2013), 393-410
8. I.I. Gihman, and A.V. Skorohod, Stochastic Differential Equations, Springer-Verlag, Berlin, 1972
9. F. Hiai, and H. Umegaki, Integrals, conditional expectation, and martingales of multivalued functions, J Multivar Anal 7 (1977), 149-182
10. E. Hüllermeier, An approach to modelling, and simulation of uncertain dynamical systems, Int J Uncertain Fuzziness Knowledge-Based Syst 5 (1997), 117-137
11. S.Y. Joo, Y.K. Kim, J.S. Kwon, and G.S. Choi, Convergence in distribution for level-continuous fuzzy random sets, Fuzzy Sets Syst 157 (2006), 243-255
12. O. Kaleva, Fuzzy differential equations, Fuzzy Sets Syst 24 (1987), 301-317
13. Y.K. Kim, Measurability for fuzzy valued functions, Fuzzy Sets Syst 129 (2002), 105-109
14. V. Lakshmikantham, and R.N. Mohapatra, Theory of Fuzzy Differential Equations, and Inclusions, Taylor & Francis, London, 2003
15. J. Li, J. Li, and Z. Xia, Delay-dependent generalized H2 control for discrete T-S fuzzy large-scale stochastic systems with mixed delays, Int J Appl Math Comput Sci 21 (2011), 585-603
16. J. Li, J. Li, and Z. Xia, Delay-dependent generalized H2 fuzzy static-output-feedback control for discrete T-S fuzzy bilinear
17. J. Liang, Z. Wang, and X. Liu, Robust passivity, and passification of stochastic fuzzy time-delay systems, Inform Sci 180 (2010), 1725-1737
18. J. Li, G.H. Huang, G. Zeng, I. Maqsood, and Y. Huang, An integrated fuzzy-stochastic modeling approach for risk assessment of groundwater contamination, J Environ Management 82 (2007), 173-188
19. Y. Liu, X. Li, and Z. Du, Reliability analysis of a random fuzzy repairable parallel system with two non-identical components, J Intell Fuzzy Systems 27 (2014), 2775-2784
20. M.T. Malinowski, On random fuzzy differential equations, Fuzzy Sets Syst 160 (2009), 3152-3165
21. M.T. Malinowski, Existence theorems for solutions to random fuzzy differential equations, Nonlinear Anal Theory Methods Appl 73 (2010), 1515-1532
22. M.T. Malinowski, Random fuzzy differential equations under generalized Lipschitz condition, Nonlinear Anal Real World Appl 13 (2012), 860-881
23. M.T. Malinowski, Strong solutions to stochastic fuzzy differential equations of Itô type, Math Comput Modelling 55 (2012), 918-928
24. M.T. Malinowski, Itô type stochastic fuzzy differential equations with delay, Systems Control Lett 61 (2012), 692-701
25. M.T. Malinowski, On a new set-valued stochastic integral with respect to semimartingales, and its applications, J Math Anal Appl 408 (2013), 669-680
26. M.T. Malinowski, Approximation schemes for fuzzy stochastic integral equations, Appl Math Comput 219 (2013), 11278-11290
27. M.T. Malinowski, Some properties of strong solutions to stochastic fuzzy differential equations, Inform Sci 252 (2013), 62-80
28. M.T. Malinowski, Random fuzzy fractional integral equations-theoretical foundations, Fuzzy Sets Syst 265 (2015), 39-62
29. M.T. Malinowski, Fuzzy, and set-valued stochastic differential equations with solutions of decreasing fuzziness, Advan Intellig Syst Comput 315 (2015), 105-112
30. M.T. Malinowski, Set-valued, and fuzzy stochastic integral equations driven by semimartingales under Osgood condition, Open Math 13 (2015), 2391-5455
31. M.T. Malinowski, Fuzzy, and set-valued stochastic differential equations with local Lipschitz condition, IEEE Trans Fuzzy Syst, http://dx. doi. org/10.1109/TFUZZ.2014.2372072, in press
32. M.T. Malinowski, Stochastic fuzzy differential equations of a nonincreasing type, Commun Nonlinear Sci Numer Simulat, to appear
33. M.T. Malinowski, and R.P. Agarwal, On solutions to set-valued, and fuzzy stochastic differential equations, J Franklin Inst, 352 (2015), 3014-3043
34. G. Maruyama, Continuous Markov processes, and stochastic equations, Rend Circ Mat Palermo 4 (1955), 48-90
35. B. Möller, W. Graf, J.-U. Sickert, and U. Reuter, Numerical simulation based on fuzzy stochastic analysis, Math Comput Model Dyn Syst 13 (2007), 349-364
36. B. Øksendal, Stochastic Differential Equations: An Introduction with Applications, Springer Verlag, Berlin, 2003
37. M.L. Puri, and D.A. Ralescu, Fuzzy random variables, J Math Anal Appl 114 (1986), 409-422
38. C. Tseng, Y. Li, and Y. Chiang, H1 fuzzy control design for nonlinear stochastic fuzzy systems, Int J Fuzzy Syst 9 (2007), 38-44
39. Z. Xia, J. Li, and J. Li, Passivity-based resilient adaptive control for fuzzy stochastic delay systems with Markovian switching, J Franklin Inst 351 (2014), 3818-3836
40. P. Xiong, and L. Huang, On pth moment exponential stability of stochastic fuzzy cellular neural networks with time-varying delays, and impulses, Adv Difference Equ 172 (2013
41. J. Yao, M. Chen, and H. Lu, A fuzzy stochastic single-period model for cash management, Eur J Operat Research 170 (2006), 72-90
42. L.A. Zadeh, Fuzzy sets, Inform Control 8 (1965), 338-353
43. L.A. Zadeh, From computing with numbers to computing with words-from manipulation of measurements to manipulation of perceptions, IEEE Trans Circuits Systems I Fund Theory Appl 45 (1999), 105-119
44. L.A. Zadeh, From computing with numbers to computing with words-from manipulation of measurements to manipulation of perceptions, Int J Appl Math Comput Sci 12 (2002), 307-324
45. C. Zheng, Y. Wang, and Z. Wang, Stability of stochastic fuzzy Markovian jumping neural network with leakage delay under impulsive perturbations, J Franklin Inst 351 (2014), 1728-1755
46. H.-J. Zimmermann, Fuzzy Set Theory, and Its Applications, Kluwer Academic Publishers, Boston, 2001